d-incentives and political economy

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4 CONTENTS

3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4 Checks and Balances 654.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.3 Optimal Symmetric Constitution . . . . . . . . . . . . . . . . . . . . . . . 694.4 Supervision and Division of Tasks . . . . . . . . . . . . . . . . . . . . . . . 734.5 Multidimensional Collusion Activities . . . . . . . . . . . . . . . . . . . . . 744.6 A Model with Three Politicians . . . . . . . . . . . . . . . . . . . . . . . . 774.7 Optimal Supervisory Structures . . . . . . . . . . . . . . . . . . . . . . . . 794.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

II Flexibility Versus Discretion in Constitutional Design 85

5 Political Economy and Industrial Policy 895.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.2 Political Interference in the Rent-E¢ciency Trade-O¤ . . . . . . . . . . . . 915.3 Ownership Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.4 Incentives against Capture as a Constitutional Rule . . . . . . . . . . . . . 955.5 Political Price Discrimination Versus Uniform Pricing . . . . . . . . . . . . 975.6 Information Asymmetries, Costly Redistribution . . . . . . . . . . . . . . . 995.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 Political Economy and the Marginal Cost Pricing Controversy 1136.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.2 The Marginal Cost Pricing Rule . . . . . . . . . . . . . . . . . . . . . . . . 1166.3 Frisch’s Comment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186.4 Smith, Edgeworth, Hotelling . . . . . . . . . . . . . . . . . . . . . . . . . . 1206.5 Project Selection and Pricing Rules . . . . . . . . . . . . . . . . . . . . . . 1276.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7 Environmental Incentive Regulation 135

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.2 The Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1377.3 Controlling the Discriminatory Power . . . . . . . . . . . . . . . . . . . . . 1387.4 Delegating Discriminatory Power to the Politicians . . . . . . . . . . . . . 1447.5 Multiple Privately Informed Interest Groups . . . . . . . . . . . . . . . . . 1457.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

III Coalition Formation and Constitutional Design 155

8 Optimal Constitutional Response 159

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1598.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1618.3 Modeling Collusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164



6 CONTENTS

features: incomplete Constitution, incomplete contract between voters and their repre-sentatives, incomplete contracts within the bureaucracy etc. Consequently, any modeling

of the whole picture will require many ad hoc assumptions and will leave us with a ratheruntractable model with non robust results. At this stage, I …nd more instructive to study,at the margin of complete contract theory, pieces of the puzzle to enlighten some majorissues of political economy: the capture of politicians by interest groups, the purpose of the separation of powers, the meaning of checks and balances, the extent of discretionto leave to politicians and its implication on economic policies, the formation of interestgroups, the role of delegation etc.

I do not ignore the limits of this piecemal approach. Nevertheless, I hope that thereader will …nd this book useful to think about political economy.

Jean-Jacques La¤ont, Toulouse April 1999



CONTENTS 7

In writing this book I have freely borrowed from a number of papers.

Boyer, M. and J.J. La¤ont (1999), “Toward a Political Theory of the Emer-gence of Environmental Incentive Regulation”, 30, 137-157.

Faure-Grimaud, A., J.J. La¤ont and D. Martimort (1998), “A Theory of Su-pervision with Endogenous Transaction Costs”, mimeo IDEI.

La¤ont, J.J. (1997), “Industrial Policy and Politics”, International Journal of

Industrial Organization , 14, 1-27.

La¤ont, J.J. (1997), “In‡exible Rules Against Political Discretion”, Nordic

Journal of Political Economy , 24, 78-87.

La¤ont, J.J. (1998), “Frisch, Hotelling and the Marginal Cost Pricing Contro-

versy”, Econometric Society, Monograph in Honor of R. Frisch , ed. Str ,Cambridge University Press.

La¤ont, J.J. and D. Martimort (1995), “Duplication of Regulators againstCollusive Behavior”, to appear in Rand Journal of Economics .

La¤ont, J.J. and D. Martimort (1998), “Collusion and Delegation”, The Rand

Journal of Economics , 29, 280-305.

La¤ont, J.J. and D. Martimort (1998), “Mechanism Design with Collusionand Correlation”, to appear in Econometrica .

La¤ont, J.J. and M. Meleu (1997) “Reciprocal Supervision, Collusion and

Organizational Design”, The Scandinavian Journal of Economics , 99, 519-540.

La¤ont, J.J. and T.T. N’Guessan (1998), “Competition and Corruption in anAgency Relationship", to appear in Journal of Development Economics .

La¤ont, J.J. and J.C. Rochet (1997), “Collusion in Organizations”, Scandina-

vian Journal of Economics , 99, 485-495.

La¤ont, J.J. and J. Tirole (1991), “The Politics of Government Decision Mak-ing: A Theory of Regulatory Capture”, Quarterly Journal of Economics ,106, 1089-1127.



8 CONTENTS



Chapter 1

Introduction

“Though I am an economist, and the tools of analysis used in this book aredrawn from economic theory, the conclusions of the study are as relevant tothe sociologist and the political scientist as they are to the economist.”

Mancur Olson (1965), p. 3.

1.1 Political Economy with a Benevolent Monarch

Modern Political Economy was …rst developed in countries ruled by Monarchs. Econo-mists looked for good policy rules to run the economy of the State. Whatever their beliefs,

they could not question the premise that the Monarch was a perfectly benevolent agent of the people. They were led to call good rules, the ones maximizing social welfare de…nedin one way or another as the welfare of the people. However, economists could questionthe benevolence of the administration, agent of the Monarch to implement policies. Thedisfunctionings of administrative bodies in charge of the State’s economy were indeed adriving force leading to the birth of liberalism as an economic policy which minimizespublic intervention in the economy.

Adam Smith (1776) recognized the role of the State in defense, justice, education,public works and institutional design to facilitate private economic activities, with thenecessary taxation for …nancing these public goods. But he was very critical of the public

administration of this State intervention. He advocated various policy rules having inmind the design of proper incentives for the various administrative bodies as a mainpurpose.

He recommended decentralization of the administration of local public goods as thebest way to accommodate those incentives.

“Public works of a local nature should be maintained by local revenue” p.689

because

“The abuses which sometimes creep into the local and provincial administra-tion of a local or provincial revenue, how enormous so ever they may appear,

are in reality, however, almost always very tri‡ing, in comparison with thosewhich commonly take place in the administration and expenditure of the rev-enue of a great empire.” p. 689

9



10 CHAPTER 1. INTRODUCTION

Similarly, he proposed to …nance highways, bridges and canals by tolls proportionalto the wear and tear, to pay for the expenses and to balance the budget of each public

work. Beyond some equity considerations, Smith’s main argument for this …nancingmethod rather than using the general revenue of the society concerned the incentives of the administration to make the proper investments.

“When high roads, bridges, canals, etc are in this manner made and supportedby the commerce which is carried on by means of them, they can be madeonly where that commerce requires them, and consequently where it is properto make them. . . A magni…cent high road cannot be made through a desertcountry where there is little or no commerce, or merely because it happens tolead to the country villa of the intendant of the province, or to that of some

great lord to whom the intendant …nds it convenient to make his court. Agreat bridge cannot be thrown over a river at a place where nobody passes,or merely to embellish the view from the windows of a neighbouring palace:things which sometimes happen, in countries where works of this kind arecarried on by any other revenue than that which they themselves are capableof a¤ording.” p. 683

Furthermore, he opposed increasing prices beyond what was needed for balancing thebudget because (p. 685-686): the tolls would be raised and become a great encumbranceto commerce; a tax on carriages in proportion to weights falls principally on the poor;the roads would be neglected, arguments which mix social welfare considerations with

incentive motives of the administration.Political Economy was already for Adam Smith the design of policies which maximize

social welfare under the incentive constraints of the administrative bodies in charge of implementing those policies. We will pursue this paradigm for political economy in the…rst part of this book with the tools of incentive theory.

1.2 The Design of Democratic Institutions

The advent of democracy eliminated the convenient myth of a Monarch maximizing socialwelfare. Montesquieu and the American Federalists addressed the task of designing moredemocratic institutions which would favor social welfare. The Constitution founding agiven State was supposed to be the mechanism organizing both the representation of thepeople by elected politicians and the structure of government. The Federalists were wellaware of the fact that interest groups would form to in‡uence policy decisions and thatappropriate incentives had to be provided to the politicians and the administration.

The Monarch was a perfect judge, perfect representative of the people and perfectdecision maker. Now the task was much more di¢cult. How to organize society when the judiciary, executive, legislative branches of government must be delegated by the people toagents who have their private interests1 and when interest groups form to capture thoseagents? Can we conceive the Constitution as a grand contract which would maximize

1 The need to take into account incentives of politicians has not been always recognized. For Rousseau(1948) the government is merely an abstract device for carrying the will of the people. We shareDowns’view that information problems are essential to understand why this approach is unrealistic.



1.2. THE DESIGN OF DEMOCRATIC INSTITUTIONS 11

social welfare under incentive constraints just as the Monarch was doing? Not easily forseveral reasons.2

The …rst one is that a contract requires penalties to be enforced and ultimately anoutside enforcing mechanism when penalties are resisted. The second one is that a Consti-tution is necessarily quite incomplete for bounded rationality reasons and residual decisionrights must be allocated to the government bodies who then acquire a possibility of discre-tionary actions. The control of the executive and legislative discretionary actions of thepoliticians and the administrative bodies can only be realized within the constitutionalgeneral rules, by a judiciary branch with limited power (for incentive reasons) and byreelection mechanisms which a¤ect the private bene…ts of politicians.

Two degrees of freedom a¤ect the analysis: a) the choice of the states of nature notcontracted for by the Constitution, b) the limits to judicial power otherwise assumed to

be benevolent.Once these choices have been made, the design of the Constitution could be again

conceived as an optimization problem of expected social welfare. The instruments avail-able to optimize are the electoral processes that select the various governmental bodies,the policy instruments made available to them, the allocation of residual decision rightsamong them, the supervision activities, i.e., the checks and balances between the variousbranches of the government, under the individual and collective incentive constraints of the various members of society: voters, politicians, bureaucrats etc.

Such an optimization was the task that the Federalists took upon themselves in theformation of the new American government (Kramnick (1987) p. 48):

“Functions of government became arenas for particular social forces to dom-inate, and the separation and independence of these functions, it would beargued, required a balancing of each against the other, through a sharing and“intermixture” of power. . . in order to produce a moderate, temperate, coolergovernment”.

At least this is the task we should assign to a normative theory of Constitutionaldesign. I do not ignore the more pessimistic view articulated by John Quincy Adams

according to whom the Constitution was calculated to increase the in‡uence, power andwealth of those who already have it. Two remarks about this criticism. First, it does notseem useless to understand how the Constitution should theoretically be designed bothin order to evaluate the current institutions and to make citizens aware of an ideal pointtowards they should strive. This is a wonderful role to be played by intellectuals. Second,the positive problem faced by a ruling group in designing its best Constitution is of thesimilar nature as the one studied here, except for the objective function to be maximized.The role of intellectuals helping the ruling class in this design is then more ambiguous.

“Another possible interpretation of Rousseau’s theory is that the government consists solely of hiredmen who carry out the policies ordered by ”the will of the people”. The argument explains the private

motives of the men in government quite simply: they obey the commands of the people with precisionin order to keep their jobs, because the slightest disobedience means immediate dismissal. As our wholestudy shows,this view is incompatible with uncertainty and the division of labor”, Downs (1957), p. 285.

2 “dans un Etat populaire, il faut un ressort de plus, qui est la vertu”, Montesquieu (1748), p. 536.




1.3 About Political Economy in Democratic Coun-

triesGiven this more complex view of political institutions, what can be the evolution of political economy? First, it should be stressed that most economists have chosen to ignorethe interaction of economic policy and politics. Some even believe that it is not “politicallycorrect” to develop policy recommendations altered by political considerations.

The …rst Nobel prize winner R. Frisch says it clearly in his Nobel lecture (1970)

“It is not the task for us as econometricians and social engineers to go into adetailed discussion of the political system”, p. 228.

Building a purely economic framework available to citizens who can then use it in theirpolitical con‡icts is a noble task which has the added value of being rather universal andinstitution independent. This might be in the long run the best service that economistscan provide to society. The role is essentially pedagogical but of limited direct use forpolicy when providing economic advice to the ruling party because: it is not a very goodadvice for this party if the political constraints of its actions are not taken into account;a policy proposal which maximizes social welfare is not what is being asked and will beprobably discarded.

Two types of political economy can be practiced. Either as an authentic adviserto a ruling party, who looks for the policies which maximize the party’s payo¤ giveneconomic and political constraints3. Or as an intellectual who proposes policies whichtake into account economic and political constraints in maximizing long run expectedsocial welfare and which could be adopted as constitutional rules. This last attitudeseems the only one available to independent economists who want to have a short runimpact on their society. This is the goal of a real political economy which integrateseconomics and political science. It is not clear, however, that such economists will betaken seriously by the rest of society, since they claim to be benevolent thus contradictingtheir whole intellectual approach, which treats all other agents as self-interested.

1.4 The Chicago View of Interest Group PoliticsDespite the dominance of the public interest view of public economic intervention, a“capture” or “interest group” theory that emphasizes the role of interest groups in theformation of public policy developed. Marx’s view that big business controls public in-stitutions is certainly part of it, as well as the work of political scientists at the turn of the century, such as Bentley (1908). The Chicago school started with Stigler’s (1971)explanation of the capture of regulatory authorities by the industries they were supposedto regulate. His theory was developed by his colleagues at Chicago, Peltzman (1976),Posner (1974) and Becker (1983). The goal of this work was to provide a positive analysis

of policy decision making which emphasized the role of interest groups in shaping these3 “Otherwise the economists’ advice may be as useless as telling a pro…t-maximizing monopolist to sell

his product as marginal cost so as to bene…t society”, Downs (1957) p. 283.



1.4. THE CHICAGO VIEW OF INTEREST GROUP POLITICS 13

policies and showed the lack of empirical relevance of the public interest view of publicpolicy.

Let us consider in some detail Becker’s (1983) major piece to stress the need for incor-porating asymmetric information in the analysis in order to build a convincing positivetheory. His general model of competition between political pressure groups is meant toprovide a positive explanation of political choices. Politicians, political parties and votersare like a black box which transmits the pressure of active groups. Competition amongthe pressure groups which demand favors determines the equilibrium structure of theeconomic instruments (taxes, subsidies, levels of public goods, etc.) which induce thesefavors. This is why this positive theory of government has often be said to be only demanddetermined.

The supply side of political favors, i.e., why and how politicians and voters o¤er these

favors, is left unmodeled. Becker (1983), p. 372 acknowledges:

“I shall not try to model how di¤erent political systems translate the activitiesof pressure groups into political in‡uence”.

Within this limited scope of demand determined political equilibrium, Becker implic-itly appeals to various incomplete information assumptions. We will henceforth arguethat a more fundamental modeling of information will enable us to develop fruitfully histype of analysis. Furthermore, it will help open the black box of the supply side.

Consider two groups of size n1 and n2, who battle over the determination of an eco-

nomic instrument, say a tax level t, which is favorable to group 1, but unfavorable to group2. The political system produces a level of t which depends on the political in‡uences of the groups

t = T (L1; L2); (1.1)

with@T

@L1> 0

@T

@L2< 0:

The in‡uence itself depends on the size of the group ni and of the resources spent bythe group in lobbying

Li = pi(ni; aini) i = 1; 2; (1.2)where ai is per member expenditure.

Each group i determines ai. In so doing, it must solve an eventual free rider problemwithin the group. Let U i(t) be the utility derived from t by group i. In the followingprogram, if f (ni) = ni, the free rider problem is completely solved. If f (ni) = 1 freeriding is total. Group i then solves

maxai

U i(t) f (ni)ai (1.3)

hence

dU idt

@T @Li

@pi

@ai

= f (ni) i = 1; 2: (1.4)

The equilibrium follows from (1.4).




Becker postulates that there exist deadweight losses, say, associated with taxes. Thiscan be written as

dU 1dt

+ dU 2dt

< 0:

Since Vickrey (1945) and Mirrlees (1971) we know that incomplete information is theexplanation of the costly information rents acquired by agents and therefore the funda-mental source of these deadweight losses. So, a major ine¢ciency of political con‡ictsfollows from the ine¢ciency of redistributive instruments due to asymmetric information.Determining precisely the deadweight losses from a careful modeling of asymmetric in-formation makes it possible to explore (without arbitrary restrictions on instruments)the supply side e¤ect of political in‡uence. Politics is then a game of redistribution of information rents within the realm of discretion left by the Constitution.

Equation (1.1) is the black box which transforms the demand for in‡uence of the dif-ferent pressure groups into outcomes. Specifying in detail political institutions is requiredto open this black box. This is what we can expect from a mature political science. Herealso behavior of voters under incomplete information will be a major building block, fora given set of constitutional rules. Becker was well aware of the role of information andthe manipulation of information which a¤ects voters’ preferences.

“These “preferences” can be manipulated and created through the informationand misinformation provided by interested pressure groups. . .

The incentive to become well informed about political issues is weaker becauseeach individual has only a minor e¤ect on political outcomes decided by themajority (or by similar rules)”, p. 392.

Inside the black box determining the supply of favors, Becker sees a principal-agentproblem between pressure groups and politicians or bureaucrats.

“A more general analysis would incorporate this principal-agent relation be-tween bureaucrats, politicians and pressure groups into the determination of political equilibrium”, p. 396.

Modern analysis of principal-agent relationships emphasizes information asymmetries.

Equation (1.2) stresses two major variables which a¤ect the political in‡uence of a group:the sheer size of the group ni if only through voting, and the lobbying resources aini,which can represent campaign contributions as well as various bribes to bureaucrats andpoliticians. Beyond models which can show how campaign contributions may a¤ect thebeliefs and the votes of citizens, we also need models of corruption which call for in-formational foundations. Equation (1.4) speci…es how a group determines its lobbyingexpenses. In particular it embodies the way the group is able (or unable) to mitigate thefree rider problem within the group. Absent asymmetric information, a major implicationof the Becker analysis is that competition among pressure groups favors e¢cient methodsof taxation (see his Proposition 4, p. 386; see also Stigler (1971), (1982), Becker (1976),(1985), Wittman (1989)). The logic is simple. With rational voters, politicians who make

ine¢cient transfers will be voted out of o¢ce.The Virginia school of political economy claims that, with poorly informed voters,

politicians will select ine¢cient sneaky methods of redistribution (the disguised transfer



1.5. THE COMPLETE CONTRACTING APPROACH 15

mechanisms in the Tullock (1983) terminology) over more transparent e¢cient methods.Becker (1976) and Wittman (1989) criticized the implicit irrationality of voters which

seems necessary for such a scheme to last. Recently, Coate and Morris (1995) builta model based on imperfect information with rational voters where ine¢cient transferschemes may be selected as follows. There are two types of politicians, good ones and badones. They are better informed than citicizens. The good ones use a public project thattransfers wealth to an interest group only if it is e¢cient to do so. Bad ones prefer to usethe public project to make transfers even when it is ine¢cient to do so, because in thisway they have a chance to protect their (false) reputation of being good. Giving e¢cientmonetary transfers to their favored interest group would reveal immediately they are bad.The choice of ine¢cient transfers is for signaling purposes. It remains to understand whydo we have in equilibrium politicians of two types, why good politicians cannot signal

themselves, and why political competition does not provide to voters enough informationto identify good and bad politicians? Also, if costless direct transfers are really available,why can’t good politicians neutralize the distribution e¤ects of public projects and operatetransparent redistributions with these transfers? Implicitly, the reasoning puts restrictionson instruments available to politicians.

In a world of asymmetric information, any public project creates information rentswhich cannot be eliminated (or only at extremely high e¢ciency costs). Costless transfersdo not exist. The more general questions are then: How does political decision makingdistort the allocation of resources away from second best incentive Pareto e¢ciency? Howcan we structure the political game through constitutional rules to avoid large distortions

from second best? Why is it not possible to eliminate those distortions?

1.5 The Complete Contracting Approach

One possibility is to introduce the fact that the collective decision maker has sociallyvaluable information which is available at the time of decision making. For example, he isthe only one who can acquire relevant information such as the real international situationor the current business conditions. E¢ciency requires to use this information but thisopens the possibility of discretionary behavior.

Nevertheless, the revelation principle tells us that maximization of expected socialwelfare can be achieved by using the optimal revelation mechanism which extracts in anincentive compatible way the politician’s information and avoids any capture of the politi-cian by interest groups. More generally one can explore the allocation mechanisms whichsolve individual and coalitional incentive problems. The politician is then a particularagent of society who has been delegated collective decisions. The emphasis here is onprivate information and on the necessary distortions required by incentive compatibility.

The outcome of such a political economy would both specify the allocation of tasks,including those of collective decision makers, as well as the rules to be followed. Fromthe revelation principle, such an optimal society would be isomorphic to a vast systemof information transmission from the periphery to the constitutional level which would

specify how to use this information for the allocation of resources.We will call this approach the complete Constitution approach. Politicians are

informed supervisors. In Chapter 2 we will describe a simple model of collective decision




making based on Tirole’s (1986) supervision model with hard information to illustrate thisapproach. Chapter 3 will propose a theory of separation of powers within this modeling

framework. Chapter 4 will pursue this line of research by considering more complexgovernments with two or more divisions between which reciprocal favors can occur.

This contractual approach to political economy has several weaknesses. It presumesa perfect benevolent court which enforces contracts. It presumes no complexity cost, nobounded rationality.

1.6 The Incomplete Contracting Approach

An alternative approach that we will label the incomplete Constitution approach

ignores asymmetric private information. Its point of departure is the non contractibilityassumption about some states of nature which are only known ex post. 4 The politicianis then the agent who has the residual rights to make collective decisions in cases wherethe Constitution provides no guidance.

The motivations for this line of thought are both the unavailability of a benevolentcourt and bounded rationality. It is a shortcut to deal with these issues despite thelack of …rm foundations. A major problem is that theory has not been able to providea satisfactory description of the limits put by the non contractibility problem in theallocation of resources. Either one accepts the Maskin-Tirole (1998) critique and …rst bestsocial welfare maximization is achieved (note that this approach still requires a benevolent

court) or arbitrary restrictions are put on possible contracts. Three degrees of freedomare then available. First the game form which selects the decision maker with residualrights of control. For example, majority voting selects the politician. Second the set of discretionary decisions available to him. Third the noncontractible events. The politicianis not controlled here by a contract but by the future decisions of voters. If he wants toremain in control he must win the future elections. Whatever feedback control providedby elections, and for a given set of noncontractible states of nature, an interesting trade-o¤ still exists: by restricting constitutionally the set of decisions of the politicians, onedecreases its discretion but one may also destroy ex post e¢ciency. Alternatively, takingas given the set of noncontractible states and without constraint on the set of decisions,one may look for interesting structures of the political game. They a¤ect how variousinterest groups in‡uence the politician who redistributes goods among agents.

This is essentially the Chicago approach which concludes that ex post e¢ciency isachieved since there is no reason why the politician would not maximize the sum to bedistributed. Becker’s model is of this nature. It is positive in so far as the mapping fromgroup formation to political outcomes is taken as given. Grossman and Helpman (1996)open slightly this black box by modeling the game of bribes between exogenously giveninterest groups. Persson, Roland and Tabellini (1997), as most of political science, focusinstead on the feedback control of various electoral modes for given sets of decisions. Notethat in all this literature, the motivation that we give here for why we need politicians in

4

There are other ways to depart from a complete contracting framework by considering limited com-mitment, renegotiation, multiprincipal governance, and beyond the transaction costs in the sense of Williamson (1989). North (1990) started the analysis of the politicial process in the transaction-costmode. See Dixit (1996) for a study along those lines.



1.7. ADDING ASYMMETRIC INFORMATION 17

terms of noncontractible states is only implicit.Rather than a contract, here the outcome of constitutional design de…nes a particular

political game that speci…es who has the residual decision rights and the family of instru-ments available to them. What the analysis can do, beyond the pure positive descriptionof equilibria, is to compare various game forms and various restrictions on instruments.

1.7 Adding Asymmetric Information

By introducing in the above approach asymmetric information, we create a natural map-ping from policy instruments to rents which de…nes the stakes of agents in policy choiceseven without ex post restriction on instruments except those imposed by individual ra-

tionality constraints. Furthermore, this second best framework convexi…es the Paretofrontier even without income e¤ects and creates a potential ine¢ciency of the politicalgame (as advocated by the rent seeking literature).

In so doing we may combine the informationally based complete constitution ap-proach with incomplete contracting. Constitutional reforms can strike a balance betweene¢ciency and discretion by restricting politicians’ instruments to improve ex ante so-cial welfare. They can also change the rules of the political game or the structure of government.

In Chapter 5 we explain the basic trade-o¤ between in‡exible rules and political dis-cretion in a random majority voting game. The marginal cost pricing controversy isreviewed in this light in Chapter 6. An application to environmental policy is developedin Chapter 7.

1.8 Endogenous Coalition Formation

Beyond the individual stakes for policy choices which can be translated into votes, groupsform to in‡uence politicians with bribes, campaign contributions, etc.

As Becker (1983) p. 393 already stressed

“an explicit modeling of coalition formation would surely add to the power of

the approach”

and Persson (1997) still notes in his discussion of the recent lobbying models

“One wonders why some regions would have organized interest groups whileothers would not. This is a di¢cult question, that still does not have a satis-factory answer, even though Olson (1965) identi…ed the important aspects of the problem”.

In this review of the rent seeking literature Tollison (1989) also says p. 521

“The plain truth is that economists know very little about the dynamics of group formation and action”.




We believe that the policy rent mapping provided by asymmetric information is essen-tial for a theory of group behavior. Such a theory should take into account the transaction

costs due to asymmetric information within the coalitions. Chapter 8 develops the gener-alization of the revelation principle for group behavior and shows how a Constitution canbe optimized to take into account both individual and coalitional incentive constraintsunder asymmetric information. Chapter 9 studies a particular type of collusive behaviorembodied in delegation. The pros and cons of delegation are discussed to assess somegains and cost of decentralization. Chapter 10 concludes.



Part I

Politicians as Informed Supervisors

19



21

“You must admit that we shall have found a way to meet your demand forrealization, if we can discover how a state might be constituted in the closestaccordance with our description. Will not that content you? It would beenough for me.”

Plato (1941), p. 473.



22



Chapter 2

The Complete Contract Approach toConstitutional Design

“The Constitution is a broad long-term contract between those ruled and therulers that speci…es the conditions on which the agents may exercice power inorder to enhance the interests of the principal.”

Lane (1996), p. 180.

2.1 Introduction

The principal-agent theory developed in the seventies and eighties has produced a largeset of insights for understanding how contracts might be established within organizations.This theory explains how a principal who o¤ers a contract to an agent should structurethis contract to overcome, at least partially, the asymmetries of information he is facingin order to maximize his expected utility. Optimal contracts with adverse selection, withmoral hazard or with non veri…ability by a third party of some variables are by nowrelatively well understood.

Despite insightful extensions to multiagent or to multiprincipal organizations, thisbody of knowledge falls short of a comprehensive theory of organizations. One major rea-son, beyond the restrictive nature of the organizations studied, lies in the non-cooperative

approach generally followed to model multiagent settings. Indeed, in this standard para-digm, if cooperation of agents is desired by the principal it can be induced by the contractshe o¤ers to the agents, each of whom maximizes his own welfare given the behavior of theother agents. What remains is that the principal is assumed to have a complete controlover the game played by the agents.1 Unwanted communication or side-contracting be-tween agents can be prevented. This is a rather unrealistic assumption. Contract theoryteaches us that the principal structures the contracts so as to minimize, at the lowestpossible e¢ciency cost, the information rents given up to the agents because of their in-formational advantages. It is quite natural to expect a collective reaction of the agents toprotect their rents.

We need to understand how agents can react to the rules of an organization, andbeyond, to understand how a principal who is aware of the incentives for collusion should

1 See La¤ont (1990).

23



24 CHAPTER 2. THE COMPLETE CONTRACT APPROACH

design the organization. Modeling coalitional or collusive behavior and characterizing theregulatory responses to such behavior is a major task of any organization theory and in

particular of a theory of government.The empirical relevance of collusion is easy to establish. A clear example is that

of auctions, for which the occurrence of cooperative behavior between bidders is welldocumented. As Porter and Zona (1993) put it: “Collusion is a very general phenomenonin auctions”. The importance of collusive behavior between economic agents has also beendocumented in many other contexts. In particular, sociologists of organizations such asCrozier (1963), Dalton (1959), Gouldner (1954), and Mintzberg (1979) have often stressedthat economists neglect group behavior. They have distinguished horizontal cliques, suchas colluding bidders in an auction, which gather members of the organization at the samehierarchical level, and vertical cliques which gather members of di¤erent hierarchical levels

(such as a foreman and a worker, an auctioneer and a bidder), and which may lead tofavoritism and extortion. The capture of regulatory institutions by interest groups hasbeen put forward very early in industrial economics by Marx, Stigler (1971), and Olson(1965). It is an important example of what economists label “vertical collusion”. Let usnote also that the corruption inside and outside organizations of less developed countriesappears more and more clearly as a major impediment to economic growth (as documentedby Mauro (1995)), and is far from being eradicated in more developed countries.

To put in perspective this literature, it is convenient to go back to the revelationprinciple. This principle tells us that, in the absence of restrictions on contracts, but withdecentralized information, any organization is equivalent to a centralized organization in

which information must be communicated in an incentive compatible way to a center whotransmits back to the agents instructions about the actions to be implemented (whenthese actions are veri…able) and recommendations for the (unobservable) e¤ort levelsto be exerted (Myerson (1982)). Accordingly, the characterization of feasible incentivecompatible allocations can be easily obtained by characterizing the revelation mechanismsin which all agents reveal truthfully their private information. The best organization fromthe point of view of a given criterion -for example social welfare or the center’s morenarrow objective- is the one which follows from the maximization of the criterion in theset of feasible incentive compatible allocations. The optimal organization is obtained inthe abstract form of revelation mechanisms. What remains then is to …nd more familiarinstitutions such as non linear prices, auctions or managerial incentive schemes whichimplement these mechanisms.

All along, a noncooperative behavior of agents has been postulated. Implicitly, thecenter is assumed to control communication between agents. It is doubtful that the centercan completely succeed in this task. Therefore it seems interesting to study the extremeopposite case where communication between agents is perfect and side contracting betweenthem becomes possible.

The …rst steps of the literature about coalition formation (such as Green and La¤ont(1979) in the study of mechanisms for the provision of public goods, Robinson (1985) inthe study of auctions, the sizeable literature on information sharing in oligopolies,. . . )assumed that the privately informed agents had access to a technology enabling them,

when they formed a coalition, to become fully informed about each other. The foundationsof such a technology and the reasons why the principal of the organization had no accessto this technology as well were never discussed.



2.1. INTRODUCTION 25

Tirole (1986) gives a more explicit version of this approach by considering a principal-supervisor-agent hierarchy in which the de…nition of the supervisor is essentially the de…-

nition of an imperfect technology giving veri…able2 (or hard) information about the agent.Because of the principal’s lack of attention or limited expertise, the use of the technol-ogy must be delegated to an intermediary who must be given appropriate incentives3 todiscover the information and transmit it to the principal.

More precisely, suppose that the agent has a cost characteristic which is his privateinformation and which can take two values or with probabilities and 1 respectively.With probability < 1 (conditionally on the agent being e¢cient) the technology of thesupervisor enables him to discover in a veri…able way the low cost characteristic . Whenthe supervisor observes (and discloses) that = , the principal has complete informationand can o¤er a contract leaving no rent to the (e¢cient) agent. When the supervisor

observes nothing, the principal o¤ers a contract which leaves no rent to a agent but apositive rent to a agent. What are the dimensions of discretion for the supervisor? Whenhe has observed , he cannot pretend that = , because the only veri…able informationhe can obtain is = , but he can pretend that he has observed nothing and conceal theveri…able information he has obtained. This opens the possibility of collusion betweenthe agent and the supervisor.

Tirole (1986) and La¤ont and Tirole (1993) make then a number of speci…c assump-tions which enable them to solve the many problems associated with the modeling of collusion and to carry out the whole program of characterizing the optimal organizationalresponse. Two agents only are concerned by the collusion, the supervisor and the agent;

so there is no issue of formation of subcoalitions4

. Collusion can only take place whenthe supervisor has observed that = (which occurs with probability ). In this case,the supervisor and the agent have complete information. The bargaining power in thecollusion is allocated to the supervisor. Alternative assumptions are possible here. Theimportant point is that the principal can anticipate the outcome of bargaining to deter-mine his optimal reaction. The number of collusion constraints is limited by the fact thatthe agent has only two possible types. The risk neutral supervisor is assumed to havelimited liability so that the principal is obliged to leave him a rent to obtain his informa-tion. Finally, and most importantly, a side contract between the agent and the supervisoris possible, despite being illegal and not enforceable by a court. This is obviously a short-cut maybe for an enforcement made possible in the context of a repeated relationship.To apprehend this limitation of contracting, La¤ont and Tirole (1993) introduces someexogenous transaction costs in the side contracting.

Under those assumptions, it is possible to characterize the optimal organizationalresponse to collusion. This is done in two steps:

First, a collusion proofness principle is proved. This principle states that any allocationof resources induced by the organization can be achieved by a revelation mechanism forthe agent and the supervisor which is robust to collusion, i.e., such that the supervisorand the agent do not wish to collude and hide information from the principal. Theadditional collusion proof constraint takes a simple but very instructive form: the payment

2

Here, veri…ability has a weaker meaning than usually. We do not mean that the information can beobserved by a jury, but only that the principal can be convinced by it of the agent’s type.

3 Furthermore the technology is costly enough so that duplicating it cannot be envisioned.4 The other coalitions (Principal + Agent, Principal + Supervisor) are ine¤ective here.



2.2. A SIMPLE SUPERVISION MODEL 27

how the Constitution7 should be designed to maximize expected social welfare given theneed for politicians as supervisors.8

2.2.1 The Optimal Constitution Without Supervision

Consider the problem of public good provision by a …rm which has private information onits cost function. Producing q units of public good has a cost q . The marginal cost cantake one of two values f; g with respective probabilities and 1 . Let = > 0.These probabilities are common knowledge, but only the …rm’s manager knows the truevalue of . There is a single …rm which can produce the public good. Denoting t thetransfer from the government to the …rm, to obtain participation of the …rm9, an individualrationality constraint must be satis…ed for all values of the informational parameter ,

namely: U t q 0: (2.1)

Consumers derive an utility S (q ), with S 0 > 0; S 00 < 0, from public good consumption.Funding of public good production requires indirect taxation with a cost of public funds10

1 + > 1, hence consumers’ welfare is

S S (q ) (1 + )t: (2.2)

Public good provision can be organized at the constitutional level. Social welfare isde…ned as

W S + U = S (q ) (1 + )q U: (2.3)

The task of the Constitution is to specify the appropriate contract to be o¤ered tothe …rm in order to maximize expected social welfare. From the revelation principle,11 weknow that it can be obtained from the optimal revelation mechanism. Such a revelationmechanism is here a pair of contracts (q; t); (q; t) which are incentive compatible.

Incentive compatibility writes

(IC ) t q t q (2.4)

(IC ) t q t q (2.5)

or, if we use the variables (U; q ) instead of (t; q ), with U = t q andU =

t

q ,

(IC ) U U + q (2.6)

(IC ) U U q: (2.7)

7 “By political constitution, we mean the actual institutional structure of government rather than thedocuments upon which this structure is bases”, Downs (1957), p. 290.

8 We will maintain the vocabulary of politicians in the whole book. Sometimes the alternative inter-pretation of bureaucrats will be more appropriate.

9 We normalize the status quo level of utility for the …rm at zero for all types. See Lewis and Sappington(1989), Maggi and Rodriguez (1995), Jullien (1997), Jeon and La¤ont (1999) for analyses of countervailingincentives arising in cases of type dependent individual rationality levels of utility.

10

For informational reasons, taxation is almost always distortive and creates deadweight losses whichare estimated around 30% of tax revenues in developed countries such as the USA and much more indeveloping countries (see Jones, Tandon and Vogelsang (1990)).

11 See Gibbard (1973), Green and La¤ont (1977) and Myerson (1979).




The individual rationality constraints are now

(IR) U 0 (2.8)(IR) U 0: (2.9)

The Constitution should select the pair of contracts which maximizes, under con-straints (2.6) to (2.9), expected social welfare, i.e.:

[S (q ) (1 + )q U ] + (1 )[S (q ) (1 + )q U ]: (2.10)

Clearly, (2.8) is implied by (2.6) and (2.9). Indeed, if a contract (t; q ) provides a nonnegative utility level to a type , a type , who is more productive, gets a positive utilitylevel if he mimics type by selecting the contract (t; q ). Therefore incentive compatibilityrequires that the contract (t; q ) gives a positive utility level to the agent. Ignoring

momentarily (2.7), observing that (2.6) and (2.9) must be binding, we have U = 0 andU = q . Substituting into (2.10) and maximizing we obtain:

S 0(q ) = (1 + ) (2.11)

S 0(q ) = (1 + ) +

1 (2.12)

with

t = U + q = q + q (2.13)

t = U + q = q: (2.14)

Note that this solution satis…es (2.7) since q > q .Under complete information about , the Constitution would equate the marginal

utility of public good to its marginal social cost, i.e.

S 0(q ) = (1 + ) (2.15)

S 0(q ) = (1 + ) (2.16)

and would leave no rent to the …rm

t = q t = q : (2.17)

Asymmetric information about leads to a trade-o¤ between e¢ciency and rent ex-traction. The higher the ine¢cient type’s production level q , the higher the socially costlyrent U = q which must be given up to the …rm when it is e¢cient. Equation (2.12)explains how the production level of the ine¢cient …rm must be decreased to optimizethis trade-o¤. The expected marginal e¢ciency cost (1 )(S 0(q ) (1 + )) must beequated to the expected marginal rent cost . Note also that no rent is given up tothe ine¢cient type and that no production distortion is required from the e¢cient type.

Let us discuss some more this essential rent e¢ciency trade-o¤ with the aid of Figure2.1.




-

6

! ! ! !

! ! ! ! ! ! !

! ! ! !

! ! ! !

! ! ! !

! ! ! !

! !

Z Z }

E

t q = 0

t q = 0

t

q

q

B

q

t

t

A

D

C

q

Figure 2.1

A -…rm (-…rm) has indi¤erence curves which are straight lines, t q = constant(t q = constant). We have drawn with heavy lines the indi¤erence curves of the twopossible types going through 0. A and B correspond to the optimal complete informationcontracts (t; q ) and (t; q ) respectively.

Utilities increase in the North-West direction since …rms want more money and lessproduction. So, if, under incomplete information we o¤er A and B, both types select B.(A; B) is not incentive compatible. One possibility to obtain an incentive compatible o¤eris to give a transfer to a …rm producing q which is so high that a -…rm is indi¤erentbetween this contract and B. C represents this contract. The pair (C; B) is now incentivecompatible and implements the same quantity allocations as the complete informationoptimum. However, it is rather costly for social welfare since a rent q with a socialcost q is given up to a -…rm, i.e., with probability .

The best incentive compatible pair described by the equations (2.11) to (2.14) is ob-tained by decreasing the quantity requested from type . This decreases the information

rent to q , but creates an e¢ciency cost since the marginal utility of production is notequated to the marginal social cost. The optimal trade-o¤ is obtained when the expectedmarginal social gain of decreasing further the information rent by one unit, i.e., (since the rent is given only to type with probability and is a transfer with a socialcost ), equals the expected marginal social e¢ciency cost of this decrease, i.e.,

(1 )d

dq

S (q ) (1 + )q

= (1 )

S 0(q ) (1 + )

;

since the e¢ciency cost occurs with probability (1 ). We obtain then equation (2.12)

(1 )

S 0(q ) (1 + )

= :

The best incentive compatible pair is represented by (D; E ) in Figure 2.1. The in-formation rent is now DA instead of CA and the quantity distortion is q q for type.




It is clear from Figure 2.1 that the incentive constraint of type is binding (D and E belong to the same -indi¤erence curve) and that the participation constraint of type

is binding (E belongs to the indi¤erence curve characterized by t q = 0). The -agentstrictly prefers E to D, i.e., the incentive constraint of type is strictly satis…ed and Dis above the -indi¤erence curve through A, i.e., the individual rationality constraint of type is strictly satis…ed. These qualitative features will be quite general.

As increases, the distortion (q q ) increases and we reach a value beyond which

it is better to give up production when = . Then, a single contract A is o¤ered. It isaccepted by type despite the fact that it yields no information rent and it is rejected bytype . The critical value is de…ned by

(S (q ) (1 + )q ) = S (q ) (1 + )q q + (1 )(S (q ) (1 + ) q ) (2.18)

or

q = (1 )(S (q ) (1 + )q )

i.e., when the expected cost of rents in the regime with two types equals the expectedsocial utility of having a -…rm in that regime. For a higher than the cost of rentsgiven up to type because of the presence of -…rms exceeds the social gain from o¤eringcontracts to types. We refer to the shut-down regime when only A is o¤ered. In thewhole book and without repeating it, we will assume that is less than .

2.2.2 The Supervision Technology

Let us now introduce a politician who observes a veri…able12 signal equal to withprobability and observes nothing otherwise ( = ). The politician is motivated by hisincome or reward13 s and has no private wealth so that his utility function can be written

V = s 0:

Note that s need not be a monetary income. It can be a private bene…t associated

with power.Consider …rst the benchmark case where the politician transmits his information truth-

fully without particular incentives. Then, his report r equates his signal .

If = r = , the Constitution is informed and can implement the complete informationallocation with an expected welfare

W FI =

S (q ) (1 + )q

+ (1 )

S (q ) (1 + )q

:

This event happens with probability .

12

For example, the politician has access to information concerning the real cost of the Franco-Germanfuture nuclear powerplant before deciding the size of the nuclear program for the XXI st century.

13 “Economic theories of government behavior, in so far as they exist, universally fail to assign anymotives to the men in governement” Downs (1957), p. 283.




If = , the Constitution is uninformed, and furthermore its posterior beliefs (Pr( == = )) remain equal to the prior beliefs

Pr( = = = ) =Pr( = = = ) Pr( = )

Pr( = )

= (1 )

(1 )(1 ) + (1 )= :

Accordingly, the Constitution o¤ers the contract characterized in (2.11)-(2.14) withan expected welfare:

W AI = S (q ) (1 + )q q + (1 )[S (q ) (1 + ) q ]:

This event happens with probability 1 .

Expected social welfare with a benevolent politician is

W FI + (1 )W AI :

The social gain provided by the benevolent politician acting as a supervisor is then

W = [W FI W AI ]

=

q + (1 )

fS (q ) (1 + )q g fS (q ) (1 + ) q g

and using a politician is valuable if this gain exceeds the cost of providing to the politi-cian the supervision technology (including his opportunity cost). However, since he isbenevolent these is no need to reward him (i.e. s = 0 in Figure 2.2).

POLITICIAN FIRM

CONSTITUTIONO¤ers

Contracts

@ @ @

@ @ @

V = s 0 U = t q 0

Supervision technology

W = S (q ) (1 + )(t + s)

+U + V

Figure 2.2




A reinterpretation of this case described as a benevolent supervisor is that it corre-sponds to a Nash equilibrium in the behavior of the politician and the …rm for contracts

o¤ered by the Constitution.The politician is o¤ered a ‡at incentive scheme s = 0 whatever the report r. He is

indi¤erent to any report and we assume that he reports truthfully. The …rm is o¤ered theoptimal incomplete information pair (D; E ) if r = and the optimal complete informationcontracts (A or B) if r = . More precisely, the …rm announces ~.

If r = , it gets D if ~ =

gets E if ~ = .

If r = , it gets A if ~ = or ~ =

r = , it gets B if ~ = or ~ = .

Knowing the politician’s strategy, a maximizing behavior of the …rm is to reporttruthfully. The allocation we associated with a benevolent politician is also obtained witha self-interested politician as a Nash equilibrium.

The key for this result is the non cooperative behavior between the two agents, thepolitician and the …rm. But is it reasonable to expect such a behavior?

The politician has some discretion in his activity as a supervisor since, when he receivesthe signal = , he may choose not to report this information14. Even though he isindi¤erent between reporting and not reporting the true signal, he understands that, byreporting r = when = , and informing the …rm of this new strategy (which is costlessfor the politician) he provides an information rent q to the …rm.

Another Nash equilibrium is that the politician always reports r = and we are backto the optimal contract under incomplete information with no politician. However, thisequilibrium does not seem very robust. The Constitution can give an in…nitesimal wage" > 0 to the politician if he reports the veri…able information . Then, the politicianprefers strictly to tell the truth.

If the politician and the …rm cannot communicate, then, in a static model, it is dif-…cult to escape from the conclusion that truthful behavior is the most natural outcome.But, the presumption that the Constitution can control communication between the twoagents appears highly unrealistic. So, let us consider the extreme opposite case where

communication between the agents is costless. The two agents will then understand thatthere is a common stake for collusion and the self interested politician will be tempted topropose to hide his signal = , if the …rm agrees to share with him the information rentthat the report r = ensures.

There is however a major di¢culty in organizing such a collusion, since the two part-ners do not have access to a jurisdiction which could implement the contract: “I do notreveal = if you pay me b”.

Nevertheless, they have strong incentives to reach an agreement. One case where itseems possible is if the hard signal that the politician has obtained cannot be replicated.Then a quid pro quo in which the politician gives the …rm the unique proof of its type in

exchange for a monetary payment does not run the risk that the politician reveals = 14 Note that there is no stake of collusion when = since the …rm’s utility level is zero whatever the

politician’s report.



2.3. OPTIMAL INCENTIVES FOR THE POLITICIAN 33

after having received the payment. Another possibility is that both agents have access to aprivate third party which has the reputation of enforcing contracts (like the ma…a). It can

also correspond to a norm of behavior enforced by repeated relationships but this settingo¤ers also new instruments to the principal who can use statistical historical information(remember that he knows the probability ). It is then a rough shortcut to a situationwhere the principal is a short run player facing long run players.

In the next section we will assume that the politician makes the collusion o¤ers andthat there is a transaction cost in the transfer from the agent to the supervisor as ashortcut to these di¢culties.

2.3 Optimal Incentives for the Politician

2.3.1 Optimal Collusion-Proof Constitution

From now on in this book we shall consider a simpler supervision technology which econo-mizes on notations. We assume that the signal can only inform about . That is, if = there is a probability that = and a probability 1 that = . If = , = always.15

Now, if the politician is benevolent and always transmits truthfully his signal when = , the constitutional level is completely informed and selects the complete informationcontract q = q ; U = 0. When = , the beliefs of the constitutional level are revisedthrough the Bayes law. The probability of a good type conditionally on = is

=(1 )

1 < :

Maximizing expected social welfare under incentive and individual rationality con-straints leads now to

S 0(q ) = (1 + )

S 0(q ) = (1 + ) +(1 )

1 :

The politician is useful. His presence leads to a decrease of the information cost of thepublic good. The expected rent given up to the …rm is now (1 ) q . The di¤erencewith the former supervision technology is that, after receiving = , the Constitutionknows that the ex post probability it is facing a type is lower ( < ) because, withprobability , some -type are identi…ed as such. The fear of giving up an information rentis accordingly lower and in the rent-e¢ciency trade-o¤ one can a¤ord a higher e¢ciencyfor a -type (q > q ).

15 Another advantage of this technology is the following one. It is di¢cult to envision cases where thesupervisor may sometimes obtain a veri…able proof of the agent’s type without assuming that the agentcan always provide himself such a proof. But, then the principal can easily oblige the agent to provide

this information under the threat of not contracting. With the new technology, the agent can, as thesupervisor, only provide veri…able information when = . Then, the principal cannot require a veri…ableproof of the agent’s type since for = such a proof is impossible to get. The agent can then claim tobe a agent.




However, the politician is self interested. Unless otherwise motivated he will o¤er tothe …rm, when = , to conceal his signal with a bene…t for the …rm of q . The

maximal amount of money that the …rm is willing to o¤er to the politician is a bribe of q with a value for the politician of

q

1 + c

The positive parameter c models the transaction cost of the side transfer between thepolitician and the …rm. We will denote k = 1

1+c. The transaction costs of side transfers

re‡ect the risks of being caught, the ine¢ciencies of bargaining and the costs incurredto avoid being identi…ed (for example bribes in kind rather than in money). They aretaken here as exogenous. In Chapter 9 we will provide a theory which endogeneizes these

transaction costs.The timing of the collusion game that we choose is described in Figure 2.3.

Agent

learns

Principal

o¤erscontractsto agent

and supervisor

Agent andsupervisor

learn

Supervisor

o¤ers aside-

contractto agent

Contractsare

executed

Figure 2.3

Providing incentives to the politician can prevent its capture by the …rm.16 Supposethat an incentive payment of s = kq is given to the politician when he reports the(veri…able) signal . The expected social cost of this payment is

s;

because it occurs with probability and has only a distributional cost since the politi-cian’s welfare is included in the social welfare function.

Expected social welfare can now be written:

[S (q ) (1 + )q ] + (1 )

(1 )

1 [S (q ) (1 + )q q ]

+(1 )

1 [S (q ) (1 + ) q ]

k q : (2.19)

Indeed, with probability the constitutional level is informed that the …rm is e¢cient.With probability 1 , it is uniformed. With posterior probability (1)

1, it will face an

e¢cient …rm for which it will have to give up an information rent q . With posterior

probability

1

1 , it will face an ine¢cient …rm. In addition, with probability , it willgive to the politician an incentive payment k q .

16 Appendix A.2.1 show that it is optimal to prevent collusion.




Reoptimizing expected social welfare yields immediately

S 0(q ) = (1 + ) (2.20)

S 0(q ) = (1 + ) +

1 (1 (1 k) ) : (2.21)

The politician is now less useful unless the transaction costs of side transfers go toin…nity (k ! 0). If k = 1, the politician is useless since he costs as much as the decreaseof information rent he makes possible.

To avoid corruption the Constitution sets up incentives for politicians. As incentivepayments are socially costly, the production level q is decreased.17 This decreases thestake of collusion q and consequently the required incentive payments. The rent of

the …rm U = (1 ) q

is now lower (q

< q

). The …rm su¤ers from the fear of corruption.Summarizing, we can state:

: The optimal constitution creates incentives for politicians to avoid theircapture by the interest group, and distorts production downward to decreasethe stake of collusion.

We have assumed that the supervision technology is costly. Otherwise it would beduplicated by the Constitution to create yardstick competition between several supervi-sors. Therefore we must note again that politicians as supervisors studied here are worthit only if their value exceeds their cost.

Proposition 2.1 emphasizes two constitutional policies in a reduced form and it isworth discussing their practical implementation.

First, one needs to provide rewards to politicians who ful…ll satisfactorily their role asinformational supervisors. This can be implemented either by the judicial power or by theelectoral process. The judicial power seems better organized to punish politicians whenveri…able proof that they misbehaved is available. A politician is deprived of his salary andof his private bene…ts in the job in such a case. One reason why the judicial power is notgiven the ability to reward politicians is probably the fear of collusion between this powerand politicians. But this is outside the framework of this chapter which maintains the

assumption of a benevolent constitution. The electoral process may reward the politicianwho proves that he does well his job. One di¢culty is for the electorate to be able tounderstand when the politician is doing his job properly in complex informational matterswe have in mind here. The need for credible sources of information which publicize thegood performances of politicians is essential to implement the desirable incentive schemesthrough the electoral system.

The second one is the less responsive nature of the contract to the politician’s infor-mation, the move toward more bureaucratic rules as a constitutional response to capture.It is indeed a well known feature of administrations and political decision mechanisms toappear little responsive to information. Proposition 2.1 gives a fundamental insight to

appreciate the role of this bureaucratic bias.17 We assume here that it is optimal to deter collusion. See Appendix 2 for a proof of this collusion-

proofness principle.




Figure 2.4 summarizes the di¤erent distortions according to the type of supervision.

-

6

output

types

q

q

q

q

q = q = q = q P P P P P P P P P P P P P P P P P P P P P P

Z Z Z Z Z Z Z Z Z Z Z Z Z Z

Z Z Z Z Z Z Z Z

/

…rst best

benevolent supervisor

non benevolent supervisor

:no supervisor

Figure 2.4

Alternatively, the Constitution could attempt to raise the transaction costs of sidecontracts. We can also note:

: The lower the transaction costs of collusion (i.e., the higher k), the lower isexpected social welfare, the higher the downward distortion of the ine¢cienttype’s production level, and the lower the expected rent of the …rm.

Except the politician, everybody loses from the prospect of collusion. In particular,the …rm would prefer to commit not to enter collusive agreements. This may have strong

implications in the following case. Without collusion, the above model is equivalent toa model with contracting between the principal and the agent before the agent discoversits type as long as the agent is in…nitely risk averse at the zero wealth level (so that theconstraint t q 0 still has to hold for any ). Then, the agent would have incentives tomake his information available in exchange for a reasonable payment and the principal’scommitment not to hire a supervisor (the payment has to be lower than the expected rentwithout supervisor but higher than the expected rent with a corruptible supervisor).

2.3.2 Equilibrium Collusion

We assume now that there are two types of politicians. With probability , we have a

type 1 politician who (as above) does not engage in collusion if he is rewarded s when hereveals that = such that

s k q :




With probability 1 , we have a type 2 politician who is more honest or su¤ers fromhigher transaction costs of side payments, and a lower payment s such that

s k q

is enough to prevent collusion.We have two possible regimes depending on the values of the parameters.

Regime 1: No collusion.The payment s is chosen so that no politician, whatever his type, wants to engage in

collusion, i.e.s = kq :

Optimal social welfare is as before and the optimal solution is characterized by (2.20)(2.21).

However, in this solution, there is now some waste of incentive payments since aproportion 1 of politicians could be made non corrupted with smaller payments s instead of s, but this type of politician cannot be identi…ed. An alternative, which isattractive if is small, is to let the proportion of politicians be corrupted to save onincentive payments. Expected social welfare is then:

(1 )[S (q ) (1 + )q ] + [1 + ][S (q ) (1 + )q q ]

+ (1 )[S (q ) (1 + )q ]

(1 )(kq ) (1 k) q : (2.22)

Indeed, with probability (1 ) it is a type 2 politician who discovers that = andreveals it (term 1 in 2.22) and he is paid k q which has an expected social cost (term4 in 2.22). With probability (1 + ) it is a -type …rm but the constitutional levelreceives the report either because the politician has observed nothing (with probability1 ) or because it is a type 1 politician who is hiding the information (with probability ). This corresponds to term 2 in 2.22. Furthermore, we include as a loss the transactioncosts of collusion which bene…t neither the …rm nor the politician (the last term in 2.22).

But to account for the fact that some of this cost could be a revenue for some intermediarieswe introduce the parameter in [0; 1].Optimizing (2.22) we get:

Regime 2: Partial collusion.

S 0(q ) = (1 + ) (2.23)

S 0(q ) = (1 + ) +

1

1 (1 k)

1

1 +

: (2.24)

This case will be relevant when is small. So, to simplify the exposition we assume that (1 +

) < 1. Then, as increases, in both regimes production q increases. The quality

of the supervision technology characterized by and low incentives for the ine¢cient type,




which are both instruments to decrease the …rm’s rent, are substitute instruments. Notefurther that, in the corruption case (regime 2), the production level of the ine¢cient type

is lower than in the non corruption case (regime 1). Indeed in regime 2, the posteriorprobability that the principal is facing a -type …rm when he receives the report r = ishigher than in regime 1:

(1 (1 ))

1 (1 )>

(1 )

1

:

Welfare in regime 1 is independent of while welfare in regime 2 is increasing in (from the envelope theorem). There is a value such that for larger than it is betterto let corruption happen. It is then so cheap to obtain honest behavior from a proportion1 of politicians that letting corruption happen with probability dominates the costly

constitution which ensures absolutely no corruption. Let us index the variables in regime1 (resp. 2) with C (resp N C ). We have Figure 2.5.

-

6

W NC

W C

Figure 2.5

Let us now consider the e¤ect of an improvement in the supervision technology.

A better supervision technology increases welfare and decreases corruption.

Proof: See Appendix 2.2.An increase of information is more favorable in the no corruption regime because

low incentives and better information are substitute instruments. Since q C < q NC theinstrument of low incentives is used more in the corruption regime. So the marginal valueof better information is higher in the non corruption regime and the set of parameter

values for which the corruption regime dominates shrinks as increases.Furthermore, in both regimes, the probability that the principal is uninformed de-

creases with and social welfare increases with .



2.4. CONCLUSION 39

The …rst part of Proposition 2.3 relies on the fact that low incentives and bettersupervision are substitute instruments. This may sound natural but the opposite result

would hold if they were complements. This would occur with the technology consideredin the beginning of this chapter18 where both and are discovered with probability .

It is interesting to discuss the reason why the principle of collusion proofness does nothold in this section. When there is asymmetric information for the Constitution about thetype of transfers that politicians require to engage in collusion, the revelation principle mayfail because it rests on the inability of the Constitution to mimic the transfers realized bythe colluding partners. We are out of the revelation principle as in the case where > f

with k = 11+f

. Then, too, transfers inside a collusion are less costly than the principal’s

transfer.An alternative interpretation is that the Constitution has the same information as the

agents about the transaction costs of these transfers, but that institutional constraints—the incompleteness of contracts— prevent him from di¤erentiating transfers accordingto the type of politician. For example it may be common knowledge that corruption iseasier in the South than in the North, but rewards to politicians are identical. It is thena general second best principle that collusion may help complete incomplete contracts.19

2.4 Conclusion

We have presented and discussed in this chapter the main building block of the analysisin Part I. The simple capture or collusion model developed by Tirole (1986) assumes that

colluding agents can sign costly contracts. This black box is not completely satisfactory,but the great merit of this model is to provide a framework for characterizing the optimalresponse to collusive activities within a model with endogenous stakes of collusion. Itis a …rst step, but a useful one to think about the optimal organization of governmentfacing interest groups. In Chapter 9 we will make some steps towards endogeneizing thetransaction costs of collusion.

18 See La¤ont and N’Guessan (1998) for other cases.19 A deeper explanation would require to give an interpretation of more or less corruptible supervisors in

terms of utility functions. Utility functions would depend on messages directly. A honest supervisor wouldsu¤er from sending a message di¤erent from the truth. A supervisor would then be characterized by two

parameters of adverse selection (his signal and his level of corruptibility). Extending appropriately thespace of actions to include messages, a collusion-proof principle would hold in this extended framework butit would entail equilibrium collusion in the restricted framework considered here. An extensive discussionof this point is beyond the scope of this book.




Appendix 2

A.2.1: Proof of the Collusion-Proofness Principle with Hard Supervisory In-formation

We assume that collusion is organized by the supervisor who has all the bargainingpower in the coalition. Note that in order to use the veri…ability of the supervisor’s signalit is necessary to consider messages which belong to the space of signals f; g.

If we consider mechanisms with abstract strategy spaces, such veri…ability restrictionsare meaningless. The collusion-proof principle requires two steps. First to characterizewhat one can implement with general mechanisms and then what one can implementwhen the supervisor’s message space is f; g with the restriction that

If = , then r = = , then r 2 f; g.

The …rst step relies on a collusion-proof principle with soft information that we willestablish in Chapter 9. Anything the principal can do with general mechanisms he canrealize with revelation mechanisms in which the informed supervisor organizing the collu-sion has a best strategy which is to recommend truthful revelation of private informationwhich is considered as soft. In this model no gain from supervision can be obtained withsoft information. This will be proved also in Chapter 9.

Then we must consider the case where the message space of the supervisor is M 2 =

f; g and let M 1 be the message space of the agent. The principal is the constitutionallevel, C . The …rm is the agent, A, or player 1. The supervisor is the politician, P , orplayer 2. The grand mechanism G o¤ered by the principal C maps messages (m1; m2)belonging to message spaces (M 1; M 2) into a transfer to the …rm t(m1; m2), a quantity of public good q (m1; m2) and a transfer to the politician s(m1; m2).

In drawing the game tree of the two stage game in which C o¤ers the grand contractG and subsequently P o¤ers a side-contract we take into account the fact that P can onlyobserve a signal if = and the fact that it is common knowledge that in this case hehas veri…able information that = .

We want to show that there is no restriction in considering grand contracts G which are

revelation mechanisms such that the best strategy of the politician is to reveal truthfullyhis message.



2.4. CONCLUSION 41

Two cases must be considered:Case 1: Nature chooses or and = . Then the report of the supervisor is constrained

to be . The game tree reduces to:

P

A

C

Q Q Q Q Q Q Q

@ @ @ @ @

@ @ @ @ @

G

Y N

Y N Y N

G is played (0; 0) (0; 0) (0; 0)

t(m1; )q (m1; )s(m1; )

If G is accepted by both players it is played. Indeed, in this case the politician has noinformation and this is known by the agent. He cannot o¤er any manipulation of reportsthat the …rm cannot do by itself.

Let m1(; ) and be the optimal strategies of the two players in G. G is then

equivalent to the revelation mechanism

(I )

8<:

T (; ) = t(m1(; ); )

Q(; ) = q (m1(; ); )

S (; ) = s(m

1(; ); )which is truthful by de…nition of the optimal strategy m

1.




Case 2: Nature chooses and =

P

A

C

m2 2 f; gs(m1; m2)q (m1; m2)t(m1; m2)

Q Q Q Q Q Q Q

@ @ @ @ @

@ @ @ @ @

G

Y N

Y N Y N

(0; 0) (0; 0) (0; 0)

P

A

@ @ @ @ @ @

G S G

Let m1(; ) 2 M 1; m

2() 2 f; g the optimal strategies of the two players when G isplayed non cooperatively.

If m2() = , there is nothing that the politician can o¤er. If m

2() = , then

the politician can o¤er a side-contract which is not the null contract. He is informedabout and makes a take or leave it o¤er to the …rm which maximizes its welfare undervarious constraints. The side-contract o¤ered is a manipulation of reports 1(; ) 2M 1; 2(; ) = and side-payments y1(; ); y2(; ) such that

y2(; ) + ky1(; ) = 0

y1(; ) 0

to take into account transaction costs,

s(1(; ); ) + y2(; ) 0

to take into account the limited liability constraint, and

t(1(; ); ) q (1(; ); ) + y1(; )



2.4. CONCLUSION 43

t(m1(; ); m

2()) q (m1(; ); m

2())

to take into account the …rm’s individual rationality constraint.De…ne

(II )

8>><>>:T (; ) = t(1(; ); ) + y1(; )Q(; ) = q (1(; ); )S (; ) = s(1(; ); ) + y2(; )T (; ) = 1

and consider the revelation mechanism composed of (I ) and (II ). It is truthtelling andimplements without collusion the allocation reached before with the side contract, at alower cost since y1(; ) + y2(; ) < 0. Furthermore, the politician cannot o¤er a newside-contract which improves on this mechanism.

A.2.2: Proof of Proposition 2.3Let

W = S (q ) (1 + )q ;

W (q ) = S (q ) (1 + )q q;

W (q ) = S (q ) (1 + )q:

By de…nition of :

W + (1 )W (q NC ) + (1 ) W (q NC ) kq NC

= (1 )W + (1 + )W (q C ) + (1 ) W (q C ) (1 )(k q C )

(1 k) q C : (2.25)

Di¤erentiating with respect to , we obtain:

(1 )d = [W W (q NC ) + (1 )W (q C )

kq NC + (1 )(kq C ) + (1 k) q C )]d:

But from (2.25)

W kq NC + (1 )(kq C ) + (1 k) q C

W (q NC ) + (1 )W (q C ) =1

(W (q C ) W (q NC )) + (1 )( W (q C ) W (q NC ))

d

d / fW (q C ) + (1 ) W (q C )g fW (q NC ) + (1 ) W (q NC )g:

The function W () + ( 1 ) W () is concave and takes its maximum at q de…ned by:

S 0(q ) = (1 + ) +

1

:

We haveq < q C < q NC :




Henced

d > 0:

Let W NC (q ) (resp. W C (q )) be the regime 1 (resp. regime 2) expected social welfareas a function of the ine¢cient type’s production level when the production level of thee¢cient type is q .

Note …rst that W NC (q NC ) is increasing in . From the envelope theorem

dW NC

d (q NC ) =

@W NC

@ (q NC )

= [W W (q NC )] kq NC

= (1 k)q NC > 0:

Now we prove that W C (q C ) is increasing in when regime 2 is optimal.

(q ) = W NC (q ) W C (q ) is proportional to

If the parameters are such that regime 2 is optimal we have

W C (q C ) > W NC (q NC ) > W NC (q C ):

Therefore

(q C ) < 0 and@

@ (q C ) < 0:

NowdW C

d (q C ) =

@W NC

@ (q C )

@

@ (q C ) +

dW C

dq (q C )

dq C

d ;

@W NC

@ (q C ) = (1 k)q C > 0 ;

@

@ (q C ) > 0 ;

dW C

dq (q C ) = 0:

Hence@W NC

@ (q C ) > 0:



Chapter 3

An Incentive Theory of theSeparation of Powers

“A society in which the guarantee of rights is not assured, nor the separationof powers provided for, has no constitution.”

Article 16 of the French Declaration of the Rights of Man of 1789.

3.1 Introduction

As the quote from the French Declaration of the Rights of Man shows, the separation of

powers is viewed as a key question of democracy. It was already in the minds of Mon-tesquieu1 and the American Federalists, but economists still have little to say about thismythical problem. In this chapter we want to explore this question within the paradigmof a complete constitution.

A …rst reason well understood by economists for duplicating regulated agencies isyardstick competition. Using the correlation of the signals obtained by these agenciesenables the principal to extract in a costless way their information rent. This idea wasmodeled by Shleifer (1985) in the case of perfect correlation and Cr er and McLean (1988)in the case of an arbitrary degree of non zero correlation.2

In Chapter 8 we will provide a detailed discussion of this idea in relation to collusive

behavior. In this chapter we will model a di¤erent reason for the separation of powers.3

We will argue that the separation of powers may act as a device against the threat of regulatory capture, and construct an incentive theory of the separation of powers. Thegeneral idea has been known for a while among political scientists (Moe (1986), Wilson(1980), Mueller (1997, Chapter 17)) but has not been formalized. The Public Choiceschool has emphasized the fact that institutional rules may be designed to discourage rentseeking behavior (see Congleton (1984), Rose-Ackerman (1978) who argue that increasing

1 “Tout serait perdu si le m e homme, ou le m e corps des principaux ou des nobles, ou du peuple,exer ient les trois pouvoirs: celui de faire des lois, celui d’ex uter des r olutions publiques, et celui de juger les crimes ou les di¤ ents des particuliers”, Montesquieu (1748), p.586 .

2

See also Auriol and La¤ont (1992).3 As reported in Moe (1986), separation of powers in a Constitution may also be bene…cial whenintertemporal commitment is limited. See Tirole (1994), Olsen and Torsvick (1993) and Martimort(1995) for agency models building on this idea.

45



46 CHAPTER 3. AN INCENTIVE THEORY OF THE SEPARATION OF POWERS

the number of individuals who must be bribed before getting an award may be optimal).However the weakness of this approach is that the rent seeking activities are only supply

determined.We de…ne the power of a politician as his ability to use his signal on the regulated

…rm to improve social welfare. When benevolent politicians are in charge of implement-ing the socially optimal contract, there is no reason for the separation of powers, i.e., forsplitting authority among di¤erent politicians. They always use their possible discretion,i.e., their power, in order to maximize social welfare. In contrast, as in Chapter 2, nonbenevolent politicians may use their power to pursue personal agendas, for example bycolluding with the regulated …rm. Then, there is scope for separation. Separation of agencies or politicians divides the information at their disposal, and consequently limitstheir discretion in engaging in socially wasteful activities. Instead of having a unique

politician implementing the privately e¢cient collusive o¤er to the regulated …rm, separa-tion introduces a Bayesian-Nash behavior between partially informed politicians. Whenthis Bayesian-Nash behavior is such that the politicians ask for prudent bribes which canalways be provided by the interest group, the outcome of this collusion game reduces thetotal collusive o¤ers they make. As a result, the transaction costs of collusive activitiesincrease and preventing collusion becomes easier. Separation improves social welfare.

In Section 3.2 we extend the model of Chapter 2 to make the point. However, thissimple extension entails a correlation of signals about the two regulated agencies whichmixes the two ideas of yardstick competition and higher transaction costs of capture. Todisentangle the two ideas, we construct in Section 3.3 a model with three types for the

regulated …rm in order to be able to allocate to the two agencies or politicians supervisiontechnologies which are stochastically independent. Section 3.4 characterizes the optimalcollusion-proof Constitution with a single politician who controls both supervision activ-ities. The case of separation of politicians is dealt with in Section 3.5. In particular wediscuss in detail the comparative statics of the gains to be expected from the separationof powers. Section 3.6 provides some criticisms of the modeling and some extensions.Section 3.7 concludes.

3.2 Separation of Powers and Yardstick Competition

In the previous chapter we have dismissed the duplication of informed supervisors byappealing to excessive …xed costs. However, the duplication of …xed costs is not alwayshigher than the sampling value o¤ered by two supervision technologies. The …rst questionto ask is if taking into account the possibilities of collusion a¤ects the choice between oneor two technologies. It is the question of the value of duplicating supervision technologieswithin the control of a single politician. The next question is if these two technologiesshould be allocated to two di¤erent politicians: the question of the separation of powers.We extend slightly the model of Chapter 2 to explore these issues.

Suppose that, in the model of Chapter 2, we have now two independent signals i

such that

Pr(i = = = ) = i = 1; 2:The timing is as described in Figure 2.3 with a preliminary decision of having one

or two politicians. Consider …rst the case of one benevolent politician with the two



3.2. SEPARATION OF POWERS AND YARDSTICK COMPETITION 47

supervision technologies. Either, the principal receives at least one informative report(with probability 2 + 2 (1 )) and he is fully informed and can implement the e¢cient

allocation for = . Or, he receives no informative report: r1 = ; r2 = . His posteriorprobability that = is now:

Pr( = jr1 = ; r2 = ) = (1 )2

(1 ) + (1 )2= ^ < :

When he receives an informative signal he is more con…dent now that he is facing anine¢cient type. This leads to a trade-o¤ more favorable to e¢ciency described by

S 0(q 2

) = (1 + )

S 0

(q

2 ) = (1 + ) +

(1 )2

1 :

Expected social welfare is

(2 )W + [1 (2 )][S (q ) (1 + )q q 2 ]

+(1 )[S (q 2 ) (1 + )q 2 ]

instead of, with one supervision technology,

W + (1 )[S (q ) (1 + )q q ]

+(1 )[S (q ) (1 + ) q ]:

The improvement of welfare is:

W =n

(1 )q (1 (2 )) q 2

o+(1 )

hfS (q 2 ) (1 + ) q 2g fS (q ) (1 + ) q g

i:

The …rst term represents the expected decrease of the information rent. Its sign isambiguous because the rent itself is higher with two technologies since q 2 > q , but it isgiven up less often. The second term is the e¢ciency gain due to a smaller distortion for

the ine¢cient type’s production.Considered as function of q , expected social welfare with two supervision technologies

W 2(q ) is always higher than expected social welfare with one supervision technology W 1(q ).

W 2(q ) W 1(q ) = q [ 2]:

If the politician is not benevolent, collusion-proofness requires expected incentive pay-ments for the politician of

k q with one technologyk (2 )q with two technologies4

4

For simplicity we assume that the transactions costs of collusion are identical between supervisorsand identical to the case with one supervisor. Neven, Nuttall and Seabright (1993) argue that sectorspeci…c agencies increases the risks of capture by producers in each sector (see also Miller, Shughart andTollison (1984).




The new di¤erence of welfare levels is

~W 2(q ) ~W 1(q ) = q (1 k)( 2):

So the gain of double supervision is now smaller because of the cost of collusion-proofness and might not compensate for the …xed cost of setting up a new supervisiontechnology, as it did so with a benevolent politician. We can then ask if the separation of powers may decrease this cost of collusion-proofness.

Now we have one politician associated with each supervision technology.5 The sepa-ration of powers is irrelevant if the politicians are benevolent. Let us consider the caseof self interested politicians who may enter collusive agreements with the …rm. Clearlythe collusion-proofness constraints depend on the ways the two politicians and the …rm

bargain under asymmetric information in the collusion game. To make things as simpleas possible, we assume that, when he has observed a favorable signal, a politician makesa take-it-or-leave-it-o¤er only to the …rm. This assumption precludes a politician fromo¤ering a side-contract to the other politician.6 Two reasons motivate this choice. First,bribes take often the form of future job opportunities in the private sector for lenientcivil servants, the so-called “revolving door” phenomenon; there does not seem to existsuch an equivalent mechanism between two government administrations. More generally, jobs’ lengths within administrations can be designed so that those collusive behaviors areless easily enforceable and more easily detected. Second, the Constitution is likely tobe able to better control and therefore to prevent monetary transfers between politicians

than transfers between the politicians and the regulated …rm. The latter assumption isequivalent to saying that side-transfers between the politicians incur in fact an in…nitetransaction cost. Alternatively, Section 3.6.3 explains why considering information shar-ing between the politicians may not be enough to have them collude when they cannotmake monetary transfers between themselves. We distinguish two cases according to thepoliticians’ behavior.

With prudent behavior, politicians make only collusive o¤ers which are accepted withprobability one.7 Then, at the symmetric Nash equilibrium of those o¤ers, there is nobribe and no cost of collusion proofness. Indeed, a politician who does not know the otherpolitician’s report will not dare to make a collusive o¤er. The power of competition is fullyexpressed by this case. If making a collusive o¤er which is rejected entails a large cost

5 We assume that these technologies are not transferable between the two politicians. In particular,one politician cannot sell ex ante, i.e., before any signal occurs, the value of his technology to the other.Necessarily, such an assumption requires that a benevolent court of justice veri…es that the control of each informational technology is the one requested by the Constitution (see also Section 3.6.3.).

6 It also precludes a politician to use a side-contract contingent on the o¤er of the other politician’sside-contract. We assume therefore that such an o¤er is not observable by the politician who has notmade it.

7 This assumption of prudent behavior can be motivated along several lines. It can be motivated byappealing to a large degree of risk-aversion of the politician. Then, he considers only the worst possiblestate of nature before making his collusive o¤er. The politician may also be afraid of denunciation bythe …rm if he makes a bribe o¤er which cannot be accepted by the …rm. Lastly, the one-shot bargaining

game between the politician and the …rm may be modeled as a sequence of repeated o¤ers by the lessinformed party (the politician). In this case, when o¤ers are repeated su¢ciently often, a politicianunable to commit himself to a bribe o¤er is going to charge the minimal bribe which is consistent withhis information (see Gul et al. (1985)).



3.2. SEPARATION OF POWERS AND YARDSTICK COMPETITION 49

(for example being denunciated by the …rm), dual supervision introduces an uncertaintywhich is very pro…table to the constitutional level.

We obtain a similar but weaker result with the traditional expected utility behaviorwhich ignores those out of equilibrium penalties.

At a non collusive Nash equilibrium, politician i does not deviate if, when he receivesthe signal i = , he obtains an incentive payment greater than his expected discountedbribe:8

si k(1 )q:

Indeed with probability the other politician is informed and has transmitted truth-fully his message so that the demand for bribe of q is rejected by the …rm which hasno rent.

The total expected cost of collusion proofness is

2 (1 )k q;

instead of (2 )k q;

with a single politician.The presence of the other politician creates a negative externality on the bribe that

the informed politician can expect and therefore a positive externality on the incentivepayment required for collusion proofness. Summarizing the discussion above we have:

a) The duplication of supervision technologies is more valuable if the quality of super-

vision ( ) is higher and if the transaction costs of collusion are higher (k low).b) The separation of powers decreases the cost of implementing collusion-proofness.

The correlation of the signals 1 and 2 suggests a yardstick competition e¤ect. Indeedwe have

p11 = Pr(1 = and 2 = ) = 2

p12 = Pr(1 = and 2 = ) = p21 = Pr(1 = and 2 = ) = (1 )

p22 = Pr(1 = and 2 = ) = 1 + (1 )2

and

= p11 p22 p12 p21 = 2 (1 ):Proposition 3.1.b could be interpreted as follows. The constitutional level must control

a moral hazard behavior which corresponds to collusion. Because of limited liability, itmust reward the politicians for honest behavior. The higher , the higher the correlationof types, and the higher the gain of the dual control in terms of collusion cost ( 2k q ).

However, there are two forces at work here. The …rst one is the correlation of signalswhich creates a possibility of yardstick competition between politicians. But the lim-ited liability constraints restrict considerably this opportunity. The second one is thatthe competition of politicians introduces an ine¢ciency in the collusion game which isfavorable to the constitutional level. In the next section we isolate the two e¤ects by

constructing a model where the signals of the two politicians are independent.8 We assume here that the politician must make his decision to report or not his signal to the Consti-

tution before knowing if his collusive o¤er will be accepted or not.




3.3 A Model with Three Types

We consider the same three-tier hierarchy Constitution-politician-…rm as above, but nowit is common knowledge that the e¢ciency parameter of the cost function has thefollowing structure :

= 1 2

where 1 and 2 are two binary random variables taking their values in f0; g.9 1 and2 may be thought of as improvements in the technology that have been or not realizedin the …rm. Let us denote = and = 2.

The random variables i for i 2 f1; 2g are drawn independently from the same prob-ability distribution on f0; g with respective probabilities (1 ; ). The probabilitydistribution of (1; 2) induces a discrete distribution P (:) on f; ; g :

P () = 2 P () = 2 (1 ) P () = (1 )2:

The Constitution wishes to maximize under the individual rationality constraints thefollowing social welfare function :

SW = S (q ) (1 + )(t + s) + U + V = S (q ) (1 + )q U V:

When politicians are benevolent (i.e., transmit truthfully their signals) and a fortioriwhen the Constitution has complete information, the outcome achieved is independent of the supervisory structure.

Two informational technologies are now available. Each informational technologyi; i = 1; 2 generates, hard information on the random variable i with probability if thisvariable is ; otherwise nothing is learned. Let i the signal provided by technology i,

i = with probability i = ; with probability 1 :

Note that each informational technology is relative to a di¤erence piece of privateinformation contrary to Section 3.2.

If no signal has been observed, i.e., (1 = ;; 2 = ;), which occurs with probability(1 )2, the conditional probabilities of each state (; ; ) are respectively:

P 0() = 2(1 )2

(1 )2; P 0() =

2 (1 )(1 )

(1 )2; P 0() =

(1 )2

(1 )2:

We denote by W 0(q 0; q 0) the expected social welfare under this full asymmetric infor-mation and with a benevolent politician where, for the next sections, we make also explicitits dependence on the levels of production requested from types and . Denoting U 0; U 0,and U 0 respectively the utility level of a …rm with characteristic ; ; and , we have:

W 0(q 0; q 0) = P 0()

S (q 0) (1 + )q

0 U 0

+

P 0()S (q 0) (1 + )q 0 U 0+ P 0() S (q 0) (1 + )q 0 U 0 :

9 This model was …rst developped in La¤ont and Martimort (1995).



3.3. A MODEL WITH THREE TYPES 51

With probability 2 (1 ), only one signal is observed, i.e., (1 = ; 2 = ;) or(1 = ;; 2 = ). The Constitution su¤ers then from a milder asymmetry of informa-

tion since it knows that 2 f; g. It updates its beliefs accordingly. The respectiveprobabilities of and are:

P 1() = (1 )

1 ; P 1() =

1

1 :

We denote by W 1(q 1) the expected social welfare under this milder asymmetry of infor-mation with a benevolent politician, where again we make explicit its dependence on thelevel of production requested from a …rm. Denoting U 1; and U 1 respectively the utilitylevel of a …rm with characteristic , and , we have:

W 1(q 1) = P 1()S (q 1) (1 + )q 1 U 1 + P 1()S (q 1) (1 + )q 1 U 1 :

When both signals are informative, i.e., with probability 2 2, the true state of natureis necessarily , and the complete information regulation is achieved. Let W 2 denote thesocial welfare in that case. We have:

W 2 = S (q 2) (1 + )q

2 U 2;

where q 2

is the complete information production and U 2 the …rm’s associated utility level.As a whole, expected social welfare with a benevolent politician becomes:

SW = (1 )2W 0(q 0; q 0) + 2 (1 )W 1(q 1) + 2 2W 2: (3.1)

A contract with a single politician is a triplet ft(r1; r2; ~); q (r1; r2; ~); s(r1; r2)g, wheret(), q () and s() denote respectively the transfer received by the …rm, its productionand the politician’s reward as a function of both the reports of the politician on the hardinformation signals (r1; r2) he may have observed and the report ~ of the …rm on its type.We assume that the politician …rst reports his signals to the Constitution, then, if thesesignals are not fully informative, the principal asks directly the …rm for its type. Notethat this sequential timing of the game and the fact that reports of the politician are hardinformation imply also that the politician’s reward does not need to depend on the …rm’sreport. Similarly, the transfer and the output of the …rm depend on its report only to the

extent that the politician has not already reported hard information on its type.First, when both pieces of information are discovered, the optimal Constitution entailsfull extraction of the …rm’s rent U 2 = 0 and the “…rst-best" level of output S 0(q

2) =

(1 + ):Under asymmetric information we can optimize the expected social welfare expressed

by (3.1) subject to incentive and participation constraints. Because the single crossingproperty is satis…ed10, it will be enough to consider only upward incentive constraintsand the ine¢cient type’s individual rationality constraint both under full and partialasymmetric information. The incentive constraints are respectively:

U 0 U 0 + q 0; (3.2)

10 If we denote V (t;q;) = t q the agent’s utility function, the single crossing property (Mirrlees(1971)) says that @

@[@V=@q=@V=@t] has a constant sign. It is clearly satis…ed here. This condition ensures

that local incentive constraints imply global incentive constraints.



3.4. SINGLE NON BENEVOLENT POLITICIAN 53

3.4 Single Non Benevolent Politician

In this section, we assume that the politician is non benevolent. Unless he is motivatedotherwise by the Constitution, the politician colludes with the …rm as follows. Whenthe politician obtains hard information about the …rm’s type corresponding to either onei = ; i 2 f1; 2g, or both 1 = 2 = , he makes a take-it-or-leave-it o¤er to the…rm. In this o¤er, he asks for the minimal bene…t which is consistent with his informationand which will be o¤ered to the …rm if the politician does not reveal his signal to theConstitution. This demand is always satis…ed whatever the …rm’s personal characteristics.

Collusion-proofness13 is achieved if the principal rewards the politician with a sched-ule of payments contingent on the messages reported about 1 and 2; s(r1; r2); whichis symmetric in (r1; r2) and prevents the politician from preferring bribes to honest be-

havior. We denote thereafter s2, s1 and s0 the politician’s reward when he has reportedrespectively two, one and no piece of favorable information. From the discussion above,these rewards must satisfy the following collusion-proofness conditions :

s2 s1 kU 1 (3.9)

s2 s0 kU 0 (3.10)

s1 s0 k min

U 0 U 1; U 0

: (3.11)

Constraint (3.9) says that a fully informed politician prefers to report both signals

rather than concealing one of them and extracting only part of an e¢cient …rm’s informa-tion rent. Constraint (3.10) says that the politician prefers to report both signals ratherthan hiding both and extracting the whole rent of an e¢cient agent. When the politi-cian has observed only one signal, collusion is avoided by giving him the bene…t he canextract with probability one in any collusive o¤er. Then, he does not know whether theunobserved piece of information yields some rent to an e¢cient agent or if it yields norent to an intermediate agent . He would ask for U 0 U 1 in the …rst case and for U 0 inthe second. Hence, constraint (3.11) must be satis…ed.

Moreover, the Constitution does not need to compensate the politician for a pair of uninformative signals (1 = ;; 2 = ;), hence s0 = 0. The expected social cost of the

politician’s rewards is then :

2 2s2 + 2 (1 )s1

:

Therefore, the Constitution’s objective function with a non benevolent politician becomes :

(1 )2W 0(q 0; q 0) + 2 (1 )W 1(q 1) + 2 2W 2

2 2s2 + 2 (1 )s1

:

The Constitution maximizes this objective function under the incentive constraints (3.2),(3.3) and (3.4) (taking into account that U 0 = U 1 = 0) and the collusion-proofnessconstraints (3.9) to (3.11). If we assume momentarily that (3.7) and (3.8) hold, we can

write (3.11) as s1 kU 0.13 There is no loss of generality in restricting the analysis to collusion-proof mechanisms. The collusion-

proofness principle holds in this context. See Chapter 2.




Both (3.10) and (3.11) are binding at the optimum of the Constitution’s programsince it must minimize the costs of implementing a collusion-proof allocation. Then, (3.7)

ensures that (3.9) is slack. Indeed, when (3.10) is binding, the politician is prevented fromreporting (1 = ;; 2 = ;) instead of (1 = ; 2 = ). He has no incentives to concealonly part of his information and to reveal only one of the signals he has learned. Notethat, since only (3.10) and (3.11) are binding, U 1 is irrelevant for collusion purpose andno distortion of q 1 away from the second-best level will be necessary in the constitutionalresponse.

Using the binding collusion-proofness constraints, we can rewrite the Constitution’sobjective function as:

(1 )2W 0(q 0; q 0) + 2 (1 )W 1(q 1) + 2 2W 2 k

2 2U 0 + 2 (1 )U 0

:

Optimizing, we …nd:

The optimal Constitution with a single non benevolent politician entails:

Under full asymmetry of information, a schedule of outputs q I 0

= q 2; q I 0 ; and q I 0

such that outputs are always lower than with a benevolent politician q AI 0 > q I 0 and

q AI 0 > q I 0 : More precisely, we have

S 0(q I 0) = (1 + ) +

P 0()

P 0()+

k 2 2

(1 )2P 0()

! (3.12)

S 0(q I 0) = (1 + ) +

P 0() + P 0()

P 0()+

k (2 )

(1 )2P 0()

!: (3.13)

This schedule of outputs is strictly decreasing when14 4 (5 + (1 2 )) 0.

Outputs under the milder asymmetry of information take the same values as for abenevolent politician q I

1= q AI

1and q I 1 = q AI

1 :

The Constitution’s response to the threat of collusion is on the one hand to giveincentives to the politician to induce him to reveal information and on the other hand

to reduce the stakes of collusion in states (1 = ; 2 = ;), (1 = ;; 2 = ) and(1 = ; 2 = ). For this purpose, the rents U 0 and U 0 must be decreased. Since(3.2) and (3.3) hold as equalities at the optimum, a decrease in q 0 helps to reduce collusionin state (1 = ; 2 = ). A decrease in q 0 helps instead to reduce collusion in all thosestates. Instead, since U 1 does not enter in any binding collusion-proofness constraint, thereis no reason to distort q 1 which keeps the same value as with a benevolent politician.

So far, we have assumed that conditions (3.7) and (3.8) which both hold for the optimalcontract with a benevolent politician are also satis…ed with a non benevolent politician. Itremains to check that these conditions are also satis…ed by the solutions described aboveto validate our analysis of the collusion-proofness binding constraints. In Appendix 3.1,

we prove that these conditions hold when (1 )2 > k , i.e., when is small enough.15

14 If it is not the case, one must consider an allocation with bunching.15 The particular assumptions on the probabilities of the di¤erent states of nature we make, in particular



3.5. SEPARATION OF POLITICIANS 55

3.5 Separation of Politicians

3.5.1 Collusion-Proofness ConstraintsThe separation of politicians alters the structures of information and therefore the op-portunities for collusion. Each politician is now endowed with only one informationaltechnology and therefore monitors only one signal.

In particular, in state , both politicians may observe a favorable signal. However,none of them knows what the other has observed. For example, one politician, say P 1, isunable to distinguish between state (1 = ; 2 = ;) and state (1 = ; 2 = ).

We look for a Bayesian-Nash equilibrium of the collusion game in which both politi-cians are prevented from colluding. When P 1 has observed a signal three cases are possible.With probability , P 2 has observed a favorable signal and the …rm is ; P 1 can ask forthe gain obtained by the …rm if he does not reveal his information, i.e., U 1. With proba-bility (1 ), P 2 has observed nothing and the …rm is ; P 1 can ask for the gain U 0 U 1that the …rm can obtain when P 1’s piece of information is not revealed. With probability1 , P 2 has observed nothing and the …rm is ; P 1 can ask for the gain U 0. Again, weassume that the politician chooses a prudent o¤er, i.e., the o¤er which is always satis…ed.

Since each politician is unaware of what has been observed and reported by the other tothe Constitution, his behavior in the bribery game is independent of the other politician’sreport as long as he follows a prudent behavior. The bribe that P 1 is asking for is thesame whatever P 2’s information and the rewards s1(; ) and s1(; ;) needed toinduce revelation from a politician informed of 1 are thus the same. As a consequence,

we denote by s1 this reward when only one signal is reported by the politician.There is now a single collusion-proofness constraint required to make this politician,

say P 1, reveal his information:

s1 k min

U 0; U 0 U 1; U 1

(3.14)

Suppose that (3.7) and (3.8) still hold (we will check ex post these conditions). Then,when each politician receives the signal i = , collusion is prevented by giving each of them a reward equal to kU 0 instead of a total payment kU 0 in the case of a single politician.The expected cost of the payments to the politicians needed to prevent collusion is thus

reduced under separation and it becomes :2kU 0:

3.5.2 Optimal Constitution under Separation

Taking into account this expression, we can rewrite the Constitution’s objective function:

(1 )2W 0(q 0; q 0) + 2 (1 )W 1(q 1) + 2 2W 2 2k U 0:

Optimizing yields the following proposition:

about , are only needed to obtain the precise characterization of the optimal mechanism and to assessthe allocative and distributional e¤ects of an organizational choice in the most striking way. Section 3.6.3shows that the main point concerning the superiority of separation does not require any assumption aslong as one insists on a prudent behavior.




Under full asymmetry of information, the optimal Constitution under separationdecreases the distortion of asymmetric information in state and increases it in

state ; q S 0 = q AI 0 > q I 0 and q S 0 < q I 0 < q AI 0 :

More precisely, it entails q S 0

= q 2, q S 0 and q S 0 such that:

S 0(q S 0 ) = (1 + ) + P 0()

P 0(): (3.15)

S 0(q S 0 ) = (1 + ) +

P 0() + P 0()

P 0()+

2k

(1 )2P 0()

!: (3.16)

This schedule of outputs is always strictly decreasing.

Under the milder asymmetry of information, q S 1

and q S 1 have the same values as with

a single politician q S 1 = q I 1 = q AI 1 and q S

1= q I

1= q AI

1:16

The rents asked in the side-contract depend now only on q 0. As a result there is nofurther distortion away from the second-best output of the intermediate agent, so q S 0 = q AI

0

and no distortion when one signal has been observed, q S 1 = q AI 1 . Moreover, since the rent

U 0 is now asked more often, the distortion in state must increase as we can read fromcomparing formulas (3.13) and (3.16). Figure 3.1 illustrates the distortions on the outputlevels with one or two politicians.

pictureFigure 3.1: Output distortions

with one or two politicians

Bureaucratic rules are exacerbated under separation. Each politician receives a singlemission, monitoring only one dimension of the agent’s performance, and follows ratherstringent rules. The amount of discretion left to each politician is captured by the size of the stake U 0. Since, this amount is reduced under separation, the growth in the numberof politicians also comes with the choice of more bureaucratic rules to be followed by each

politician.

3.5.3 Comparative Statics: Rent and Welfare

From Propositions 3.2 and 3.3, it follows that separation decreases the rent of asymmetricinformation in state (since U 0 is an increasing function of q 0). The e¤ect seems apriori ambiguous in state . The distributive consequences of separation are indeed morecomplex. Chapter 2 has shown that an interest group often loses from the institutionalresponse to the threat of capture since the stakes of the relationship are reduced. Here,

16 Again, one can check that conditions (3.7) and (3.8) also apply under separation. Indeed, P 0()

P 0()>

P 1()

P 1()implies q S 0 > q S 1 and therefore that (3.7) holds. Similarly, we have q S 1 = q I 1 > q I 0 > q S 0 where the

…rst inequality comes from (3.8) being satis…ed with a single politician. Hence, (3.8) is satis…ed underseparation also.



3.5. SEPARATION OF POLITICIANS 57

we allow for heterogenous interest groups having di¤erent pieces of private information.Then, the institutional response to the threat of capture a¤ects di¤erently the interest

groups depending on their respective information. Some groups may lose, some may win,but what matters is that globally the principal wins. More precisely, only the e¢cient…rm may win from separation. Hence, everything happens as if the e¢cient …rm has astronger bargaining power in the collusion game with two politicians rather than one. Thee¢cient …rm may be thought to be an intermediate one by both politicians. The gainof the e¢cient one is made at the expense of the intermediate one. In fact, an e¢cient…rm gets a higher rent under separation when the probability is small enough. Indeed,in this case, a rather large distortion of q 0 (one term on the right-hand-side of (3.12) hasa denominator which is (1 )2P 0() = 2 (1 )(1 ) and which becomes relativelysmall when is small), and a rather small distortion of q 0 (one term on the right-hand-

side of (3.13) has a denominator which is (1 )2

P 0() = (1 )2

and which becomesrelatively high when is small), must be introduced to reduce the stake of collusion withone politician. Separation increases more this …rst output level than it reduces the second,resulting in an increase of the overall e¢cient type’s rent.

As separation weakens the collusion-proof constraint in state (1 = ; 2 = )and does not a¤ect the cost of collusion-proofness in other states, expected social welfareobviously increases with separation. We obtain in addition the following proposition.

For small enough whatever S () or for S () quadratic, i.e., S (q ) = jS "jq2

2+

q for some , whatever , the following results of comparative statics hold:

Under full asymmetric information, the rent in state is larger with separation thanwith one politician if and only if 1 (3 2 ). The rent in state is always lowerwith separation.

The welfare gain from separation of politicians SW is positive and of the secondorder in :

SW =(1 + )k 2 22

jS 00j

1 +

1 +

(1 )(3 (1 + 2 ) )

2(1 )2(3.17)

+k

(1 )2

2

(1 + (1 2 ))

4(1 )

:

Proof : See the Appendix 3.2.Since 3(1+2 ) 0 and 2 (1+ (12))

4(1) 1,17 all terms in (3.17) are non negative. As

expected, welfare increases unambiguously because the separation of politicians increasesthe transaction costs of collusion. The following reasoning helps to explain the magnitudeof this di¤erence in expected welfare. For a given pro…le of quantities and therefore of rents, one can envision the objective of the Constitution as an implementation problem : tominimize the social loss associated with politicians’ rewards subject to a set of collusion-

proofness constraints. By relaxing one of these constraints, separation improves social17 This inequality holds for values of such that the no bunching condition given in Proposition 3.2 is

satis…ed.




welfare by a term which is proportional to the gain on this constraint, i.e., U 0 2U 0 if thisdi¤erence is small which is the case for small enough. The next step is to optimize the

pro…le of rents and quantities subject to incentive and participation constraints. When is small enough, one introduces distortions of the quantities which are of the …rstorder in . This makes U 0 2U 0 = (q 0 q 0) …nally be of the second order in .Moreover, by direct inspection, we …nd:

SW is increasing in k, , , and 1jS 00j

.

SW increases with the e¢ciency of the collusive transaction, the cost of public funds,and with the curvature of the Constitution’s objective function. All these parametersincrease the social gain of separation in terms of the politician’s rewards, i.e., k(U 02U 0)

increases. This is obviously the case for k and which directly increase the bene…ts of separation by reducing the burden of collusion borne by taxpayers. But a greater curvatureof the consumer’s utility function also increases the convexity of the rent since it increasesthe di¤erence between q 0 and q 0.

Of particular interest is the dependence of the welfare gain on the e¢ciency of theside-contracting transaction and on the cost of public funds. First, countries with an in-e¢cient taxation system face high values of and are likely to be those which bene…t themost from separation. Second, countries where capture and corruption are easier to beenforced (k close to one) are also likely to bene…t from an e¢cient design of their politicalinstitutions. It is striking that both features above are present in most developing coun-tries. In particular, provided that transaction costs of side-contracting remain unchangedin the political process, our result suggests that the decentralization of regulatory rightsamong di¤erent bodies is particularly attractive in these countries. A good internal de-sign of the government helps all the more that the government is ine¢cient to levy taxesand that corruption is easily enforced. Montinola, Qian and Weingast (1993) o¤er someevidence concerning this issue in the case of the implementation of federalism in China.

Separation of powers appears more desirable in developing countries. However, it islikely to be also more di¢cult to implement there. Low transaction costs of collusion willmake easier for the two regulators to collude.

3.6 Generalization of the Results3.6.1 Prudent Behavior and Various Preferences

As we discussed in Sections 3.3 and 3.4, the outcome of the collusive game between thepoliticians and the …rm depends on the relative ranking of U 0 U 1, U 0 and U 1. Focusingon the case of a linear marginal cost has helped us in ranking these three quantities. It hasalso illustrated why being able to get two pieces of favorable information enables a singlepolitician to obtain more bargaining power vis àvis the …rm than what can be achievedby politicians as a pair under separation.

However, the results have a much greater generality and are robust to any speci…cation

of the ranking of the information rents that could arise even if the production technologiesdo not have constant returns to scale, or if the informational structures were not additiveas we have assumed so far.



3.6. GENERALIZATION OF THE RESULTS 59

We generalize our approach as follows. The …rst step is to compute the minimalrewards s2 needed to get two pieces of information with a single politician. Since the

politician may conceal only one signal even if he has learned both (equation (3.9)), adeviation consisting in hiding only one dimension of the information yields him:

s1 + kU 1 = k

min(U 0 U 1; U 0) + U 1

= k

min(U 0; U 1 + U 0)

:

Since the politician can also hide both signals (equation (3.10)), such a deviation yieldshim kU 0. The binding collusion-proofness conditions (3.9) and (3.10) require therefore too¤er the rewards:

s2 = k

max(min(U 0; U 1 + U 0); U 0)

= kU 0

whatever the ranking of the di¤erent information rents.Therefore, the social cost of implementing a collusion-proof allocation with one polit-

ican is:

C I = k

U 0 + 2(1 )min(U 0; U 0 U 1)

:

Under separation, this cost becomes now (see (3.14)):

C II = k

2 min(U 0; U 0 U 1; U 1) + 2(1 )min(U 0; U 0 U 1; U 1)

:

The comparison of these two costs is immediate. The term obtained when only one signal

has been observed is obviously lower under separation. Moreover, when two signals havebeen observed, separation is also less costly since we always have:

2min(U 0; U 0 U 1; U 1; ) 2min(U 0 U 1; U 1) U 0 U 1 + U 1 = U 0:18

Hence, separation always dominates when the politicians play prudently in making theircollusive o¤ers to the …rm. This shows how the prudent behavior that we requested isthe only ingredient needed to show the bene…t of separation.

However, di¤erently from Sections 3.3 and 3.4, the exact writing of the collusion-proofness constraints may now involve also U 1. The corresponding output q 1 may also

possibly be distorted in both cases. Both the allocative e¢ciency and the distributionof rents are again a¤ected by separation and allocative and distributive consequences of separation could be derived as we did in Section 3.4. In particular, social welfare increaseswith separation and the new distribution of rents may favor some groups against others.

3.6.2 Discriminatory Side-Contracting O¤ers

As we have argued above, the assumption of prudent behavior is quite appealing in thecontext of side-contracting. We consider now the case where politicians can make side-contract o¤ers that the …rm may reject with positive probability. To make comparisons

with the case of prudent o¤ers that we have analyzed in Sections 3.3 and 3.4, we assumealso that U 0 U 1 > U 1 > U 0.

18 The last inequality is strict when U 0 U 1 6= U 1 and holds generically.




A single politician who is only already aware of one dimension of the …rm’s type asksfor a bribe U 0 U 1 instead of a prudent one U 0 when the expected pro…t of doing so is

greater, i.e., when: (1 )(U 0 U 1) > (1 )U 0:

Under separation, each politician asks for a bribe U 0 U 1 instead of a prudent oneU 0 or an intermediary one U 1 when:

(1 )(U 0 U 1) > maxfU 1; U 0g:

Both inequalities above hold in particular when is close to zero and close to 1.The cost of implementing collusion-proofness with a single politician is then:

C I = k( 2 2U 0 + 2 2 (1 )(U 0 U 1)):

Similarly, the cost of implementing collusion-proofness with two politicians is now:

C II = k(2 2 2(U 0 U 1) + 2 2 (1 )(U 0 U 1)):

C II > C I since U 0 > 2U 1. The sum of the collusion-proof rewards needed to preventcollusion in state (1 = ; 2 = ) under separation is larger than what is needed toprevent collusion from a single politician. With discriminatory o¤ers, each politician isready to run the risk of having his side-contract o¤er being sometimes refused against

the high payo¤ that he may get when this o¤er is accepted. The optimal contract un-der separation has to prevent deviations which are mutually inconsistent since a singlepolitician would never ask for a total bribe which would exceed the …rm’s rent in state(1 = ; 2 = ), i.e., U 0.

3.6.3 Collusion Between the Politicians

We now investigate the possibility that the politicians may collude. We assume again thattransfers between them are not feasible but we allow them to report to each other thehard information signal they may have obtained on the …rm’s type. Then, a three partybargaining takes place with the …rm. Because politicians who share the same informationshould have an equal bargaining power, each of them gets half of the minimal …rm’sinformation rent consistent with their pooled information.

Collusive strategies in the politicians’ game are as follows: before getting his signal,each politician credibly commits to share or not information with the other. We will lookat the Nash equilibrium of this game. By both sharing, each politician gets:

V SS = 2 2U 02

+ (1 )U 0:

When politician 1 shares information but politician 2 does not, politician 1 always asksfor 1

2U 0

and his payo¤ is:

V SN = 2 2U 02

+ (1 )U 02

:



3.7. CONCLUSION 61

When politician 1 does not share information but politician 2 does, politician 1 asks for

U 0 U 1 when he knows for sure that the …rm is . He asks instead for U 02

when only

politician 2 has observed a signal and for U 0 when he is the only one to have observed asignal. His payo¤ becomes:

V NS = 2 2(U 0 U 1) + (1 )3U 0

2:

Lastly, when both politicians refuse to share information, each of them gets:

V NN = 2 2U 0 + (1 )U 0:

It is straighforward to check that not sharing is a dominant strategy of this game when

(3.7) and (3.8) are satis…ed. Indeed, V NN > V SN and V NS > V SS . Hence politicians arecaught in a prisoner’s dilemma and refuse to share information which would have beenbene…cial to transfer to improve side-contracting.19

3.7 Conclusion

The separation of power among politicians may be an optimal governmental responseto the threat of regulatory capture. Separation reduces the non benevolent politicians’discretion, and the sum of their gains from collusion may be lower than if the politicians

were cooperating. Under asymmetric information, the supply of possible bribes alwaysstrictly exceeds the total demand of the politicians when their collusive o¤ers are satis…edwhatever the …rm’s personal characteristics. This result is robust to changes in the reg-ulated …rm’s preferences and the timing of the collusion game. It shows how importantit is to have structural foundations for the collusive activities, since the organization of government a¤ects those activities. Shleifer and Vishny (1993) propose a positive theoryof the government organization, and argue that complementary permits should be o¤eredby the same agency. The reason is that an agency does not take into account the demandfor bribes of other regulatory bodies when it makes its own bribe proposal. A standardmodel of oligopoly competition is used to show that an equilibrium with excessive briberytakes place under separation. The di¤erence with our normative approach is twofold.First, because information plays no role in the Shleifer and Vishny (1993) analysis, it ishard to see why bribes are in fact o¤ered in the …rst place: the supply side of the mar-ket for bribes is exogenous. Here, the foundations of corruption are explicit. Second, inour model, competition between competing agencies is optimally organized by the Con-stitution itself and not an exogenous starting point. We can take into account how theorganizational response a¤ects the cost of the threat of corruption.

We have also assumed that the transaction costs of side-contracts were the same withone or two regulators. In fact, these transaction costs are lacking theoretical foundationsin the current literature20. They may depend on several factors including the frequency of the relationship between the politician and the …rm, the importance of their future gains

19 However, as we suggested already in Section 5, more research on the di¢culties of implementingseparation of powers is required.

20 See Part III for a way of endogeneizing these transaction costs.




of cooperation, their information on each other, the level of trust that has been developedbetween them. All these quantities are likely to di¤er when one considers separation and

consequently transaction costs may change. Neven et alii (1993) have suggested that thetransaction costs of collusion decrease when politicians have more specialized tasks. Inthe same vein, we have assumed so far that the collusion technology has constant marginalreturns. For obvious psychological reasons a politician may not like to engage in collusiveactivities without being promised a high enough return. Clearly, those increasing returntechnologies favor also the choice of separation.

The basic message of this chapter is that monopoly in information acquisition maybe a curse for the government when collusion is a concern. Information per se introducesincreasing returns in the bene…ts of side-contracts. The argument is robust to a broad setof assumptions, both on the rankings of rents and on the timing of the side-contracting

game. Therefore, it might be considered as a general principle in governmental design.The framers of the Constitution may decide to divide powers between various politiciansand administrators to limit the social costs of side-contracting. However, implementingthis separation of powers may prove to be di¢cult.




B is the gain of separation in terms of politician’s wage. It is a positive number (sinceq S 0 > q S 0 ) and of the second order in . After computations, we …nd :

A = 3 4k222(1 + (1 2 ) )

4S 00(1 )2(1 ) 0:

B = 2 2k(1 + )2

jS 00j

1 +

1 + (1 )

(2 (1 + ))

(1 )2

2(1 )

!

+

1 +

2k

(1 )2

:

Adding A and B yields formula (3.18).

Moreover, those Taylor expansions are exact in the case of a quadratic utility functionS (q ) = jS "jq2

2+ q . is large enough to ensure that outputs are positive.



Chapter 4

Checks and Balances

“A little attention to the subject will convince us, that these three powersought to be in di¤erent hands, and independent of one another, and so bal-lanced, and each having that check upon the other, that their independenceshall be preserved.”

Essex Result of 1778 in Handlin and Handlin (1996).1

4.1 Introduction

In Chapter 2 and 3 we have studied the supervisory role of governmental bodies or politi-cians with respect to regulated sectors of the economy. Chapter 3 has provided somefoundations for the separation of this supervision function between several bodies. In-deed, we see that governments are organized with several ministeries, that the Consti-tution sets up executive, legislative and judiciary branches. In this chapter, we studythe design of reciprocal supervision between governmental bodies of the same hiearchicallevel, very much like the two politicians of Chapter 3. It is a way to explore the model of checks-and-balances launched by James Madison in The Federalist Papers in 1787.

First we will study how the constitutional level which has two politicians to run twosectors can design reciprocal supervision between politicians. We assume that each politi-

cian is also a supervisor of the other politician and study how the Constitution can detercollusion between politicians. We will argue that such a design creates opportunities forreciprocal favors between politicians which are very costly for the Constitution and whichmay justify the limitation of these horizontal supervision activities either in the form of relatively ine¢cient supervision technologies or in the form of asymmetric supervision.We will also investigate under which circumstances it may be better to let politicianscollude.

Reciprocal favors have been documented mainly in the organization literature but arehighly relevant for analysing governments. When the manager of a …rm cannot monitordirectly his employees, he must use a supervisor or foreman. Among the several functions

1 As emphasized by Casper (1997) the Essex Result considerably complicated the debate over separa-tion of powers by invoking the notion of checks and balances. The Essex Result was a critique by thetowns of Essex Country of the 1778 draft of the Constitution of Massachusetts which was rejected.

65



66 CHAPTER 4. CHECKS AND BALANCES

of a supervisor stands his role as bridging partially the informational gap between themanager and his employees. In a code of ethics for a foreman Deb (1963) notes:

“the foreman must control cost in his shop... the foreman will not take recourseto passive supervision by mainly avoiding disputes or di¤erences with his menor dodging troubles; will not attempt to attain cheap popularity with workersat the cost of duties”.

An interpretation of this code of conduct is that the foreman must achieve low costif indeed the technology is a low cost technology, even when the manager does not knowit. In so doing he will hurt the employees who will see their e¤ort level increased or theirinformation rent decreased. Hence, the second rule saying that he should not collude withthe workers.

Also, Dalton (1959) mentions in his discussion of the relationships between foremenand workmen (the line) :

“toleration of minor rule-breaking by the line in exchange for aid from the linein crises” p. 104.

Actually, this chapter was motivated by the observed practice in some Universities of an exchange of favors between a chairman of a department who tolerates that professors donot ful…ll their service obligations (such as the number of hours they teach) in exchangeof the favor of not reporting that the chairman himself is not accomplishing all of hisduties. But, such exchanges of favors are very common both in the administration andin …rms. Also we know the dangers of using teacher evaluations by students as inputs incompensation of professors which may induce demagogical behavior.

The peer monitoring literature has emphasized the virtues of reciprocal monitoring toalleviate limited liability constraints (see Banerjee, Besley and Guinnane (1992), Besleyand Coate (1995), Stiglitz (1990), La¤ont and N’Guessan (1999)). Similarly the literatureon teams (Holmstr and Milgrom (1989), Itoh (1993)) has claimed the bene…ts of collusionof agents when it is based on superior information. Here, we are stressing some dangersof peer supervision.

The separation of powers advocated by Locke and Montesquieu is only one aspect of the organization of governments, …rms or regulatory bodies. It can be rationalized eitheras an instrument of information extraction through yardstick competition (see Neven,

Nuttall and Seabright (1993), Chapter 3) or an instrument to discourage rentseeking andcorruption (Congleton (1984), Chapter 3) or to improve the accountability of electedo¢cials (Persson, Roland and Tabellini (1997)). Even Locke and Montesquieu2 had inmind a more complex design by giving the executive a share in legislative power and byacknowledging the judicial role of the House of Lords. Similarly, when the US Constitutionwas drafted, as emphasized by Kramnick (1987) in his introduction to the FederalistPapers:

2 “Mais, si dans un Etat libre, la puissance l islative ne doit pas avoir le droit d’arr er la puissanceex utrice, elle a droit, et doit avoir la facultéd’examiner de quelle mani e les lois qu’elle a faites ont

éex ut s. . . ”

“Quoiqu’en g al la puissance de juger ne doive re unie à aucune partie de la l islative, cela estsujet àtrois exceptions. . . ”

“La puissance ex utrice doit prendre part àla l islation par sa facultéd’emp her”, Montesquieu (1748),p. 589.



4.2. THE MODEL 67

“the Anti-federalists still have a valid point in insisting that the Constitutioncreated was much more a mixed government of shared powers, much more a

government of checks and balances, than a separation of powers”, p. 53.

“The President was given legislative power by the Constitution through hisveto power”, p. 50.

“the state judiciary came to be regarded by Federalists not only as needingseparation and independence, but also as a potential check on the social forcesdominating the state legislature”, p. 49.

and, through section II article 4, the Senate was given a control of the President bythe impeachment procedure. Furthermore, the American Constitution requires Senateapproval in the appointment of Supreme Court judges and a few other key federal o¢ces

as well as rati…cation of foreign treaties, congressional approval of a declaration of warand judicial review of federal legislation and administrative acts.

Taking as given the separation of powers or tasks, we analyze in this chapter thedesign of checks or controls that the framer of the Constitution might want to set up asa complement to the incentive schemes imposed on each power.

Section 4.2 sets up a model in which two politicians supervise each other. The optimalsymmetric Constitution is characterized in Section 4.3. An asymmetric Constitution isstudied in Section 4.4 where it is shown when it can dominate the optimal symmetric one.Another kind of manipulation of information is considered in Section 4.5 which exploitsthe design of Section 4.3. Then, it is shown that letting collusion happen is sometimes

an optimal strategy. Section 4.6 extends the analysis to the case of three politicians andSection 4.7 compares various systems of checks and balances. Section 4.8 concludes.

4.2 The Model

We slightly extend the model of Chapter 2 to include two activities, each one controlledby a politician. Politician 1 runs the production of public good 1 with a cost function

C 1 = 1q 1

where q 1 is the production level and 1 in f;g is a productivity parameter, privateinformation of politician 1. Let = Pr(1 = ). Politician 1’s utility level is:

U 1 = t1 1q 1

with a utility level for the rest of society

S (q 1) (1 + )t1:

Similarly, politician 2 has a cost function

C 2 = 2q 2

with 2 in f; g, = Pr(2 = ),

U 2 = t2 2q 2;




S (q 2) (1 + )t2:

The random variables 1 and 2 are independent. Social welfare is:

W = S (q 1) + S (q 2) (1 + )(t1 + t2) + U 1 + U 2

= S (q 1) + S (q 2) (1 + )(1q 1 + 2q 2) (U 1 + U 2):

To simplify the analysis of reciprocal supervision we have integrated vertically eachpolitician with the sector he supervises. There is no asymmetry of information left betweenthe politician and the …rm he controls. The results of this chapter could be easily extendedto a more general set up by bringing together Chapters 3 and 4.

The complete information benchmarks are de…ned by

S 0(q 1) = (1 + )1; t1 = 1q 1;S 0(q 2) = (1 + )2; t2 = 2q 2:

Each politician i will behave strategically with respect to his private information i, asthe …rm in Chapter 2. In addition, politician 1 exerts a costless supervision of politician 2which is modeled as follows: Politician 1 observes a signal 1 about politician 2’s e¢ciency2. The supervision technology is, as in Chapter 2, such that

1 = with probability if 2 = ;= otherwise:

When 1 = , politician 2 is aware of it. Symmetrically politician 2 observes 2 2f; g about 1. The timing of contracting is as follows:

1

Constitutionselects

politicians

and o¤erscontracts

2 3 4 5

Politicians Politicians Politicians Contractslearn their report their announce are

type i signal their type executedand their

signali

if necessary

When collusion between politicians happens, it takes place between time 2 and 3. Allpoliticians are ex ante identical and are selected randomly by the Constitution.3 We alsoassume that politicians are in…nitely risk averse at the zero pro…t level so that ex postindividual rationality constraints must be satis…ed.

Consider as a second benchmark the case where politicians behave strategically with

respect to their private information concerning their sector, but perform benevolentlytheir supervisory function about the other politician.

3 “Le su¤rage par le sort est de la nature de la d ocratie”, Montesquieu (1748), p. 533.



4.3. OPTIMAL SYMMETRIC CONSTITUTION 69

Consider politician 1 for example. Two cases are possible. Either the Constitution isinformed about 1 (by politician 2). In this case which happens with probability the

complete information allocation is achieved

S 0(q ) = (1 + ); t1 = q :

Or the Constitution remains uninformed but has new beliefs following the signal 2 = which are characterized by

=(1 )

1 < :

The control problems concerning the two politicians are separable. For politician 1,with the signal 2 = , the optimal contract is characterized as in Chapter 2 with newbeliefs . We obtain:

S 0(q ) = (1 + )

S 0(q ) = (1 + ) +(1 )

1

U 1 = (1 ) q U 1 = 0:

The situation for politician 2 is similar.Let us denote W = S (q )(1+)q the complete information welfare for an e¢cient

type; and

W AI = S (q ) (1 + )q q + (1 ) S (q ) (1 + ) q the expected social welfare with beliefs . The global expected welfare is then:

2W + 2(1 )W AI

4.3 Optimal Symmetric Constitution

Suppose now that politician i can be captured by politician j in his supervisory task, asthe politician could be captured by the …rm in Chapter 2. Consider for example politician

1 who has observed 1 = . If he sends the (veri…able) report r1 = to the Constitution,the complete information allocation with no rent for politician 2 is achieved. He caninstead hide his signal to the bene…t of politician 2. And similarly for politician 2’ssupervisory activity. The incentive constraints of the politician concerning his messageabout himself and about the other politician are separable. (See Appendix A.4.1)

Invoking the collusion proofness principle we can specify the collusion-proof constraintsin the various states of nature. Consider …rst the two symmetric states of nature f1 =; 2 = g and f1 = ; 2 = g. Let s2 (resp. s1) the reward to politician 2 (resp.1) from the Constitution when the politician 2 (resp. 1) makes the report r2 = (resp.r1 = ) and the politician 1 (resp. 2) makes the report r1 = (resp. r2 = ).

Collusion-proofness requires:

s1 k q 2

s2 k q 1




with an expected cost for symmetric solutions

2 (1 )kq:

The most interesting case occurs in the state of nature f1 = ; 2 = g. Then,the two politicians can exchange the favors of not reporting their true signal. We arguethat this type of collusion is easier than the previous (asymmetric) ones which requireda transfer between the politicians which is potentially dangerous. Here it is enough thatthe two politicians exchange phone calls to implement their collusion.

More precisely, we make a non linearity assumption in the transaction costs of sidetransfers by postulating a discount factor k0 larger than k in the case of reciprocal favors.Let s

1and s

2the rewards to politician 1 and 2 for the reports fr1 = ; r2 = g. Collusion-

proofness requiress1

+ s2

k0(q 1 + q 2)

i.e., an additional expected cost for the Constitution at a symmetric solution:

2( )2k0q:

The Constitution must select optimal contracts taking into account these supervisioncosts and the usual incentive and individual rationality constraints. Solving these con-straints as usual and inserting into the social welfare we can decompose the Constitution’sobjective function into six di¤erent states.

With probability (1 )2, both politicians are ine¢cient. No rent and no supervision

payment need to be given up, hence a contribution to the objective function

2(1 )2

S (q ) (1 + )q

:

With probability (1 ) (1 ) one politician is ine¢cient and the other is e¢cientbut not identi…ed as such. A rent q must be given up to the e¢cient politician, hencea contribution (since there are two such cases)

2(1 ) (1 )

S (q ) (1 + )q + S (q ) (1 + )q q

:

With probability (1 ) a politician is ine¢cient; the other one is e¢cient and

identi…ed as such by the supervisor. A supervisory payment k q must be paid hence acontribution (there are two such cases)

2(1 )

S (q ) (1 + )q + S (q ) (1 + )q kq

:

With probability 2 2 both politicians are e¢cient and they have been identi…ed. Thehigh supervisory payments needed to avoid reciprocal favors must be paid, hence:

2 2 2

S (q ) q k0 q

:

With probability 2(1 )2 both politicians are e¢cient and have not been identi…edas such. Information rents must be given up, hence:

2 2(1 )2

S (q ) q q

:




Proposition 4.1.a is in line with our former results. The optimal constitutional responseto collusion is the creation of incentives for politicians and a reduction in the stake of col-

lusion. Proposition 4.1.b is more novel. It shows that the control of communication —herein the form of supervision— is an essential part of the design of governments and organi-zations. It must be arranged in a way which minimizes the ful…lment of collusion-proof constraints and this can take the form of restricting communication between politicians.

To obtain the optimal Constitution we have made the incentive payments for super-vision functions of both politicians’ messages. Suppose that the reward to a politician isonly allowed to be a function of his own message. Collusion proofness now requires:

s1 + s2 k0(q 1 + q 2)

s1 kq 2

s2 kq 1

i.e., imposes for a symmetric solution the cost2 (1 ) + 2 2 (1 ) + 2 2 2

k0q

in addition to the expected cost of rents2 (1 )(1 ) + 2 2(1 )2 + 2 2 (1 )

q:

Suppose instead that the Constitution gives up preventing collusion in state f1 =

; 2 = g. Collusion is prevented in the other cases with expected incentive payments of only:

[2 (1 ) + 2 2(1 ) ]kq;

but an expected cost of rents:2 (1 )(1 ) + 2 2 2 + 2 2(1 )2 + 2 2 (1 )

q:

Comparing expected costs we see immediately that it is better to let collusion happenif and only if

<

k0 k

1 k :

Such a condition can hold only if there is a non linearity in transaction costs, i.e.,k0 > k. Full collusion-proofness is more desirable if the quality of auditing ( ) and theprobability of an e¢cient type ( ) are high enough. The cost of collusion-proofness in thecase of reciprocal favors is then particularly high. We obtain:

If the reward of each politician supervisory activity can only depend on hisown report, it is better to let collusion happen in the state of nature f1 =; 2 = g if < (k0 k)=(1 k).

Contractual incompleteness makes collusion a second best response. If the rewardswere provided through private bene…ts generated by successful elections and if politicianswere running in di¤erent elections we would be in such a case.



4.4. SUPERVISION AND DIVISION OF TASKS 73

4.4 Supervision and Division of Tasks

So far we have restricted the analysis to symmetric supervisory structures which give riseto the possibility of exchanges of favors. A natural idea is to break this opportunity bysuppressing (for example) the messages that politician 2 might send to the Constitutionabout politician 1’s e¢ciency. This can be achieved by providing politician 2 with anine¢cient supervision technology or by committing not to listen to politician 2’s reportabout politician 1.

The Constitution’s objective function can now be written:

W II = (1 )2[S (q 1) (1 + )q 1 + S (q 2) (1 + )q 2]

+ (1 ) (1 )[S (q 1) (1 + ) q 1 + S (q 2) (1 + )q

2 q 2]

+ (1 ) [S (q 1) (1 + ) q 1 + S (q ) (1 + )q k q 2]

+ (1 )[S (q 1) (1 + )q

1 q 1 + S (q 2) (1 + )q 2]

+ 2(1 )[S (q 1) (1 + )q

1 q 1 + S (q

2) (1 + )q

2 q 2]

+ 2 [S (q 1) (1 + )q

1 q 1 kq 2 + S (q ) (1 + )q ]:

Optimizing we obtain:

S 0(q 1) = S 0(q

2) = (1 + )

S 0

(q 1) = (1 + ) +

1

S 0(q 2) = (1 + ) +

1 (1 (1 k) ):

More production is required from politician 2 because he can protect his rent less oftenthan politician 1. To show simply the possible superiority of asymmetric regulation oversymmetric regulation, we restrict the possibilities in the asymmetric case by imposingequality of production levels. Then it is easy to compute the di¤erence of objectivefunctions which is such that:

=

W II W I

q = (1 k) + 2 2

2

(k0

k):

The additional cost of asymmetric supervision is that with probability (1 ) therent of politician 1, q , is given up instead of the lower supervision payment kq , sinceno message is sent now by politician 2. The (possible) gain from asymmetric regulationis that, with probability 2 2, a supervision payment k q and a rent q to politician2 are paid instead of the more costly supervision payments 2k0q . Hence we have:

If

1

2

1 k

k0 kit is optimal to create a partial division of tasks by assigning the supervisoryactivity to a single politician.




Note that such a dominance requires the non linearity of transaction costs (k < k0)and that the condition for the superiority of asymmetric control can be interpreted as a

minimal quality of supervision (in particular > 12 if k0 = 1).A more complete comparison calls for optimizing simultaneously supervision tech-

nologies and structural control. For each type of Constitution, we optimize the (costless)supervision technologies. For < 1=2, it is optimal in both cases to have the best technol-ogy ( = 1) and, as above, a complete comparison would require computing the optimal(di¤erent) production levels in the asymmetric case. However, for > 1=2 and k0 = 1, theoptimal supervision technology corresponds to = 1

2 in the case of symmetric supervision

and = 1 in the case of asymmetric control. Then, we obtain:

If

> 12

and k0 = 1;

asymmetric control with the optimal supervision technology ( = 1) alwaysdominates symmetric supervision with the optimal supervision technology( = 1

2 ).

Proof: Constrain production levels to be equal in the asymmetric case for k0 = 1 andspecialize welfare for the relevant supervision technology. Then

W I =1

2 W II ( = 1) = 1

2 (1 k) q < 0:

4.5 Multidimensional Collusion Activities

So far we have implicitely assumed that an e¢cient politician, when undetected by theother politician was unable to provide to the other politician a veri…able proof of hise¢ciency. Then, collusion-proofness is desirable as proved along the lines of Chapter 2.Suppose now that each politician, when e¢cient, has a veri…able proof of his type that of

course he can hide from the Constitution.This opens a new dimension of collusion which is not independent of the way the

Constitution structures transfers to elicit supervisory messages. Because of the low trans-action costs of reciprocal favors in the state (1 = ; 2 = ), the Constitution mustprovide, to avoid collusion, higher transfers in this state than in the other states. Thisinstrument to deter collusion triggers another type of collusion by creating an incentive,for an e¢cient politician who has identi…ed the other politician as e¢cient but has nothimself been identi…ed, to identify himself to the other politician by showing his veri…ableproof of e¢ciency.4 Then, they can both transmit the informative signals r1 = ; r2 = and bene…t from the high transfers s.

4 We assume that a politician can provide information about his own type which enables the otherpolitician to obtain a veri…able proof of his true type, but that the constitutional level would not be ableto do so.



4.5. MULTIDIMENSIONAL COLLUSION ACTIVITIES 75

Suppose that this illicit identi…cation strategy can sometimes be detected and punishedby the Constitution. The gain for the colluding partners is then only

2k 0q with < 1

when they follow this strategy and therefore the expected cost for the Constitution is thenonly (there are two such cases)

2 2 (1 )2k 0 q:

The Constitution’s program can now be written:

maxfq;qg W

II I

2(1 )

2

(S (q ) (1 + ) q )

+ 2(1 ) (1 )

S (q ) (1 + )q + S (q ) (1 + )q q

+ 2(1 )

S (q ) (1 + )q + S (q ) (1 + )q kq

+ 2 2 2

S (q ) (1 + )q k0q

+ 2 2(1 )2

S (q ) (1 + )q q

+ 2 2 (1 )

S (q ) (1 + )q 2k 0q + S (q ) (1 + )q

with a solution:

S 0(q ) = (1 + )

S 0(q ) = (1 + ) +

1

h1 (1 )(1 k) 2 (1 ) (1 k 0)

2 (1 k0)i

: (4.3)

Note that such a communication pattern between politicians occurs only if they gainfrom the lower costs of collusion (k0 > k) despite the risk of penalty if identi…cation isobserved by the Constitution. This happens if and only if

1 + k < 2k 0 (4.4)

which is also the condition under which the distortion in (4.3) in larger than in (4.2).The reason for this greater distortion is that the Constitution must …ght this additionaldimension of collusion.

We will now assume that if the Constitution allow collusion in the state f1 = ; 2 =g, it alters the transaction costs of using the identi…cation strategy. The probability of being detected when the illicit identi…cation occurs is higher, inducing a transaction cost 0 which discourages this activity5, i.e.,

2 0

k0

< 1 + k < 2k0

: (4.5)5 This can be justi…ed by the fact that the required policing of collusion is more limited and more

attention can be focused on the illegal identi…cation.




Allowing collusion in the state f1 = ; 2 = g is more costly for the Constitutionsince a rent q is given up for each politician instead of a supervisory payment k0q .

However, by deterring the other dimension of collusion it can improve upon the collusion-proof contract.

When collusion is allowed, the Constitution’s program is:

maxfq;qg

W IV =

2(1 )2(S (q ) (1 + )q )

+ 2(1 ) (1 )

S (q ) (1 + )q + S (q ) (1 + )q q

+ 2(1 )

S (q ) (1 + )q + S (q ) (1 + )q kq

+ 2 2( 2 + (1 )2)

S (q ) (1 + )q q

+ 2 2 (1 ) S (q ) (1 + )q kq q + S (q ) (1 + )q yielding

S 0(q ) = (1 + )

S 0(q ) = (1 + ) +

1 (1 (1 )(1 k)) q:

Comparing W II I and W IV we obtain:

If transaction costs are such that (4.4) and (4.5) hold, then letting collusionhappen dominates symmetric control in a neighborhood of = 0, for smallenough or k0 close enough to one.

Proof: Using the envelop theorem note …rst that

d

d (W IV W II I )

=0

= 0

since the welfare levels di¤er only by terms in 2. To compare the second derivatives at = 0, it is enough to look at the partial second derivatives since

@ 2

@ @ q (W IV W II I )

=0

= 0

:

Then

@ 2

@ 2(W IV W II I ) = 4 q [ (1 k0) + (1 )(2k 0 1 k)] :

Under (4.4), 2k 0 1 k > 0. So for small enough or k0 close enough to one,

@ 2

@ 2

(W IV W II I ) > 0;

hence the superiority of collusion over symmetric control in a neighborhood of = 0.



4.6. A MODEL WITH THREE POLITICIANS 77

When there are multiple collusive activities and when there are externalities betweenthe transaction costs of preventing these various activities, it may happen, as above,

that allowing collusion in one activity decreases so much the cost of preventing the othercollusive activity that it dominates full collusion-proof mechanisms. It occurs when thereare negative externalities in the costs of controlling various collusive activities.

With the additional collusion activity, social welfare di¤ers from W I only with prob-ability 2 2 (1 ): For the same production level of the ine¢cient type

W I W II I = 2 2 (1 )[2k 0 (1 + k)] q:

Symmetric control with both types of collusion is dominated by asymmetric control if and only if

(1 k) + 2 2 2(k0 k) + 2 2(1 ) (2k 0 (1 + k)) > 0

or

>1 k

2 [ (k0 k) + (1 )(2k 0 1 k)]: (4.6)

We obtain

If 0 is such that (4.5) fails and therefore collusion is dominated by symmetriccontrol and if (4.6) holds, it is optimal to create a division of tasks by assigningthe supervisory authority to a single politician.

Finally, note that there is a range of parameters for which allowing collusion in thestate f1 = ; 2 = g is the best policy. For small enough, collusion dominatessymmetric control from Proposition 4.5 and furthermore

d

d [W II W IV ] =0 =

1 k

k q < 0:

This is due to the fact that collusion avoids the transmission of information betweenpoliticians as asymmetric control does but at a negligible cost of the order of 2 for small, instead of a cost of the order of for asymmetric control.

4.6 A Model with Three Politicians

We consider the straightforward extension of the model to the case of three politicians topursue the analysis of checks and balances. The third politician controls the productionof public good 3 with a cost function

C 3 = 3q 3

where q 3 is the production level and 3 in f; g is a productivity parameter, privateinformation of politician 3. Again, let = Pr(3 = ). Politician 3’s utility level is

U 3 = t3 3q 3:




Now social welfare is:

W =3X

i=1

[S (q i) (1 + )iq i U i] :

Politician i may observe a signal ji on politician j’s e¢ciency characteristic j which is

either uninformative or provides (with probability ) a veri…able proof that j = when itis indeed the case. We will study the design by the Constitution of supervisory activitiesand the design of incentive contracts for the politicians. The timing is as described inSection 4.3.

To limit the number of cases to consider we will assume that the costs of supervisionare such that three signals only can be a¤orded. Furthermore, we assume that duplicatingthe supervision of politician j by the same politician i has no value. Given the symmetryof the problem we are left with two types of supervisory structures:

Those which involve a reciprocal supervision such as

1 2

3

32

21

12

or

3

1

2

23

21

12

Case a Case b

or those which avoid reciprocal supervision:

1 2

3

3

1

2

212

1

323

2 133

1

Case c Case d

@ @ @ @

@

@ @ @

In the previous sections, we have shown that reciprocal supervision creates the oppor-tunity of exchanges of favors between politicians which are very costly for the principal.Below, we will discard the structures with reciprocal supervision and concentrate the

analysis on the comparison between case c and case d. In case d, each politician super-vises and is supervised but no reciprocal supervision takes place. We will call this caseChecks and Balances (CB). Case c is asymmetric, with the characteristic that politician



4.7. OPTIMAL SUPERVISORY STRUCTURES 79

1 is not supervised, but exerts two supervisions, and politician 3 is supervised twice. Wewill call this case Specialized Supervision (SS ).

4.7 Optimal Supervisory Structures

In the case of benevolent supervision for case d (CB structure) we obtain the globalexpected welfare

W CB = 3W + 3(1 )W AI :

In case c (SS structure) we must treat each politician separately. Politician 1 is neversupervised. So the optimal contract corresponds to = 0, i.e.:

S 0(q +1 ) = (1 + )

S 0(q +1 ) = (1 + ) +

1

and an expected social welfare:

W AI 1+ =

hS (q

1) (1 + )q

1 q +1

i+ (1 )

S (q +1 ) (1 + )q +1

:

Politician 2 is supervised once as in the CB structure, hence:

S

0

(q

+

2 ) = (1 + )

S 0(q +2 ) = (1 + ) + (1 )

1

and an expected welfare W AI 2+ = W + (1 )W AI .

For politician 3,

Pr(3 = =31 = and 3

2 = ) = (1 )2

1 + (1 )2= ^;

hence a solution

S 0(q +3

) = (1 + )

S 0(q +3 ) = (1 + ) + (1 )2

1

with an expected welfare

W AI 3+ = [1 (1 )2]W + (1 )2

hS (q

3) (1 + )q

3 q +3

i+(1 ) S (q +3 ) (1 + ) q +3 :

The global expected utility is

W SS = W AI 1+ + W AI

2+ + W AI 3+ :




The comparison of the two supervisory structures is as follows: For = 0, they areequivalent and for = 1, CB dominates SS since CB corresponds to complete information

while SS has incomplete information about politician 1.Let us consider a neighborhood of = 0 to compare the two informational structures

in the case where S (q ) = q q2

2. Appendix 4.2 shows that

dW CB

d

=0

=dW SS

d

=0

and thatd2W CB

d 2

=0

>d2W SS

d 2

=0

if is small enough:

Therefore, CB dominates SS in the neighborhood of = 0. This is expected since

the gains from supervising twice politician 3 are proportional to 2 which is negligible for small. The CB structure corresponds to a better allocation of the scarce supervisionresources.

Suppose collusions by pairs of two politicians are now possible. This will decrease thevalue of each structure without changing the ordering in a neighborhood of = 0 sincethe incentive costs of collusion-proofness are linear in and identical between the twostructures at = 0.6

However, the picture changes when collusions of three agents are taken into account.To simplify the exposition of the main point suppose that the transaction costs of collusionwhen a politician must be compensated for hiding his message are very high say k = 0.

In the SS structure, a collusion of three politicians requires compensation for politician1 and therefore will not occur. On the contrary in the CB structure, reciprocal favorswith low transaction costs k0 > 0 can occur when all politicians are e¢cient. If allpoliticians have observed an informative signal (this happens with probability 3) theycan organize the suppression of the information without any compensation, hence a costfor the Constitution to avoid collusions

3k0 3 3 q

where q is de…ned in the optimal collusion-proof mechanism, i.e.

^q = 1 (1 + )

(1 )

1

k0 3 3

1 In a neighborhood of = 0, the …rst and second derivatives of W CB are unchanged;

then the ranking of structures is unchanged since in SS collusion is not possible.However, SS may dominate CB for high enough. Indeed, for close to one, only

politician 1’s regulation entails a signi…cant distortion. But for k0 2 close enough to 1,the distortion in SS is similar but happens for the three politicians.

For SS to dominate, the transaction costs of reciprocal favors must be small enough(k0 high) and must happen often enough ( close to one and close to one). This lastcondition is due to the fact that the reciprocal favor e¤ect is proportional to 3, theprobability that they are all e¢cient, whereas the informational advantage of the CB

structure is proportional to .6 Hence, …rst derivatives of welfare with respect to remain identical between themselves at = 0 and

second derivatives are unchanged.




Appendix 4

A.4.1 Separability of incentive constraintsWe can distinguish 9 cases :

1. 1 = ; 2 = with probability (1 )2

2. 1 = ; 2 = ; 1 = with probability (1 ) (1 )

3. 1 = ; 2 = ; 2 = with probability (1 ) (1 )

4. 1 = ; 2 = ; 1 = ; 2 = with probability 2(1 )2

5. 1 = ; 2 = ; 1 = with probability (1 )

6. 1 = ; 2 = ; 2 = with probability (1 )

7. 1 = ; 2 = ; 1 = ; 2 = with probability 2 (1 )

8. 1 = ; 2 = ; 1 = ; 2 = with probability 2 (1 )

9. 1 = ; 2 = ; 1 = ; 2 = with probability 2 2.

In the …rst four cases, the Constitution receives from the politicians only messagesabout themselves. There is no loss of generality in considering only revelation mechanisms

(t; t) (q; q )

with the (binding) incentive and individual rationality constraints :

t = q t = q + q

In case 5, we must avoid the deviation r1 = ; ~2 = , which requires (with t5 = q )

t5 q + k q t + s;

and similarly in case 6.In case 7 we must avoid two deviations :

~1 = and~2 = with r1 =

which requires :

t17 q + q = tt27 q + kq t + s;

and similarly in case 8.



4.8. CONCLUSION 83

In case 9 we must avoid the simultaneous deviations:

t1

9 q + k

0

q t + s=t29 q + k0q t + s=:

So, it appears that the transfers for truthful revelation of the soft information , ~1 =1; ~2 = 2, and the transfers for truthful revelation of the hard information, r1 = ; r2 =, can be treated separately as we have done in the text.

A.4.2 Comparison between CB and SS W CB = 3W + 3[(1 )W ( ) + (1 ) W ( )]with

W ( ) = S (q ) (1 + )q q

W ( ) = S (q ) (1 + ) q

and

S 0(q ) = (1 + ) +(1 )

1

For

S (q ) = q q 2

2;

d q

d =

1

d

d W CB = 3W 3W ( )

d2

d 2W CB

=0

= 3 dW

dq

d q

d =

3( )2

1

W SS = W AI 1+ + W AI

2+ + W AI 3+

dW AI 1+

d 0

dW AI 2+

d = (W W ( ))

d2W AI 2+

d 2

=0

=( )2

1

W AI 3+ = (1 (1 )2)W + (1 )2 W

=( ) + (1 ) W ( )

with

W =

( ) = S (q ) (1 + )q q +3

W ( ) = S (q +3 ) (1 + )q +3

and

S 0(q +3 ) = (1 + ) + (1 )2

1

dW AI 3+

d = 2 (1 )(W

W = ( ))d2W AI

3

d 2= 2 (W W

=( )) +

4( (1 ))2

1 :



Part II

Flexibility Versus Discretion inConstitutional Design

85



87

“Stripped to its essentials, Wicksell’s message was clear, elementary and self-evident. Economists should cease pro¤ering policy advice as if they were em-ployed by a benevolent despot, and they should look to the structure withinwhich political decisions are made. Armed with Wicksell, I, too, could dareto challenge the still-dominant orthodoxy in public …nance and welfare eco-nomics.”

Buchanan (1987), Nobel lecture.



88



Chapter 5

Political Economy and IndustrialPolicy

“Side payments will insure that the orthodox Pareto optimality surface willbe reached, but the redistribution that will take place through the collective-choice process will not represent the “optimal” shifting among positions onthis orthodox optimality surface”.

Buchanan and Tullock (1965) p. 195.

5.1 IntroductionA major task of political economy is to explain the pattern of government intervention inindustries, that is to say industrial policy. The “public interest” approach views the gov-ernment or the regulatory agencies as benevolent maximizers of social welfare. It derivespolicies which correct market imperfections such as monopoly pricing or environmentalexternalities. In the last ten years this paradigm has been substantially improved bytaking into account the various informational asymmetries faced by the social maximiz-ers. Industrial policy can then be viewed as resulting from an optimal trade-o¤ betweene¢ciency distortions and information rents. For example, in the case of natural monop-

olies, industrial policy selects cost-reimbursement rules of regulated …rms in a family of rules which arbitrate di¤erently between the e¢ciency of production and the size of theinformation rents captured by the …rms. Price-cap regulation favors e¢ciency, cost-plusregulation favors rent extraction. A public interest approach under incomplete infor-mation can explain why such a choice matters and how the optimal choice depends oncost-demand informational characteristics and on the industrial structure.1

This approach has been challenged in various ways. In political science authors as di-verse as Montesquieu, the American Federalists, Marx, Truman (1951) Bernstein (1955)have been concerned by the potential for capture. Governments may favor special interestgroups. By taking a more disaggregated view of government, distinguishing regulatory

agencies from political executives, by recognizing the multiprincipal nature of govern-ments, the political science literature has emphasized the rents that can be captured by

1 See La¤ont and Tirole (1993), Ch. 2.

89



90 CHAPTER 5. POLITICAL ECONOMY AND INDUSTRIAL POLICY

various intermediaries who are needed in the implementation of industrial policies (Niska-nen (1971), Kaufman (1961), Wilson (1980)).

This point of view can be formalized as we did in Part I by recognizing the hierarchicalstructure of government still maintaining, at the constitutional or governmental level, thepublic interest paradigm. Then, we can ask questions such as : How should industrialpolicy be designed at the constitutional level to deal with the capture problems -captureof regulatory commissions by …rms or interest groups such as environmentalists, captureby …rms of politicians who can in‡uence regulatory commissions etc? How should thegovernment or agencies be structured to mitigate the costs of capture?

The public interest approach has been also challenged by economists —the Chicagoschool and the Virginia school— who take as given and essentially uncontrollable thepolitical system. These authors study how the various interest groups in‡uence the de-

mocratic process or the elected politicians to extract rents. Implicitly these politicianscontrol the various agencies in charge of implementing policies. For example, Peltzman(1976) and Becker (1983-1985) develop models of political in‡uence of interest groups.The Virginia school emphasizes how politicians and bureaucrats compete for the rents as-sociated with bribes and kickbacks. The deadweight losses generated by the rent seekingactivities must be added to the original deadweight loss associated with the original rent,for example due to monopoly pricing, in order to obtain a complete assessment of socialcost.

These positive approaches su¤er from methodological limitations. By ignoring infor-mational asymmetries, these theories are unable to explain the rents and discretions that

are so essential in their theories.

2

In the absence of informational asymmetries, regu-lated …rms would be unable to extract rents and therefore would have no incentive toin‡uence industrial policy. Similarly voters and legislators would be able to control theiragents (governments or commissions) who could not get away with policies favoring inter-est groups over the common good. By blackboxing the supply side of in‡uence activitiesthey have ignored a crucial agency relationship between the people and the politicians,between politicians and bureaucrats, a relationship that has been analyzed in the politicalscience literature.

There exists a large literature attempting to test interest group theories of industrialpolicy. However, dissatisfaction remains. For example in his 1989 survey for the Handbook

of Industrial Organization , R. Noll says:

“While the …ndings of the studies of the economic e¤ects of regulation areconsistent with interest group theories, their scope is too narrow to constitutea test of them. The reason is that they do not link the e¤ects of regulation tothe causal variables that are the focus of the political theories -the elementsof transactions costs and information imperfections that would permit an in-e¢cient political equilibrium that delivered distributive bene…ts in ways thatare predicted by the nature and sources of these factors”.3

Recognizing the uncontrollable nature of the political system in a …ne tuning way in

2

We have discussed in Chapter 1, Section 1.6 the incomplete contract approach.3 Similarly Neven (1994) shows that a few variables describing political institutions and regimes su¢ceto account for 90% of the variance of state aids in the European community. He then calls for a structuralapproach.




information. For example, they can organize among themselves an auction to choose thepolitician who is willing to pay ex ante the expected information rent he will capture.

The transfers paid to the …rm are still …nanced by indirect taxes with a deadweight lossof and the Constitution imposes non discriminating indirect taxes.

Accordingly, majority 1, say, maximizes type 1 consumers’ expected welfare underincentive and individual rationality constraints or

max

S (q ) (1 + )t

+ U

+ (1 )

(S (q ) (1 + )t) + U

with

U 0

U U + q t = U + q

t = U + q

or

max

S (q ) (1 + )q

((1 + ) 1)q

+ (1 )

S (q ) (1 + ) q

yielding

S

0

(q

M 1

) = (1 + ) (5.3)S 0(q M 1) = (1 + ) +

((1 + ) 1)

(1 ): (5.4)

We assume (1 + ) > 1 to simplify the analysis. Otherwise majority 1 would like tomaximize the information rent and we would have to take into account type 2 consumers’individual rationality constraints.

Similarly, for majority 2 we obtain:

S 0(q M 2) = (1 + ) (5.5)

S 0(q M 2) = (1 + ) +((1 + ) 1)

(1 ): (5.6)

We must distinguish two e¤ects of the delegation of public policy to politicians.When = 1, public good production is higher than the optimal production when

= (compare (5.4), (5.6) with (5.2)). The reason is that majority i appropriates fullythe information rent, hence a per capita rent of U

higher than in the expected social

welfare. Therefore each majority in turn will overvalue the information rent in the rente¢ciency trade-o¤. Note that the lower is, the higher the distortion. When = 1,there is no distortion since each majority in turn represents the whole population. When

= 1 and > 1, relatively to the social optimum, majority 1 produces too little publicgood in both states of nature and while majority 2 produces too much. In general,the two e¤ects described above combine.



5.4. INCENTIVES AGAINST CAPTURE AS A CONSTITUTIONAL RULE 95

For any > 12

, the deviation is greater for q M 1 p than for q M 1.

When > 1 the quantity q 0 pt of the social optimum increases and this can only favor

public production which was excessive before.However, for large and a social value of the public good which is such that S 000 < 0,

for close to one and close to 1=2, the excessive production of public ownership may bemore damaging that the underproduction of private ownership. Then, private ownershipmay be preferable.8

5.4 Incentives against Capture as a Constitutional

Rule

Let us pursue the analysis under private ownership by type 2 consumers, when = 1 andwhen there is a regulatory agency that we model as the supervising politician of Chapter2. The agency receives a signal = when = with probability . Otherwise, itreceives signal = ;.

The agency can be potentially captured by the …rm as in Chapter 2. However, if majority 2 has control, one may argue that the …rm will not enter a collusive agreementwith the agency since the political principal coincides with the owner of the …rm. 9 Wewill compare two regimes. In regime 1 no incentives for the agency are created. In regime2 incentives to avoid any capture of the agency are put in place.Regime 1: Then, under majority 2 there is no capture of the agency even without

incentives. Social welfare isW = W + (1 )W M 2

where W is the complete information welfare when = and where W M 2 denotes theconditional welfare when the agency gets no informative signal.

W M 2 = (1 )

1

S (q M 2) (1 + )q M 2 q M 2

+

(1 )

1

S (q M 2) (1 + ) q M 2

with q M 2 and q M 2 de…ned by:

S 0(q M 2) = (1 + )

S 0(q M 2) = (1 + ) +((1 + ) 1) (1 )

1 ;

since majority 2 appropriates the information rent.

8 Note also that if type 1 consumers have the ownership, a greater than one favors private ownership,since, when majority 2 has the majority, the underproduction e¤ect due to the non internalization of theinformation rent is partially compensated by the fact that type 2 values more the public good than the

average consumer.9 The argument is a little loose since the manager may have di¤erent incentives than the majority.However, the members of the majority should be able to …nd a contract which gives up no surplus to athird party such as the regulatory commission.




On the contrary, under majority 1, the …rm will capture the agency to protect its rent.The transaction costs of capture are

(1 k) q M 1

since then occur only for an e¢cient …rm which is identi…ed by the agency.Majority 1 maximizes its own welfare without any information from the agency.Social welfare is then

S (q M 1) (1 + )q M 1 ~q M 1

+ (1 )

S (~q M 1) (1 + )~q M 1

(1 k) ~q M 1

W (~q M 1) (1 k) ~q M 1:

where ~M 1

q is here the solution10

of

S 0(~q M 1) = (1 + ) +(1 + )

1 +

(1 k)

(1 ):

Without an incentive scheme for the agency we get an expected welfare of

1

2

W + (1 )W M 2 + W (~q M 1) (1 k) ~q M 1

: (5.11)

Regime 2: Alternatively, one can decide constitutionally to design incentives for theagency so that it never accepts bribes, at a social cost11

k q M 1:

Social welfare is then

W + (1 )W (q M ) kq M 1

where W (q M ) is social welfare when majority M chooses its policy after message ;. Ma- jority 1 solves

max (1 )

S (q M 1) (1 + )q M 1 (1 + ) q M 1

+(1 )

S (q M 1) (1 + )q M 1

kq M 1

hence

S 0(q M 1) = (1 + ) +

(1 + ) (1 )

(1 )+

k

(1 )

:

Similarly, majority 2 solves12

max (1 )

S (q M 2) (1 + )q M 2 ((1 + ) 1) q M 2

10 We take into account the facts that the transaction costs of collusion are supported only by the

members of majority one and that majority 1 does not appropriate the information rent.11 Incentive payments to avoid collusion are calibrated to avoid capture when M 1 has the majority(which is the case when it matters) but are paid always. These payments are shared by all consumers.

12 Here the incentive payments for the agency are taken as given.



5.5. POLITICAL PRICE DISCRIMINATION VERSUS UNIFORM PRICING 97

+(1 )

S (q M 2) (1 + )q M 2

kq M 1

henceS 0(q M 2) = (1 + ) +

((1 + ) 1) (1 )

1 :

Note that W M 2 = W (q 2) as q M 22 = q M 2.

We obtain an expected welfare of

W + (1 )1

2

hW (q M 1) + W (q M 2)

i k q M 1: (5.12)

Consequently it is better to set up constitutionally incentives for the regulatory agencyi¤ (5.12) is larger than (5.11), i.e.:

1

2

(1 ) W (q M 1) (1 ) q M 1

(1 ) W (~q M 1) ~q M 1

+1

2(1 k) ~q M 1 k q M 1 (5.13)

i.e., if

expected supervision gains + expected transaction costs of capture

cost of incentives for agency.

The expected supervision gains are double: …rst, with probability one saves oninformation rents, and secondly and relatedly one can a¤ord a higher level of productionfor the ine¢cient type.13

5.5 Political Price Discrimination Versus Uniform Pric-

ing

We return to the general preferences of section 5.1 and we assume that the good is now aprivate good, but that the Constitution cannot di¤erentiate the two types of consumers inpricing. We assume that is known and that the public …rm which produces the privategood is controlled by the majority in power. In this section we assume that is certain.

If , the size of the majority, was contractible the Constitution could design the nonlinear tari¤ which maximizes expected social welfare, i.e. would solve

max [S (q 1) T 1] + (1 )[S (q 2) T 2]

(1 + ) [(q 1 + (1 )q 2) T 1 (1 )T 2]

13 See Faure-Grimaud and Martimort (1999) for a study of the relationship between political principalsand their bureaucracy in which they show that a more independent bureaucracy plays a stabilizatione¤ect with respect to the excessive ‡uctuations that political majorities would implement.




s.t.

S (q 1) T 1 S (q 2) T 2 (5.14)S (q 2) T 2 S (q 1) T 1 (5.15)

S (q 1) T 1 0 (5.16)

S (q 2) T 2 0: (5.17)

In this case of two types only, a general non linear tari¤ is represented by the pair(q 1; T 1); (q 2; T 2) where T i is the payment required to obtain the quantity q i. (5.15) and(5.16) are the self selection constraints and (5.17) (5.18) the consumers’ individual ratio-nality constraints. The solution to this program is

S 0

(q 2) = (5.18)

S 0(q 1) =

1 ( 1) 1+

1

; (5.19)

T 1 = S (q 1) T 2 = S (q 1) + (S (q 2) S (q 1)):

This is the usual optimal second degree price discrimination. However, if is notcontractible, we can either design this tari¤ on the basis of the expectation of (here12

) or delegate to political majorities the choice of a tari¤. If type 1 has the majority itsolves:

max [S (q 1) T 1 (1 + ) [ (q 1 + (1 )q 2) T 1 (1 )T 2]]

under the constraints (5.14) to (5.17). If we assume that (1 + ) < 1, type 1 majoritystill wants to extract rents from type 1 consumers14 and the usual incentive and individualrationality constraints are binding

T 1 = S (q 1) T 2 = S (q 1) + [S (q 2) S (q 1)]

and

S 0(q M 12 ) = (5.20)

S 0(q M 11 ) =

1 (1 )

: (5.21)

If type 2 has the majority it solves

max [S (q 2) T 2 (1 + ) [((1 )q 1 + q 2) (1 )T 1 T 2]]

under constraints (5.14) to (5.17). Hence

S 0(q M 22 ) = (5.22)

S 0

(q M 21 ) =

1 ((1+)1)(1)(1+)(1)

: (5.23)

14 In the opposite case, we would have to take into account individual rationality constraints.




alternance between A and B is detrimental because asymmetric information convexi…esthe (incentive compatible) Pareto frontier (see Figure 5.2).15

-

6

@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @

C

D

B

A

type 1’s

utility level

type 2’s

utility level

Figure 5.2

It generates an average vector of utilities C which is inside the Pareto frontier. Anine¢cient allocation rule D may be ex ante supervisor.

This is reminiscent of Chapter 13 in Buchanan and Tullock (p. 192). Let us reconstructtheir argument.

First they

“assume that the marginal utility of income declines as the individual receivesmore income in any particular time period”, p.192 .

Second, in the face of income uncertainty they recognize that the market fails.

“the risk in question would be essentially uninsurable”, p. 193.

Actually, it is a moral hazard argument which is behind their idea of non insurability.

“Since the private individual, by modifying his current behavior, is able toa¤ect his claims for compensations, a privately organized insurance plan might

be impossible”.15 See Appendix 5.2 for another and more explicit example with no restriction on the instruments that

can be used by politicians.



5.7. CONCLUSION 101

It is the combination of marginal disutility of income and moral hazard which convex-i…es the Pareto Frontier.

Then, actors move to public insurance as follows.

“Suppose that a constitution is adopted which openly and explicitely statesthat net-income transfers among individuals and groups will be carried outby simple majority voting... It seems certain that ’redistribution’, consideredas an activity, will be carried out relatively ’too far’ under these conditions”,p. 194.

Finally, they conclude that

“Side payments will insure that the orthodox Pareto optimality surface willbe reached, but the redistribution that will take place through the collective-choice process will not represent the ’optimal’ shfting among portions on thisorthodox optimality surface”, p.195 .

Even in the absence of income e¤ects, we have shown that public ownership andmajority rule create socially costly transfers which convexity the Pareto frontier andconsequently the ’shifting’ among positions on the Pareto frontier due to the democraticalternance is socially detrimental as in the Buchanan-Tullock analysis.

Only an institutional reform which would share equally among all citizens the infor-mation rent could solve the problem. Insurance of the political risk alone would not be

enough.

5.7 Conclusion

We have given several examples of normative constitutional analysis. The ingredientsof the analysis are informational asymmetries which explain the origin of rents, and po-litical games which choose residual decision makers for ex ante non contractible socialdecisions. The more instruments politicians have ex post, the closer to the (incentivecompatible) Pareto frontier they are and probably the less convex this frontier is, but themore discretion they have in favoring their constituencies. Constitutional choices strikea balance between these two problems. The next two chapters give further examples of this approach.



5.7. CONCLUSION 103

Consider now the equilibrium with majority 1. Then = . Di¤erentiating the …rstorder conditions (5.21) (5.22) we have:

dq M 12

d =

S 0

S 00;

dq M 11

d =

1

S 0

S 00:

Welfare is:

W M 1( ) = (S (q 1) T 1) + (1 )(S (q 2) T 2)(1 + ) [(q 1 + (1 )q 2) T 1 (1 )T 2]= (1 )( 1)S (q 1)(1 + ) [(q 1 + (1 )q 2) S (q 1) (1 ) (S (q 2) S (q 1))] :

Hence:

dW M 1( )

d = (1 )S (q 1) + (1 )( 1)S 0

dq 1d

+ (1 + )(1 )(S (q 2) S (q 1)):

d2W M 1( )

d =1

= 2(1 )S 0dq 1

d =1

+ (1 + )(1 )S 0

"dq 2d

=1

dq 1d

=1

#

= [2(1 ) (1 + )(1 )]1

(S 0)2

S 00 (1 + )(1 )

(S 0)2

S 00

=1

(2 1 + )

S 02

(S 00):

Since welfare is the same in all cases for = 1, in a neighborhood of = 1, welfarewith pooling is better if

(1 )2

1 + +

2

1 + > (2 1)

(1 (1 + ))

(1 + )(1 )

+

1 + (2 1 + )

1

:

Consequently, we see that political discrimination is better if is large and closeto 1. Alternatively if is close to 1=2 and small then pooling dominates.




A.5.2: An ExampleWe consider an economy with only two agents who have di¤erent tastes about a

public good decision. Each agent can be viewed as representing a large number of similarvoters. Each period the level of a public good must be decided. Agent 1 has preferencesrepresented by the utility function:

1q q 2

2+ t1

where q is the quantity of public good (whose cost is imbedded in the utility function forsimplicity or assumed to be zero), t1 is a quantity of private good (money) and 1 2 [; ]is a taste parameter which is private knowledge of the agent.16

Each period, 1 is drawn from a probability distribution with a cumulative distribution

function F () on [; ] with the regularity condition 1F ()f () non increasing.

Similarly agent 2 has preferences represented by

2q q 2

2+ t2

where 2 is also drawn (independently of 1) from the distribution F ().The e¢cient public decision rule is de…ned by

q (1; 2) =1 + 2

2:

The democratic rules of this admittedly quite simple economy is summarized by thefact that each period agent 1 (or agent 2) controls the government, and therefore thedecision over the public good, with probability17 1/2.

There is no discount factor, and the “majority” controlling the government mustrespect constitutional rules which we take here to be that the individual rationality (IR)constraints of the “opposition” must be preserved.

Let us see …rst what would happen under complete information.If type 1 has control (has the majority) he maximizes his utility under the constraint

that type 2 has a non zero utility level18, the IR constraint, or:

(I) maxq 1q q 2

2+ t

2q q 2

2 t 0 (5.25)

(5.26) is the IR constraint. We have written transfers in a form which expresses the factthat agent 1 has power and can impose a transfer in private good to agent 2 as long as,with the choice of public good, agent 2’s IR constraint is satis…ed.

16 Exceptionally, we consider a case of continuous types in this appendix. The reader unfamiliar withthe relevant technics (see Guesnerie and La¤ont (1984)) can take as given the characterization of the

incentive constraints.17 The democratic alternance may re‡ect very small random changes of the sizes of the two populations,changes which can be neglected in the welfare analysis.

18 We assume that the public project can be realized only if both agents participate.



5.7. CONCLUSION 105

The solution of program (I) is immediately:

q CI (1; 2) =1 + 2

2(5.26)

tCI (1; 2) = 2q CI (1; 2) [q CI (1; 2)]2

2: (5.27)

When agent 1 is in power the expected utility of agent 2 is

U M 12 = 0

and the expected utility of agent 1 is

U M 11 = E 1;2

1q CI (1; 2)

[q CI (1; 2]2

2+ tCI (1; 2)

: (5.28)

Substituting (5.26) and (5.27) in (5.28) we obtain:

U M 11 = (E)2 +

1

2V ar ; (5.29)

where

E =

Z

dF () V ar =

Z

( E)2dF ():

By symmetry, we have

U M 21 = 0 U M 2

2 = (E)2 +1

2V ar

and …nally for each agent an expected utility of

1

2(E)2 +

1

4V ar :

Figure 5.3 summarizes the analysis.




6

-

@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @

M

M 1

M 2

EU 2

EU 1

12

(E)2 + V ar

12

(E)2 + V ar

Figure 5.3

M 1 (resp. M 2 ) represents the expected utilities conditionally on 1 (resp. 2) havingcontrol. M represents the vector of global expected utilities. Note the essential pointthat M belongs to the ex ante Pareto optimal frontier under complete information. Itcorresponds to the e¢cient public decision with a symmetric treatment of the agents.In such a world the ‡uctuation in the allocation of resources due to the democratic rule(restricted here to the ‡uctuation in transfers) has no social cost.

We assume now that, when agent 1 has control, he does not know agent 2’s tastecharacteristic. The revelation principle tells us that there is no loss of generality inrestricting the policies of agent 1 to choosing in the family of revelation mechanisms,i.e. public good decision functions q (1; 2) and transfer functions t(1; 2) which inducetruthful revelation of agent 2’s taste in a Bayesian equilibrium.

Then, agent 1’s best policy is to maximize his expected (with respect to 2) welfareunder the incentive and individual rationality constraint of agent 2. Let us …rst derivethese constraints

U 2(2; ~2) = E 1

"2q (1; ~2)

[q (1; ~2]2

2 t(1; ~2)

#

is agent 2’s expected utility when he is of type 2 and envisions to claim he is a ~2 typein a revelation mechanism q (~1; ~2); t(~1; ~2).



5.7. CONCLUSION 107

Let U 2(2) = U 2(2; 2), i.e., his utility when he tells the truth.The …rst order condition of incentive compatibility tells us that the rate of increase of

agent 2’s utility level, _U 2(2), equals the expectation of the level of public good decision:

_U 2(2) = E 1q (1; 2):

A necessary link exists between the use which is made of agent 2’s information (namelythe public good decision) and the rent that must be given up to him to induce truthtelling.

The second order condition of incentive compatibility puts a sign constraint on thepublic good decision function, which does not matter if the objectives of the two agentsare not too con‡ictual:

E 1q (1; 2)

non decreasing.The individual rationality constraint19 is:

U 2(2) 0 for any 2 2 [; ]:

Agent 1’s optimization program can then be written20 as (by noting that t = E 1

2q

q2

2

+ U 2)

maxq(;)

E 1;2

(1 + 2)q (1; 2) [q (1; 2)]2 U (2)

s.t.

_U 2(2) = E 1q (1; 2)

U 2(2) 0 for any 2 2 [; ]

E 2q (1; 2) non decreasing.

The solution of this problem21 is

q M 1(1; 2) =1

2

1 + 2

(1 F (2))

f (2)

:

Hence,

_U 2(2) = 12

E 11 + 2 (1 F (2))

f (2)

U M 12 = E 2U 2(2) =

1

2

Z

Z

Z 2

1 + ~2

1 F (~2)

f (~2)

d~2

dF (2)dF (1)

U M 11 = E 12

h(1 + 2)q M 1(1; 2) [q M 1(1; 2)]2

i U M 1

2 :

19 This IR constraint is an interim constraint, i.e., it is written after agent 2 has discovered his privateinformation, but before knowing agent 1’s information.

20 We assume here that majority 1 chooses the mechanism before knowing its private information

parameter. However, the mechanism is played after agents learn their information.21 We make assumptions on F () and [; ] such that q M 1 is always non negative. Note that we canalso add constants to the utility functions when the public good is realized to make sure that the IRconstraints are satis…ed for the chosen probabilistic speci…cations.




In particular

U M 11 + U M 1

2 = (E)2 + 12

V ar E 14(1 F ())

f ()2:

Note that by symmetry

U M 21 = U M 1

2 U M 22 = U M 1

1 :

Since U M 11 + U M 1

2 < (E)2 + 12

V ar, the allocation M 1 which corresponds to expectedutilities under majority 1 is now below the complete information Pareto frontier.

The global expected utility of agent 1 is

1

2U M 11 +1

2U M 21 =1

2 (U M 11 + U M 12 ):

Figure 5.4 summarizes the analysis. M 1 and M 2 represent the expected utility alloca-tions under majority one and two respectively and M the average of those. The incompleteinformation generates a loss with respect to the full information Pareto frontier.

6

-

@

@ @ @ @ @ @ @ @ @ @ @ @ @ @ @

@ @ @ @ @ @ @ @

M

M 1

M 2

EU 2

EU 1

A()

A()

@ @ @ @ @ @ @ @ @ @ @ @

@ @ @ @ @

B()

B()

M

M M

M 1

M 2

A() = (E)2 +1

2

V ar

B() = A() 1

4E

1 F ()

f ()

2



5.7. CONCLUSION 109

Figure 5.4

De…ne now the bureaucratic rule

q = E 1 + 2

2

with no transfer which maximizes ex ante social welfare and leaves no discretion to politi-cians. Then:

EU 1 + EU 2 = (E)2:

M represents in Figure 5.4 the associated expected utility allocation. M can Pareto

dominate or be Pareto dominated by M according to the following proposition.The bureaucratic rule dominates democratic political discrimination if

V ar < E 1

2

(1 F ())

f ()

2

:

If the importance of asymmetric information measured by V ar is not too great, thebureaucratic rule which is not responsive to private information but avoids the excessive‡uctuations of majority decision making dominates the more informed democratic decisionrule.

Under incomplete information the allocations obtained either by the democratic ruleor the bureaucratic rule should not be compared with the Pareto frontier under completeinformation. The relevant normative benchmark is the Pareto frontier under incentiveconstraints, called incentive Pareto frontier, that we derive below. It is the convexity of this frontier which creates the possible trade-o¤ between in‡exibility (or insensitivity toinformation) of rules and political discretion inducing a socially costly risk.

The ex ante Pareto frontier under incentive constraints that we call the incentivePareto frontier is determined by varying in [0; 1] in the following program:

maxq(;) E 1;2 1q

q 2

2 + t+ (1 )2q

q 2

2 ts.t.

_U 1(1) = E 2q (1; 2)_U 2(2) = E 1q (1; 2)

U 1() 0U 2() 0

with

U 1(1) = E 21q (1; 2)

[q (1; 2)]2

2 + t(1; 2)U 2(2) = E 1

2q (1; 2)

[q (1; 2)]2

2 t(1; 2):




If > 12

, the coe¢cient of t in the social welfare function is negative. Consequently,the IR constraint of agent 2 is binding while the one of agent 1 is not. The optimization

program can be rewritten:

maxq(;)

E 1;2

(1 + 2)q q 2

2 1

2 U 2(2)

s.t.

_U 2(2) = E 1q (1; 2)

U 2() = 0

with an optimal public decision rule:

q (1; 2) =1

2

1 + 2

(2 1)

2

1 F (2)

f (2)

and a symmetric solution when > 1

2. When = 1

2, none of the IR contraints is binding

and the e¢cient public decision is implemented.

The incentive Pareto frontier is represented by the dotted non linear curve M 1 M 2 (seeFigure 5.5).

6

-

@ @ @ @ @ @ @ @ @ @ @

@ @ @ @ @ @ @ @ @ @ @ @ @

M

M 1

M 2

EU 2

EU 1

A()

A()

@ @ @ @

@ @ @ @ @ @ @ @ @ @ @ @ @

B()

B()

M

M M

M 1

M 2

M 1

M 2

Figure 5.5



5.7. CONCLUSION 111

So, we see that asymmetric information convexi…es the incentive Pareto frontier. Thesocial cost of ‡uctuations in decision making follows from this convexity, as well as the

potential superiority of a bureaucratic rule which is not even incentive Pareto e¢cient.So far we have assumed that each majority was selecting its mechanism before knowing

its private information. Suppose now on the contrary that such a selection is made at theinterim stage. We have now an informed principal problem and we must take into accountthe information transmitted by the ruling majority’s o¤er of mechanism. From Maskinand Tirole (1990), we know that it is as if the agent was informed about the majority’scharacteristics. When majority 1 occurs, this changes the IR constraint of agent 2 froman interim constraint to an ex post constraint

U 2(1; 2) 0 for any 1; 2:

However, it is easy to see that it does not change the decision rule and that, becauseof the linearity of agent 2’s utility in 1, it does not change expected utilities either. Sothe information transmission is harmless.



Chapter 6

Political Economy and the MarginalCost Pricing Controversy

“Le meilleur de tous les tarifs serait celui qui ferait payer à ceux qui passentsur une voie de communication un p ge proportionnel àl’utilitéqu’ils retirentdu passage...”

“Il est ident que l’e¤et d’un tel tarif serait : d’abord de laisser passer autantde monde que si le passage ait gratuit ; ainsi point d’utilitéperdue pour lasoci ; ensuite de donner une recette toujours su¢sante pour qu’un travailutile p se faire.”

“Je n’ai pas besoin de dire que je ne crois pas àla possibilité d’application de cetarif volontaire ; il rencontrerait un obstacle insurmontable dans l’improbitéuniverselledes passants, mais c’est làle type dont il faut chercher às’approcher par un tarif obligatoire.”

Jules Dupuit (1849), p. 223.

6.1 Introduction

In a very elegant Econometrica paper, Hotelling (1938) provided the appropriate formulasassessing the social costs of marginal departures from marginal cost pricing when theinterrelations between commodities are taken into account. In so doing he generalized thework of Dupuit (1844) and Marshall (1890). He went further. He advocated marginal costpricing for the industries with large …xed costs and more generally increasing returns :

“This proposition has revolutionary implications, for example in electric powerand railway economics, in showing that society would do well to cut rates

drastically and replace the revenue thus lost by subsidies derived largely fromincome and inheritance taxes and the site value of land” Hotelling (1939),p. 151.

113



114CHAPTER 6. POLITICAL ECONOMY AND THE MARGINAL COST PRICING CONTROVERSY

In his introduction he suggested that Dupuit also advocated marginal cost pricing.A whole generation of economists took it for granted and did not question the historical

origin of the policy consisting of pricing commodities at marginal cost and …nancing thede…cit with the general budget. Ekelund (1968) convincingly demonstrated1 that Dupuitnever proposed marginal cost pricing. Actually from Adam Smith (1776) to Edgeworth(1913), most major …gures of economics warned against the dangers of de…cits …nancedby the general budget. A. Smith (1776) was particularly clear on this point :

“It does not seem necessary that the expence of those public works should befrom (that) public revenue... The greater part of such public works may easilybe so managed, as to a¤ord a particular revenue su¢cient for defraying theirown expence...” p. 682 (1937 edition).

A. Smith seems to suggest prices proportional to marginal cost so as to cover costs,what in France we call the Allais rule :

When the carriages... pay toll in proportion to their weight or their tunnage,they pay... in proportion to the wear and tear...” p. 683.

What is most interesting are the reasons given by A. Smith to motivate his proposal.A major argument is an informational one :

“When high roads, bridges, canals... are in this manner made and supportedby the commerce which is carried on by means of them, they can be made

only where that commerce requires them and consequently where it is properto make them.” p. 683.

Of course it is not quite right2 but the next argument, a political economy one, iscompelling :

“A magni…cent high road cannot be made through a desert country wherethere is little or no commerce, or merely because it happens to lead to thecountry villa of the intendant of the province, or that of some great lord towhom the intendant …nds it convenient to make his court. A great bridgecannot be thrown over a river at a place where nobody passes, or merely to

embellish the view from the windows of a neighbouring palace.” p. 683.1 According to Ekelund, Dupuit was emphatically opposed to the caprice of political in‡uence in the

granting of subsidies. His opposition was based on the belief that the political selection of projects to besubsidized would not be grounded in economic criteria. Dupuit clearly saw that the usefulness of a roadis maximized when its toll is zero :

“L’utilitéd’une voie de communication est la plus grande possible lorsque le p ge est nul”,p. 247.

However, he understood the deadweight loss of the …nancing :

“On comprend que pour traiter ainsi la seule question de savoir si on doit ou on ne doit pasablir des p ges, il y aurait à examiner par quel imp ou par quelle aggravation d’imp

ils devraient re remplac et quels seraient les e¤ets de ces imp s”, p. 247.

Dupuit’s viewpoint will be formalized by Edgeworth (1913).2 It is a su¢cient but not a necessary test.



6.1. INTRODUCTION 115

A. Smith understands that the decision process for public works must be delegatedand he worries about the incentives created by the delegation of pricing rules to policy

makers. Note that he does not question the benevolence of the executive power itself sincehe relies upon it to conduct an appropriate redistribution policy through third degree pricediscrimination :

“When the toll upon carriages of luxury, upon coaches, post-chaises, etc. ismade somewhat higher in proportion to their weight, than upon carriages of necessary use, such as carts, waggons, etc. the indolence and vanity of therich is made to contribute in a very easy manner to the relief of the poor...”p. 683.

Walras (1897) follows essentially Smith’s point of view :

“L’Etat interviendra soit pour exercer lui-m e le monopole soit pour l’organiserde fa n àce qu’il soit exercésans b ice ni perte.”

without being clear on the allocation of …xed costs in the multiproduct case :

“Le monopole des chemins de fer devrait re exercépurement et simplement,soit par l’Etat soit pour son compte, au prix de revient.”

However, he mentions the point of view of J.B. Say (1840) who wants to treat the com-munication means, roads, canals,..., as public goods and who therefore proposes marginalcost pricing (zero price) in a special case3. Walras also considers that communicationmeans produce some public goods (if only for the armed forces...) which justify subsidies.

Hotelling was aware of a number of criticisms of marginal cost pricing but he dismissedthem all on the following grounds :

First, the …nancing of the de…cits induces debatable e¤ects on the distribution of wealth. He argues mainly that the marginal cost pricing rule will be applied for manydi¤erent projects and :

“A rough randomness in distribution should be ample to ensure such a dis-tribution of bene…ts that most persons in every part of the country would bebetter o¤ by reason of the program as a whole.” Hotelling (1939), p. 259.

Second, in his answer to R. Frisch (1939), Hotelling (1939) recognizes, followingA. Lerner (1937), that the income tax he plans to use to …nance de…cits

3 One motivation of Say is that price equal to average cost may not be su¢cient to balance the budgetof some projects despite their social usefulness:

“Les frais de confection d’un canal, m e les frais indispensables, peuvent re tels que lesdroits de navigation ne soient pas su¢sants pour payer les int s de l’avance ; quoique les

avantages qu’en retirerait la nation fussent tr sup ieurs au montant de ces int s. Il fautbien alors que la nation supporte gratuitement les frais de son ablissement, si elle veut jouir du bien qui peut en r ulter.”




“is a sort of excise tax on e¤ort and on waiting, ... is to some extent objec-tionable because it a¤ects the choice between e¤ort and leisure...”

If this turns out to be a real problem, Hotelling …nds an easy escape by appealing toland taxes, externality taxes :

“public revenue should be derived primarily from rents of land and other scarcegoods, inheritance and windfall taxes, and taxes designed to reduce sociallyharmful consumption.”

Hotelling’s argument rests on the assumption that lump sum taxes somehow exist.In practice it is recognized that the social cost of public funds is not negligible, rangingfrom .3 in developed countries to more than 1 in developing countries. A …rst line of criticism that will be followed eventually even by great defenders of marginal cost pricingsuch as W. Vickrey is that, even after using land taxes and externality taxes, the …nancialneeds for the government are such that distortive taxes need to be used at the margin.Second best optimality then requires some form of Ramsey pricing, with the well knowninformational di¢culties about price elasticities, creamskimming and bypass.

The third main criticism Hotelling considers is the fact that it is necessary to …ndout whether the creation of the project is a wise social policy ; and sometimes to selecta limited number of proposed investments, corresponding to the available capital, fromamong a large number of possibilities. He then provides an answer which ignores bothincentive and political questions :

“When the question arises of building new railroads, or new major industriesof any kind, or of scrapping the old, we shall face, not a historical, but amathematical and economic problem... This will call for a study of demandand cost functions by economists, statisticians, and engineers, and perhapsfor a certain amount of large scale experimentation for the sake of gaininginformation about these functions.” p. 269.

The intellectual framework of Hotelling is clearly the paradigm of the benevolentsocial maximizer who can become informed by social experimentation. The two mainlines of criticism that Hotelling considered but dismissed are related to this point of view.Incomplete information makes lump sum taxation ine¤ective and pushes us towards a

second best world leading to Ramsey pricing. However, the potential lack of benevolencefor decision makers may question this conclusion.

This introduction leaves us with many questions that we will consider in turn. First,what is then the exact intellectual origin of the policy of pricing at marginal cost withpublic funding of de…cits. Second, what was the content of the marginal cost controversy.Third, how can we discuss today the incentives and political economy issues concerningpricing rules of increasing returns industries, for simplicity restricting the discussion tonatural monopolies.

6.2 The Marginal Cost Pricing RuleSchumpeter attributes to a German economist, W. Launhardt (1885), the paternity of the rule :



6.2. THE MARGINAL COST PRICING RULE 117

“the work of W. Launhardt... contained the theorem –his argument for gov-ernment ownership is based upon it– that the social advantage from railroads

will be maximized if charges be not higher than –as we should say– marginalcost. It follows from this that the whole overhead would have to be …nancedfrom the government’s general revenue –the theorem that has been much dis-cussed in our own day after having been independently discovered by ProfessorHotelling.” Schumpeter (1954), p. 948.

The idea came up also in the debates following the discussions of Marshall’s idea thatdecreasing returns to scale industries should be taxed and increasing returns to scaleindustries should be subsidized.

Pigou (1952) quali…ed Marshall’s suggestion :

“provided that the funds for the bounty can be raised by a mere transfer thatdoes not in‡ict any indirect injury on production” p. 224.

“Those results, ..., are results in pure theory”. p. 226.

Pigou then raised the practical di¢culty of determining the type of returns to scale(the empty boxes controversy) but hoped that economists would be able to …ll those boxeswith statistical techniques in the future. J. Robinson (1934) also clari…ed fairly confuseddiscussions :

“The obvious example is a railway system which is working at falling averagecost and which is limited to just cover its costs... The whole problem really

boils down to the familiar di¢culty that when any concern is running at fallingaverage cost it is impossible to …x a price which both enables it to cover itscost and enables consumers to buy the output whose marginal cost to the…rm is equal to the marginal utility to them. The di¢culty can be removedby subsidizing the …rm... Whether, on general grounds, such subsidies aredesirable, or feasible, is another story”.

The idea of pricing at marginal cost and …nancing the de…cit with public moneybecame familiar during the controversy of socialism (Lange and Taylor (1938), Lerner(1937)). It was even an alledged advantage of public ownership over private ownership for

which subsidies were not even considered. Finally, we can also note the political economydefense of marginal cost pricing by Vickrey (1948):

“Whether the operation is in private or in public hands, if rates are set abovemarginal cost in an attempt to cover the entire costs of the operation, thesolution of the problem of how to …x rates so as to achieve this end with theleast possible misallocation of resources calls, at best, for the exercise of veryre…ned judgment, even in a milieu free from contending interests. In practice,moreover, contention by interested parties makes the achievement of a closeapproach to the best solution even more di¢cult...”

“This uncertainty often produces a situation in which it becomes very easy for

the decisions to be made primarily on the grounds of political expediency...Such considerations can be excluded from rate-…xing problems only by settingrates at marginal costs”.




He also voices a very modern argument in our world of deregulation :

“Subsidized operation at marginal cost will usually eliminate the need thatis often felt for surrounding such de facto public monopolies with legal pro-hibitions against competition. As long as it is necessary to cover costs fromrevenues, it is often deemed necessary to prohibit private competitors fromoperating in the same …eld, in order to prevent “skimming the cream” andimpairment of revenues or uneconomical duplication of services...With rates at marginal cost, however, no such prohibitions would be necessaryand, indeed, they would be undesirable”.

6.3 Frisch’s Comment

It is interesting to see the type of criticisms Frisch made of Hotelling’s paper. We arguedabove that Hotelling was thinking in terms of an informed benevolent social maximizer.Frisch’s comment goes even further with all the virtue of logic within a well de…ned model.Quite rightly within the model he considers, and in the same spirit as Kahn (1935), Frisch(1939) p. 145 points out:

“The only relevant question is whether the excise taxes are proportional ornon proportional to the prices that existed before the imposition of the excisetaxes. It is the non proportionality of the excise taxes, and only this, that

produces a reduction in satisfaction.”

He then claims that Hotelling is considering a case of measure zero, that there is acontinuum of other systems leading to the same result.

“One consists in telling the individual that under any circumstances his incometax will be so adjusted to the other facts of the situation that his total taxwill equal t.” (i.e. will be constant).

and later

“There exists an in…nity of others that are equally good, namely all thosewhose excise taxes are proportional to the original prices...”

Frisch is saying that all decompositions of taxes between excise taxes and incometaxes which keep consumer prices proportional and which raise the same total revenueare equivalent. Hotelling’s answer is also quite interesting. He recognizes Frisch’s logicalpoint, but criticizes the other systems proposed by Frisch on informational grounds whichare outside the model : tax evasion of excise taxes, di¢culty in taxing all commodities,non linear taxation possibilities with income taxes.

In his 1987 paper in the New Palgrave, Vickrey, who wrote fourty papers on marginalcost pricing, recognizes the second best nature of the problem and the need for taking

into account the marginal cost of public funds. Marginal cost pricing cum funding of thede…cit with public funds must acknowledge this cost. The second criticism anticipated byHotelling was the need for testing the validity of the project. Two questions are raised



6.3. FRISCH’S COMMENT 119

here : …rst, assuming costs are imperfectly known what is the best pricing method —themain point raised by Coase (1946) ; second, if subsidies exist, one must take into account

their rent seeking implications. As Vickrey (1987) puts it :

“One reason for wanting to avoid such a subsidy is that if an agency is con-sidered eligible for a subsidy much of the pressure on management to operatee¢ciently will be lost and management e¤ort will be diverted from controllingcosts to pleading for an enhancement of the subsidy.”

Hence, the tendency to revert to self-…nancing projects :

“This e¤ect can be minimized by establishing the base for the subsidy in amanner as little susceptible as possible to untoward pressure from manage-ment. But it is unlikely that this can be as e¤ective in preserving incentivesfor cost containnent as a requirement that the operation be …nancially self-sustaining.”

These historical debates show that there are two major criticisms against marginalcost pricing. The …rst is due to the social cost of public funds which is non negligible andleads to some form of Ramsey pricing. However, such pricing methods raise informationalissues4. More importantly Ramsey pricing opens the possibility of political manipulationsof price elasticities as well as the need to control entry (with possibilities of capture)to avoid creamskimming. The second criticism of marginal cost pricing is based on the

political manipulations of …xed costs which may lead to ine¢cient decisions.Therefore, it appears that two attitudes are possible. One is to stick to pure theory

and conclude that asymmetric information requires Ramsey pricing or some generalizedversion developed in La¤ont and Tirole (1993). A more policy oriented attitude musttake into account political constraints, i.e., the fact that the regulatory pricing rules willbe mandated by politicians who have some discretion because the Constitutions, beingquite incomplete contracts, cannot control them perfectly.

Such a political economy of pricing is required. Clearly, the various pricing rules aresensitive to di¤erent types of political in‡uence and a complete theory should consider, ineach policy case, the most relevant dimensions of discretion. The policy conclusions will

certainly be country and industry speci…c, since they should, broadly speaking, trade-o¤ the ine¢ciencies of the pricing rules which derive from marginal cost pricing or Ramseypricing and the political distortions they are associated with.

Some, as Frisch (1970), might think that it is not politically correct to develop sucha theory. Frisch’s attitude is based on a quite idealistic view of the politicians and of the relations between economists and politicians. In his Nobel lecture he calls for acooperation between them :

“This will be of basic importance for clarifying what the political authoritiesreally are aiming at”

and later, describing the dialogue between authorities and experts :4 La¤ont and Tirole (1996) argues that these informational issues are best dealt with by delegating

pricing to the …rm through a price cap combined with a pro…t sharing scheme.




“the expert will have to end by saying politely : your Excellencies, I am sorrybut you cannot have at the same time all these things on which you insist.

The excellencies, being intelligent persons, will understand the philosophy of the preference questions...”

Taking into account interest groups and the private agendas of politicians is necessaryto move from the world of pure theory to public policy as Frisch clearly wished to. Thenext two sections are a …rst step towards such a political economy of pricing rules 5. Theyimply a view of the relations between economists and politicians which is quite di¤erentfrom Frisch’s view.

6.4 Smith, Edgeworth, Hotelling

The economics of incentives has provided the tools needed for modeling the rents capturedby interest groups as a function of the underlying economic parameters. Therefore, it is anessential input into political economy which is often described as a game of redistributionof rents. We will now give some simpli…ed examples of political games in which the“constitutional” choice of the pricing rules for natural monopolies can be discussed.

We already mentionned that A. Smith proposed to in‡ate marginal costs proportion-ally to cover costs. Edgeworth (1913) proposed price discrimination to help cover costs6

with less e¢ciency distortions. These two rules have di¤erent implications on the e¢ciencydistortions under majority voting and also on the realization of the project.

We consider a natural monopoly producing q units of a private good with a costfunction

C = q + K: (6.1)

As in Chapter 5, the population of consumers is composed of two types, type 1 inproportion with the utility function S (q ) for the good produced by the monopoly andtype 2 in proportion 1 with the utility function S (q ), with > 1. takes thevalue > 1

2with probability and the value 1 with probability 1 . The policy

decisions of this simple model are the production level and the …nancing of the naturalmonopoly. If = , type 1 has the majority and takes the policy decisions within theconstitutional constraints which maximize the welfare of type 1 consumers. And similarly

with type 2 when = 1 .The constitutional constraints are represented by various rules. Consider …rst the

Smith rule. Let q i the consumption of type i; i = 1; 2. Budget balance is achieved byprices which in‡ate the marginal cost by a factor such that revenues cover costs:

( 1)

q 1 + (1 )q 2

= K: (6.2)

Consumers’ optimization leads to :

S 0(q 1) = (6.3)

5

See also Section 5.5 in Chapter 5.6 “If a railway cannot be made to pay with rates and fares assigned on the principle of cost of service,it is better that it should practise discrimination than that it should not exist” p. 223. As we saw aboveDupuit was led to a similar idea as an approximation of his ideal pricing.



6.4. SMITH, EDGEWORTH, HOTELLING 121

S 0(q 2) = : (6.4)

The solutions q 1; q 2; are di¤erent according to the value of and therefore accordingto the type of majority. We index the solutions by an upper index i, i = 1; 2 dependingon the majority.

Then expected welfare is

W S = n

h

S (q 11) 1q 11

i+ (1 )

hS (q 12) 1q 12

io+ (1 )

n(1 )

hS (q 21) 2q 21

i+

hS (q 22) 2q 22

io: (6.5)

Let q 11( ); q 12( ); 1( ) and q 21( ); q 22( ); 2( ) the solutions of (6.2) (6.3) (6.4) in

the case of majorities 1 and 2 respectively. Substituting these expressions into W

S

, weobtain W S ( ). To compare the Smith rule with other rules in the neighborhood of = 1,we will need the derivative of expected social welfare with respect to , at = 1.

dW S

d ( ) =

h q 11 (1 )q 12

id 1

d + (1 )S (q 12)

+ (1 )h

(1 )q 21 q 22

id 2

d + (1 )S (q 22): (6.6)

For = 1; q 11 = q 12 = q 21 = q 22 = q and

d 1

d =1

=( 1)(1 )S 0

( 1) + qS 00(6.7)

d 2

d

=1

=( 1)S 0

( 1) + qS 00(6.8)

where S 0; S 00 (and later S ) are evaluated at q . Hence

dW S

d

=1

=

h(1 ) + (1 )

iS

h(1 ) + (1 )i q ( 1)S 0

( 1) + qS 00: (6.9)

Consider now the Edgeworth rule, that we interpret here as second degree price dis-crimination. Let (T 1; q 1), (T 2; q 2) a non linear schedule. Incentive compatibility andbudget balance7 require

S (q 2) S (q 1) T 2 T 1 h

S (q 2) S (q 1)i

(6.10)

T 1 + (1 )T 2 = hq 1 + (1 )q 2i+ K: (6.11)

7 We assume that we are in a domain of parameter values such that individual rationality constraintsare not binding. This will be the case if the valuations of the commodity considered are high enough.




Under majority 1, the type 2 incentive constraint is binding and the optimal non linearprice is the solution of

max h

S (q 11) T 11i

(6.12)

s.t. (6.10) (6.11)

yielding :

S 0(q 11) =

1 (1 ) (6.13)

S 0(q 12) = (6.14)

T 11 = hq 11 + (1 )q 12i+ K (1 ) hS (q 12) S (q 11)i (6.15)

T 12 = T 11 + h

S (q 12) S (q 11)i

: (6.16)

Under majority 2, the type 1 incentive constraint is binding and the optimal non linearprice is the solution of

max h

S (q 22) T 22

i(6.17)

s.t. (6.10) (6.11)

yielding :

S 0(q 21) = (6.18)

S 0(q 22) =

(1 ) (6.19)

T 21 = h

(1 )q 21 + q 22

i+ K

hS (q 22) S (q 21)

i(6.20)

T 22 = T 21 + S (q 22) S (q 21): (6.21)

Then expected welfare is8

W E

= S (q

11) + (1

) hS (q 12) S (q

11)i h

q 11 + (1

)q 12i K

+ (1 )

S (q 12)

hS (q 12) S (q 11)

i h

q 11 + (1 )q 12

i K

+ (1 )

(1 )

S (q 21) +

hS (q 22) S (q 21)

i h

(1 )q 21 + q 22

i K

+

S (q 22) (1 )

hS (q 22) S (q 21)

i h

(1 )q 21 + q 22

i K

(6.22)

anddW E

d =1= h(1 ) + (1 )iS (6.23)

8 The index E refers to the Edgeworth rule.




We illustrate in Figures 6.1 and 6.2 the distortions implied by political discrimination.If we continue to assume that, when social welfare is maximized, individual rationality

constraints are not binding, we obtain the …rst best optimal allocation such that S 0(q 1) =S 0(q 2) = . From (6.13) (6.14), q 11 < q 1 and q 12 = q 2 . From (6.18) (6.19), q 21 = q 1 andq 22 > q 2 .

So political discrimination is excessive in two ways : …rst, it leads to marginal priceswhich are di¤erent from marginal costs and induces larger di¤erences in quantities con-sumed than at the optimum ; second, it leads to higher di¤erences in utility levels. Ma- jority 1 tries to use majority 2 to fund the project through the budget balance equation.To increase this funding still respecting incentive constraints leads majority 1 to in‡ate

hS (q 2) S (q 1)

iby decreasing S (q 1) (given that type 2’s incentive constraint is binding).

Majority 2 must satisfy type 1 incentive constraint T 2 T 1 S (q 2) S (q 1) and chooses,to increase T 1, both to increase T 2 and q 2. Again, this mechanism is less e¤ective whenthe size of the majority increases and the distortion is then decreased.

pictureFigure 6.1

The allocation marked by in Figure 6.1 is the …rst best allocation most favorable totype 1 given the incentive constraints, i.e.

T 2 = T 1 + hS (q 2) S (q 1)i:

The allocation marked by which obtains under majority 1 leads to a higher welfareof type 1 and lower welfare of type 2 and more (marginal) price discrimination.




6

-

S

S

T

q

*q 21 = q 1

q 2

q 22

4

4

*

Figure 6.2

The allocation marked by in Figure 6.2 is now the …rst best allocation most favorableto type 2 given the incentive constraints, i.e.

T 2 = T 1 +h

S (q 2) S (q 1)i

:

The allocation marked by 4 in Figure 6.2 which obtains under majority 2 leads toa lower welfare of type 1 and a higher welfare of type 2 and to more (marginal) pricediscrimination.

From above we can note that the distortions of the Smith rule concern both types andincrease with the size of the …xed cost and decrease or increase for both types with theheterogeneity parameter according to the way changes with (see (6.7), (6.8)). TheEdgeworth rule introduces a price distortion only for the type who has the majority (see(6.13) (6.19)). Furthermore, these distortions are higher for both types when heterogeneityis high. They are also higher when the majorities are thin ( close to 1/2)9.

Intuitively we can expect the Smith rule to be bad when …xed costs are high and theEdgeworth rule to be bad when heterogeneity is high and majorities thin. Let us comparemore formally those rules. We denote the price elasticity for the Smith rule at = 1.From (6.9) (6.23) we obtain immediately :

9

The independence of the Edgeworth rule with respect to the …xed cost is due to the fact that weconsider only the case where individual rationality constraints are not binding. This is also the reasonwhy the Edgeworth rule which …nances the project from direct payments from consumers is …rst bestoptimal if = 1.




For K > 0 and = 1, the Edgeworth rule is …rst best optimal and the Smith rule isnot. For close to 1, if

> 1

(6.24)

the Edgeworth rule’s advantage increases with ; if

<

1(6.25)

the Edgeworth rule’s avantage decreases with suggesting that political second degreediscrimination may become dominated by proportional marginal cost pricing with budgetbalance.

When …xed costs decrease, 1

increases and for a given price elasticity of demand(6.25) may be satis…ed. Similarly when the price elasticity decreases. Therefore, under(6.25) when heterogeneity increases, the Smith rule improves relatively to the Edgeworthrule. Example 1 of Appendix 6.2 shows that for a high enough heterogeneity the Smithrule dominates.

For > 1 and K = 0, the Smith rule is …rst best optimal and the Edgeworth rule isnot.

Then,dW E

dK = 1 (6.26)

dW S

dK =

8>>>>><>>>>>:1

1 (1)

S00(q11)+

(1)

(S00(q12))

q11+(1)q12

9>>>>>=>>>>>;

(1 )

8>>>>><>>>>>:

1

1

(1)(1)

S00(q21)+

(S00(q22))q12+(1)q22

9>>>>>=>>>>>;

< 1 (6.27)

As K increases, the Edgeworth rule improves relatively to the Smith rule and eventu-ally becomes better. The larger is K , the more useful is price discrimination for coveringcosts without creating too large distortions between marginal prices and marginal costs.So despite the fact that second degree price discrimination opens the possibility of dis-cretionary political discrimination, when …xed costs are large enough discrimination isbetter (see example 2 in Appendix 6.2). The distortions due to the discretion imbeddedin the Edgeworth rule become less damaging than the distortions due to proportionalmarginal cost pricing when the …xed cost is large enough. This is simply because they

are independent of the …xed cost as noted above.A way to decrease the discretion imbedded in second degree price discrimination may

be to impose a pooling contract (q; T ) selected by each majority. To the …rst order around




= 1, this pooling contract is equivalent to the Edgeworth rule. To the second order itis dominated by the Edgeworth rule (see Appendix 6.1).

A further way to …ght discretion is to impose a single quantity-transfer and cover costswith a uniform transfer. We refer then to the Egalitarian rule and index it by Eg . ThenT = q + K and expected welfare is :

W Eg =h

+ (1 )(1 ) +

(1 ) + (1 )

i

S (q ) q K

yielding

S 0(q ) =

+ (1 )(1 ) + h

(1 ) + (1 )i

and

dW Eg

d

=1

=h

(1 ) + (1 )i

S

d2W Eg

d 2

=1

=h

(1 ) + (1 )i2 S

02

(S 00):

For = 1, the Edgeworth and Egalitarian rules coincide and we obtain immediatelyIn a neighborhood of = 1, the Egalitarian rule dominates the Edgeworth rule if :

h(1 ) + (1 )

i2

>2 1

:

h(1 ) + (1 )

i:

This condition holds in particular of close enough to 1/2. If the size of the majoritiesis not large enough, the political distortions of the Edgeworth rule are greater than thee¢ciency distortions of the Egalitarian rule. Since for close to 1, the Smith rule isdominated, the Egalitarian rule is then the best rule so far.

Consider now the Hotelling rule (index H ) when we take into account the cost of …nancing the de…cit with distortionary taxes. Let 1 + be the cost of public funds. TheHotelling rule is then characterized by

S 0(q 1) = (6.28)

S 0(q 2) = (6.29)

a cost of public de…cit, (1 + )K , and a welfare

W H = E

nh

S (q 1) q 1

i+ (1 )

hS (q 2) q 2

io (1 + )K (6.30)

dW H

dK = (1 + ) (6.31)

dW H

d

=1

=h

(1 ) + (1 )i

S: (6.32)

Suppose that is such that the Smith rule and the Hotelling rule coincide for = 1.As increases, if

>

1



6.5. PROJECT SELECTION AND PRICING RULES 127

the Hotelling rule dominates, if

<

1the Smith rule dominates.

As …xed costs increase, the social costs of the Hotelling rule (due to the distortionaryfunding) are linear in those costs, while those of the Smith rule (due to distortionarypricing) are increasing non linearly. For …xed costs low enough, the Smith rule dominates.Also for large enough, the Hotelling rule dominates the Edgeworth rule which thensu¤ers from high political discrimination (see example 1 in Appendix 6.2).

6.5 Project Selection and Pricing Rules

In Section 6.4 we have examined the limits of marginal cost pricing when public funds arecostly. In this case, the cost of funding through indirect taxation must be compared withthe distortions of political discrimination. Actually the main criticism voiced against mar-ginal cost pricing is the political discretion it creates when …xed costs can be manipulatedto …nance with public funds projects which are not socially valuable.

Suppose for example that the …xed cost can take two values K; K , with probabilities and 1 and K > K . Suppose that, when K = K , the project should not be realizedwith the Hotelling rule, i.e., for = or = 1 :

hS (q 1()) q 1()i+ (1 )hS (q 2()) q 2()i < (1 + ) K (6.33)

with

q 1() = arg maxq

hS (q ) q

iq 2() = arg max

q

hS (q ) q

ibut that it is realized if funding of the …xed cost is uniform and if type 2 has the majoritybecause

S (q 2()) q 2() (1 + ) K > 0 (6.34)

while it is not realized if type 1 has the majority

S (q 1()) q 1() (1 + ) K < 0: (6.35)

When K = K it is done in both cases. The expected loss due to the political manip-ulation of the Hotelling rule is then

(1 )(1 )

(1 + ) K (1 )

hS (q 1()) q 1()

i

hS (q 2()) q 2()

i(6.36)

where 1 is the probability of majority 2.Under the Smith rule, the project is (here) always realized10 when it should be

S (q 1( 1)) 1q 1( 1) > 0 (< 0) (6.37)10 Of course, as already mentionned this is not always the case. A general theory would take into

account the lost opportunities induced by such a rule.




if ( 1 1)q 1( 1) + (1 )q 2( 1) = K ( K ) (6.38)

S (q 2( 2)) 2q 2( 2) > 0 (< 0) (6.39)

if ( 2 1)

h(1 )q 1( 2) + q 2( 2)

i= K ( K ) (6.40)

However, consumption distortions occur with an expected loss of :

Z 1

hq 1(b) + (1 )q 2(b)

idb

+(1 ) Z 2h(1 )q 1(b) + q 2(b)idb: (6.41)

Clearly, depending on the value of ; ; K; K , either of the two regimes can dominate.Suppose we have parameter values so that they are equivalent. Let us see the marginale¤ect of an increase of both …xed costs.

For the Hotelling rule the marginal loss is:

(1 )(1 )(1 + ): (6.42)

For the Smith rule, it is:

q 1( 1) + (1 )q 2( 1)i d 1

dK

+(1 )

(1 )q 1( 2) + q 2( 2)

d 2

dK

: (6.43)

Di¤erentiating (6.38) and (6.40) and denoting 1 (resp: 2) the price elasticity of globaldemand when majority 1 (resp. 2) happens, we have :

hq 1( 1) + (1 )q 2( 1)

i

d 1

dK = 1=

1

1 1

11

h(1 )q 1( 2) + q 2( 2)

i

d 2

dK = 1=

1

2 1

22: (6.44)

We obtain:The Smith rule dominates the Hotelling rule when …xed cost increases if

(1 )(1 )(1 + ) >

1 111

1

+1

1 212

2

(6.45)

In the symmetric case, = 1=2 for 1; 2 close to 1 and for a constant elasticity of

demand, (6.45) simpli…es to :

(1 )(1 + ) >

2

1

1

1

2

: (6.46)



6.6. CONCLUSION 129

The Hotelling rule is dominated by the Smith rule if the cost of public funds is large,

the probability of a bad project is large, the elasticity of demand is low. Clearly, Smith didnot take into account the elasticity of demand, i.e., assumed implicitely a zero elasticityin which case the superiority of his rule is obvious. Also, we see from (6.41) (6.42) thatfor 1 and 2 close to 1, the e¢ciency losses of the Smith pricing rule are second orderwhile the e¢ciency loss of bad projects being realized remain of the …rst order, and indeed(6.46) is then satis…ed.

6.6 Conclusion

In a world of complete information where transfers between social groups do not carrylarge deadweight losses, even if the democratic game leads to politicians who favor theirelectorate, economists should help politicians optimize their objectives. As majoritieschange, economic agents will see their relative positions change, but the average utilitylevels will not be too far from optimal11.

In a world of asymmetric information and incentive constraints, transfers betweensocial groups may become very costly leading to poor average performances. The dis-cretion allowed by the Constitution enables a majority to capture some rent but thisis very costly for the other group. In this world two striking results emerge about theeconomists-politicians relationships. First, by working for politicians (for example by pro-viding information) economists may help the politicians’ agenda of favoring a majority at

the expense of the other groups, leading to a worse outcome on average. Secondly, theeconomists have an alternative way for being socially useful. By suggesting constitutionalrules which decrease the discretion of politicians even at the cost of some e¢ciency losses,economists can enhance expected social welfare12.

As an example we have shown that despite the ine¢ciencies of the allocation of re-sources it embodies, the constitutional constraint of the Smith rule can improve expectedwelfare because it dominates alternative rules which open too large opportunities of po-litical discrimination. Indeed, it is particularly interesting from a political economy per-spective since it prevents both the political manipulations of …xed costs, Adam Smith(1776) was worried about, and the cross-subsidies manipulations William Vickrey (1948)

had emphasized.

11 The argument here requires that the Pareto frontier be fairly ‡at and that risk aversion be not large.12 The budget balance rule discussed today in the USA is an example of such a rule (see the pioneered

work of the Virginia school (for example Brennan and Buchanan (1977)).




Appendix 6

A.6.1 The Edgeworth rule versus a pooling contract selected by each majority.Under the Edgeworth rule and majority 1, we have by di¤erentiating (6.13) (6.14).

dq 1d

=1

=(1 )

S 0

S 00;

dq 2d

=1

= S 0

S 00

and the second derivative of welfare with respect to at = 1, with majority 1 is :

(1 )(2 1)

S 02

(S 00):

Similarly, di¤erentiating (6.18) (6.19) we obtain :

dq 1d

=1

= 0 ;dq 2d

=1

=1

S 0

(S 00)

and a second derivative of welfare

(2 1)

S 02

(S 00)

and an expected second derivative

d2W E

d 2

=1

=(2 1)

S 02

(S 00)

h(1 ) + (1 )

i:

Under pooling, majority 1 (i.e. > 1=2) solves :

max h

S (q ) T i

T = q + K

or S 0(q 1) = and T 1 = q 1 + K .

Majority 2 solvesmax

hS (q ) T

iT = q + K

or S 0(q 2) = and T 2 = q 2 + K .Expected welfare is :

n

h

S (q 1) q 1 K i

+ (1 )h

S (q 1) q 1 K io

+(1 )n(1 )hS (q 2) q 2 K i+ hS (q 2) q 2 K iodW P

d

=1

=n

(1 ) + (1 )o

S



6.6. CONCLUSION 131

From abovedq 1

d =1

= 0 ;dq 2

d =1

= S 0

S 00

andd2W P

d 2

=1

= (1 )(2 1)S 02

(S 00):

Then

d2W E

d 2

=1

d2W P

d 2

=1

= (2 1)

(1 ) + (1 )

(1 )

S 02

(S 00)

(2 1)(1 )

S 02

(S 00

)

0




A.6.2 Examples:Example 1:

S 0(q ) = 10 q K = 15 = 3=4 = 1 = :1

For large enough the Smith rule dominates the Edgeworth rule.

For large enough the Hotelling rule dominates the Egalitarian rule and the Edge-worth rule.



6.6. CONCLUSION 133

Example 2:

S 0(q ) = 10 q = 3=4

= 1 = 3 = 1

For K large enough the Edgeworth rule dominates the Hotelling rule and for K evenlarger the Smith rule.

.



Chapter 7

Toward a Political Theory of theEmergence of EnvironmentalIncentive Regulation

“There is yet no satisfactory theory about the emergence of incentive basedmechanisms.”

Hahn (1990).

7.1 IntroductionA large number of instruments have been considered to regulate polluting activities -Pigouvian taxes, quotas, subsidies for pollution reduction, marketable emission permits,1

deposit refund systems,2 assignments of legal liabilities,3 etc. As a result, the choiceof policy instruments has become one of the major questions debated in environmentaleconomics.4 Most of the discussion has taken place within the benevolent social maximizerparadigm. But, starting with Buchanan and Tullock (1975), the necessity of lookingfor political economy explanations of the choice of instruments has been recognized. 5

However, dissatisfaction remains. Lewis (1997) concludes his survey as follows: “I see thenext progression in [environmental regulation] as being a positive analysis asking whichkind of environmental policies will be implemented under information and distributionconstraints when special interests try to intervene to a¤ect policy.”

The purpose of this chapter is to use the methodology of this part of the book toconstruct a formal political economy theory of environmental regulation. Economists’general preferences for sophisticated incentive mechanisms is reconsidered in a political

1 Crocker (1966) and Dales (1968a, 1968b) …rst proposed marketing emission permits.2 See Bohm (1981).3 There is a large literature on this topic; see in particular Segerson (1995), Boyer and La¤ont (1996,

1997) and the references therein. See also Gupta, Van Houtven and Cropper (1996) for an empiricalanalysis of EPA’s decisions regarding the cleanup of Superfund sites.

4

Cropper and Oates (1992) devote a large part of their survey to this question. See also Segerson(1996) and Lewis (1997).

5 Beyond the debate about the Buchanan-Tullock paper (Yohe (1976), Dewees (1983), Coelho (1976)),see also Boyer (1979), Noll (1983), Hahn (1990), Hahn and McGartland (1989).

135



136 CHAPTER 7. ENVIRONMENTAL INCENTIVE REGULATION

economy approach resting on two main features: private information of economic agents,which explains the rents accruing to them as functions of policy choices, and the incom-

plete contract nature of constitutions, which explains the need for politicians as residualdecision makers.

Incomplete information is by now well understood as being a major obstacle to …rstbest e¢cient regulation. It is only recently that the mechanism design approach has beendeveloped for environmental economics.6 A revelation mechanism can be viewed as acommand and control instrument and nevertheless, it is clearly optimal here: once anoptimal revelation mechanism has been obtained, the question of its implementation byvarious economic instruments or institutions, such as regulatory proceedings, taxes andmarkets, arises but, by de…nition, those institutions implement then the same allocationas the command and control approach.7

In such a framework the question of instrument choice is empty. Such a questionoften arose in the literature because authors were not careful enough in de…ning theirinstruments. For example, Yohe (1976) correctly shows that the alleged di¤erence betweenquotas and price controls in Buchanan and Tullock (1975) disappears when instrumentsare appropriately de…ned. He writes: “When the equivalent quantity control is properlyspeci…ed, both the economist’s general preference for taxation and the regulatee’s generalpreference for quotas will disappear.”

Two types of meaningful comparisons of instruments are then possible. In the …rsttype, one considers constraints on instruments (the analysis should explain the originof these constraints) and various constrained instruments can be compared. This is the

essence of Weitzman’s (1974) comparison of prices and quantities in a situation whereasymmetric information calls for non-linear prices as optimal instruments, as Roberts andSpence (1976) pointed out. Another example is the case of non-convexities due to negativeexternalities.8 There, quotas are equivalent to non-linear taxes. Pigouvian (linear) taxesare then dominated by quotas. Similarly, taxes and subsidies which are equivalent whenthey are accompanied with appropriate lump sum transfers di¤er in their absence withrespect to the long run, entry and exit decisions of …rms. 9

In the second type, one considers instruments which could be equivalent in the com-plete contracting framework and one introduces imperfections elsewhere in the economythat cannot be corrected by the regulator (then a good explanation of this inability of the

regulator must be given). This is the case in Buchanan’s (1969) example of a pollutingmonopolist when the subsidies required to correct monopolistic behavior are not available.Then, the Pigouvian tax is clearly dominated by a quota which implements the secondbest tax, as devised for example by Lee (1975) and Barnett (1980), and which dependson the …rm’s market power.

A systematic analysis of instrument choice should then be conducted in well de…nedsecond best frameworks, which are all methodological shortcuts of an incomplete contract

6 See Baron (1985a), La¤ont (1994) and Lewis (1997). Early applications were essentially reinterpretingGroves mechanisms by treating environmental externalities like public goods (see for example Dasgupta,Hammond and Maskin (1980)).

7

See La¤ont (1994) for an example.8 See Starrett (1972), Baumol and Bradford (1970).9 See Kamien, Schwartz and Dolbear (1966), Bramhall and Mills (1966), Kneese and Bower (1968),

and Dewees and Sims (1976).



7.2. THE BASIC MODEL 137

analysis. Constraints such as limited commitment, renegotiation-proof commitment, col-lusion, favoritism, and multiprincipal structures10 should be considered. Political economy

constraints can be viewed also as a special case of this methodology. The lack of …nely-tuned constitutional control of the politicians (the incomplete contract feature) who haveprivate agendas introduces ine¢ciencies in the regulatory decision process. It then maybecome desirable to impose constraints on politicians which favor particular instrumentsor to force the use of apparently crude instruments.

Section 7.2 presents the model which introduces pollution in our basic set up. Section7.3 develops this model taking as given the delegation of environmental policy to politicalmajorities. More speci…cally we compare the policy consisting in the choice of a singlepollution level, a typical command and control regulation, with the policy consisting inthe choice of a menu of pollution-transfer pairs, a typical incentive regulation. We deter-

mine the conditions under which the higher discretion associated with the second policyis compensated by its greater e¢ciency potential. Section 7.4 explores the foundation of the delegation of environmental policy to politicians. Section 7.5 extends the model to asituation where two types of interest groups, stakeholders in the …rm and environmental-ists, may bene…t from the capture of the government through the size of information rentsthat the regulation mechanisms leave them. The distortions due to the political processare studied in this more general model, as well as the impact of a dynamics of reelectionbased on campaign contributions and the comparison of instruments is extended to thiscase. Concluding comments are gathered in Section 7.6.

7.2 The Basic Model

We consider a natural monopoly which is delegated the realization of a public projectwhich has social value S and costs C (; d) = (K d) where K is a constant, d is the levelof pollution accompanying the completion of the project, and is a cost characteristicwhich is private information of the …rm. For a given pollution level, measures thee¢ciency of the …rm in realizing the project, a higher meaning a higher cost.

Two alternative assumptions are then possible regarding the cost of reducing pollution.The more e¢cient the …rm is, either the more e¢cient it is also in reducing pollution or theless e¢cient it is in that regard. In terms of a general cost function C (; d), if we assume

C > 0, we have the choice between C d < 0 and C d > 0. In order to obtain explicitsolutions and carry out numerical simulations, we choose a speci…c cost function whichcorresponds to C d < 0. This assumption seems to be the most interesting because, witha one-dimensional asymmetry of information, the positive correlation between ability toproduce and to reduce pollution seems more compelling than the alternative assumptionand leads to more striking results. However, we will point out how our results changewith the alternative assumption C d > 0. We assume that can take two values f; gwith = and is the probability that = .

Let t be the compensatory monetary transfer from the regulator to the …rm which hasthen a rent equal to

U = t (K d) :10 See Baron (1985b) for an early study of the distortions due to the uncoordinated activities of two

regulators in the context of environmental problems.




The social disutility of pollution is V (d) (with V 0 > 0, V 00 > 0). Consumers’ welfare is

S V (d) (1 + ) t:

The utilitarian social welfare is then

W = S V (d) (1 + ) (K d) U: (7.1)

We assume that S is large enough to make the realization of the project always de-sirable. Under complete information, a benevolent social welfare maximizer would setV 0(d) = (1 + ) and t = (K d) to nullify the rent of the …rm which is socially costlybecause > 0. The chosen pollution levels would depend on and .

Under incomplete information about , the …rm’s individual rationality and incentive

compatibility constraints must be taken into account. Only the type- …rm receives a rentthat is equal toU =

K d

;

where d is the pollution level requested from the less e¢cient type …rm by the separatingregulation mechanism

(t; d); (t; d)

. The …rm of type can always pretend to be of type

and realize the project with a pollution level of d at a cost of (K d); since it is entitledto a transfer t(K d) (K d), it realizes a pro…t (rent) of at least ( )(K d), adecreasing function of d, which must then be a lower bound on its welfare or pro…t whenit acts according to its real type. Note that this rent decreases with the pollution level of the ine¢cient …rm.11

The optimal pollution levels obtained from the maximization of the expected valueof social welfare (7.1) under the informational constraints can be characterized by thefollowing program:

max(d;d) W (d; d) =

S V (d) (1 + )(K d) (K d)

+ (1 )

S V (d) (1 + )(K d)

:

(7.2)

yielding:V 0(d) = (1 + )

V 0(d) = (1 + ) + 1 :

(7.3)

7.3 Controlling the Discriminatory Power of Politi-

cians through Constraints on the Choice of In-

struments

We have a continuum [0; 1] of agents in the economy. As in Chapter 5, let represent eachperiod the measure of consumers who do not share the …rm’s rent, the non-stakeholders,

11

This feature which follows from our assumptions on the cost function (C > 0; C d < 0) will implythat to reduce the costly rent of the e¢cient …rm, one should let pollution increase. However, this strikingresult would be reversed with the alternative assumptions (C > 0; C d > 0) as in C (; d) = K d=, or(C < 0; C d < 0) as in C (; d) = K d.



7.3. CONTROLLING THE DISCRIMINATORY POWER 139

and 1 be the measure of those who share the rent, that is, the stakeholders. Let be drawn independently each period, taking the value 2 (1

2; 1) with probability 1

2and

1 with probability 12 . When = , the non-stakeholders majority, of measure ,is in power; when = 1 , the stakeholders majority is in power and the measure of this majority is also .

We will assume that politicians have the discretion of using their private informationabout the economy as exampli…ed here by , the social cost of public funds, whose distri-bution is common knowledge but whose value is either observed by the government (themajority in power) only or is commonly observed ex post but cannot be made veri…able bya court. We consider the value of either to be a proxy for speci…c economic conditionsthat the government in power is better equipped to observe (from con…dential reports of the public service bureaucracy, for example) or to refer to complex economic conditions

which cannot be written in a constitutional contract.The constitutional contract may on the other hand impose constraints on the choice

of instruments for pollution abatement. We want to compare two instruments. The…rst, corresponding to a rather sophisticated incentive regulation of the …rm is a menu of abatement levels and associated transfers in which …rms and will selfselect themselves,and the second, corresponding to a single abatement level based on E, the expected valueof , and imposed on both types of …rms. In the …rst case, we let the political majoritiesdecide on the menu of abatement levels while in the second case, they are constrained bya unique level. In each case, they can use their private information on .

Let us consider …rst the sophisticated separating mechanism. If = , we have

majority 1 which maximizes the welfare of non-stakeholders who bene…t from the project,su¤er from the pollution externality and must pay taxes to …nance the project (the costof the project plus the rent of the …rm), namely12

(S V (d) (1 + ) t) =

S V (d) (1 + ) (K d) (1 + ) U

: (7.4)

This objective function overestimates the social cost of the …rm’s rent relative to (7.1)since 1 + > . Similarly, if = 1 , majority 2 maximizes the welfare of stakeholderswho are similar to type 1 agents except that they share the …rm’s rent, namely

(S V (d) (1 + ) t) + U =

S V (d) (1 + ) (K d)

1 +

1

U

:

(7.5)This objective function underestimates the social cost of the …rm’s rent since 1 +

1= < .13

Majority 1 maximizes over the pollution levels the expected value of the welfare of non-stakeholders given by (7.4), that is solves:

max(d;d) W 1(d; d) =

S V (d) (1 + )(K d) (1 + )(K d)

+(1 )

S V (d) (1 + )(K d)

:(7.6)

12

This formulation presumes that the majorities cannot change the funding of …rms through indirecttaxation which is uniformly spread across all agents.

13 We assume that 1 + 1= > 0. Otherwise, we would have to take into account the agents’individual rationality constraints, since majority 2 would like to make U as large as possible.




HenceV 0(d1) = (1 + )

V 0(d1) = (1 + ) + (1 + ) 1

;(7.7)

with associated transfers given by t = (K d1) and t = (K d1)+(K d1). Majority2 maximizes similarly W 2(d; d), the expected value of stakeholders given by (7.5). Thisleads to:

V 0(d2) = (1 + )

V 0(d2) = (1 + ) + (1 + 1=) 1

:(7.8)

We obtain (assuming that each majority is in power half the time) the expected social

welfareE W (d; d) =

1

2E W (d1; d1) +

1

2E W (d2; d2) (7.9)

where W (dm; dm) is the expected level, with respect to the …rm’s type, of social welfare(7.1) evaluated at pollution levels chosen by majority m as a function of .

Comparing (7.3), (7.7) and (7.8), we observe that the pollution level of the moree¢cient …rm is optimal whatever the majority in power since d1 = d2 = d. But thepollution level of the less e¢cient …rm is either too large (under a non-stakeholders majority government) or too low (under a stakeholders majority government): d1 > d

> d2.

These apparently surprising distortions need some explanations. Since both majorities

take fully into account the social cost of pollution V (d), they di¤er only in their treatmentof the information rents accruing to the stakeholders of the more e¢cient …rm. Majority1 (non-stakeholders) overvalues the social cost of the …rm’s information rent (it uses aweight of (1 + ) instead of ) because it does not share these rents. For that majority,the cost of inducing abatement from the less e¢cient …rm, which is the source of the rentof the more e¢cient …rm, is therefore larger than its social cost net of the rent. Majority1’s regulation therefore leads to too much pollution from the less e¢cient …rm because itdoes not value the positive e¤ect of a more stringent abatement level d on the e¢cient…rm’s rent. In contrast, majority 2 (stakeholders) undervalues the social cost of the …rm’sinformation rent (it uses a weight of (1 + 1=) < ) because it captures the totalityof that rent. For that majority, the net cost of inducing abatement is less than its socialcost. Majority 2’s regulation leads therefore to too little pollution from the less e¢cient…rm.

We consider now the case of a non discriminating pollution abatement mechanismthat the constitutional contract may impose on the politicians. The latter have then amore limited discretion for promoting the interest of their constituency. Each majoritycan now select only a single abatement level, rather than a menu of pollution abatementand transfer levels.

If the non-stakeholders majority is in power, it now solves

maxd

W 1(d) = [S V (d) (1 + )E(K d) (1 + )(K d)] (7.10)

yielding

V 0(d1) = (1 + ) E + (1 + ) = (1 + ): (7.11)




Similarly, the stakeholders majority chooses a pollution level d2 characterized by

V 0(d2) = (1 + )E + (1 + 1=) = (1 + ) 1 : (7.12)

We obtain an expected social welfare level given by (assuming that each majority is inpower half the time):14

E W (d) =1

2E W (d1) +

1

2E W (d2) (7.13)

where W (dm) is the social welfare (7.1) evaluated at the single pollution level chosen bymajority m as characterized by (7.11) and (7.12).

The emergence of the delegated incentive separating mechanism (DIM) hinges on itsex ante comparison with the delegated pooling mechanism (DPM) obtained above. Wecarry out this comparison for small asymmetries of information represented by .

: For close enough to , we have E W (d; d) > E W (d), that is, the dele-gated (separating) incentive mechanism (DIM) chosen by the political majori-ties dominates the delegated pooling mechanism (DPM) selected by politicalmajorities if and only if

var() > H (; ; E) 2

1

22 1 + 2 2(1 )E (E)2: (7.14)

The proof of this proposition along with all other proofs in this chapter is given in theappendix to this chapter.

In this context of political delegation, the emergence of the sophisticated separatingincentive mechanisms discriminating between the pollution abatement levels requestedfrom the di¤erent …rms, will be associated with increases in E, var() and and withdecreases in . When E or var() are large, the larger sensitivity of the separatingincentive mechanism dominates. Increases in have two e¤ects. A larger implies astrong concern for rents accruing to the …rm with probability but also larger distortionsfrom social welfare maximization in the objective function of the majorities since

W (d1; d1) =W 1(d1; d1)

+ (K d1) (7.15)

W (d2; d2) =W 2(d2; d2)

+ (1

1

) (K d2): (7.16)

It turns out that the second distortions are larger and therefore a large favors a nondiscriminating policy (DPM).

Similarly, increases in the asymmetry of information have a priori an ambiguous

e¤ect. However, we can show both in the case of a quadratic V (d) function and with14 Again, d2 < d < d1, where d is the optimal non discriminating pollution abatement level under the

same informational constraints.




Figure 7.1THE DIFFERENTIAL EXPECTED WELFARE

E W (d) E W (d; d)as given by (7.13) and (7.9) as a function of

for V (d) = 14

d4, E = :4; var() = 0; = :8; K = 5; = 1; = :85

-bb-error = =

: For close to , majority 1 prefers the optimal DIM over the optimal DPM i¤

var() > H 1(; ; E) 1

2

2

2 1 2E (E)2 (7.17)

while majority 2 does it i¤

var() > H 2(; ; E) 2

1

2

2

2 1 2(1

)E (E)2 (7.18)

Comparing H 1(), H 2() and H (), we obtain directly the following corollary:: We have

H 1

(;

; E) < H (;

; E) < H 2

(;

; E): (7.19)The non-stakeholders (majority 1) are more active proponents of delegating discre-

tionary power to politicians over environmental policy, that is of a DIM scheme, than




the stakeholders in environmentally risky businesses (majority 2). Majority 1 prefers aDIM scheme as soon as the variance of reaches the threshold H 1() while majority 2

still prefers to stick to the DPM scheme until the variance of has reached the higherthreshold H 2(). Indeed, the net cost of pollution abatement is higher for majority 1 andtherefore raises the value of the more e¢cient incentive pollution abatement mechanismDIM above that of the cruder DPM as soon as H 1() is reached. If unanimous approvalis needed for constitutional reform in favor of a sophisticated separating incentive mech-anism with delegated discretion, it will happen less often than socially desirable becauseH 2() > H (), that is, because of the resistance of the stakeholders in environmentallyrisky businesses.

7.4 Delegating Discriminatory Power to the Politi-cians

The gain from delegating discretionary power to politicians comes from the use they canmake of their information, which in the present context is their knowledge of the social costof public funds . The cost of such delegation is the excessive ‡uctuation of their decisions(d; d) as a function of , as private agendas are taken into account by successive majorities.Alternatively, the constitutional convention may decide not to delegate such discretionarypower but instead impose an incentive mechanism ((t p; d p); (t

p; d

p)) determined at the

constitutional level to maximize expected social welfare. This incentive mechanism can

be characterized as the solution to the social maximization program

max(d;d) W (d; d) =

S V (d) (1 + E)(K d) (E)(K d)

+(1 )

S V (d) (1 + E)(K d) (7.20)

yieldingV 0(d p) = (1 + E)

V 0(d p

) = (1 + E) + (E) 1

:(7.21)

The pollution levels d p and d p now depend on E.At the constitutional level, the choice then is between imposing a separating incen-

tive regulation mechanism which maximizes expected social welfare on the basis of theexpected value E, a mechanism that we will denote as a constitutional incentive mecha-nism (CIM), or delegating to the political majorities the choice of a separating incentiveregulation mechanism which will then be a function of the value of , that is, the dele-gated separating mechanism DIM. In the latter case, the choice of pollution regulationmechanisms will re‡ect private agendas. The emergence of the latter delegated incen-tive mechanism which depends on hinges on its ex ante comparison with the formerconstitutional incentive mechanism.

: The di¤erence in expected welfare between the CIM and the DIM converges to 0 as ! 0 and var() ! 0. For a given , the CIM dominates if var() is small. Fora given var(), the DIM dominates if is small.



7.5. MULTIPLE PRIVATELY INFORMED INTEREST GROUPS 145

Clearly, the CIM dominates the DIM chosen by the majorities when the variance of is small for a given level of asymmetric information, as represented by . Indeed,

the CIM is optimal when var() = 0 while the DIM is not. By continuity, for lowlevels of the variance in , allowing political majorities to use the observed value of inchoosing ex post an incentive mechanism generates little social value but it generates asigni…cant social cost given the pursuit of private agendas. As var() increases, the valueof adjusting policies to the realized value of increases and therefore it may eventuallybecomes better to leave political majorities greater latitude in setting policies and choosingthe mechanism.

Similarly, for a given variance in , the delegation of authority to politicians is so-cially valuable and indeed optimal if = 0. By continuity, for small values of ,the delegation of authority allows the politicians to …ne tune the choice of the incentive

mechanism to the realized value of while the pursuit of their private agendas generateslittle unwarranted distortions in pollution abatement. Since is small, maximizing anymajority welfare function is almost equivalent to maximizing the social welfare functionbecause there are (almost) no rents. Again, as increases, for the same given varianceof , one expects that the distortions generated by the pursuit of private agendas willeventually exceed the bene…t of …ne tuning the incentive abatement mechanism chosenby the majorities and will therefore lead to the dominance of the CIM.

It has been suggested that one of the main concerns of politicians is to remain in powerthrough reelection. One may wonder what e¤ects such reelections concerns have on therelative social welfare value of di¤erent regulation regimes from an ex ante constitutional

point of view. We will model in the next section the interaction between reelectionobjectives and the pursuit of private agendas by assuming that the probability of reelectionis negatively a¤ected by the pursuit of private agendas.

7.5 Multiple Privately Informed Interest Groups

In the previous sections we have seen how the delegation of environmental policy to politi-cians enables them to distribute information rents to interest groups. In this section wewant to explore the extent to which competing interest groups may mitigate the distor-tions in the allocation of resources that politicians might …nd pro…table. For this purpose,

we extend the model by introducing, in addition to reelection concerns of majorities, …rstthe …nancing of political coalitions or majorities through campaign contributions and sec-ond an information asymmetry regarding the damages of pollution. In the same way as is private information of stakeholders, the disutility of pollution is now assumed to beV (d) with 2 f; g, = and is the probability that = .16 The parameter is private information of the environmentalists, who su¤er the pollution damage, haveno stake in the polluting …rm and will be compensated for the cost of pollution. Thiscompensation assumption should be interpreted as a reduced form formulation of a polit-ical constraint on the level of hardship that a majority can impose on the minority; thisassumption can also be interpreted as a threshold under which civil disobedience would be

triggered. Since is private information of the environmentalists who are compensatedfor the cost of pollution, they will also be able to capture an information rent. This is

16 As for , the value of is assumed to be drawn anew every period.




one reason why the environmentalists will here favor higher pollution levels which providethem with higher information rents. Their information rent is:

U 1 = s V (d)

where s is the transfer from the government. The stakeholders who do not su¤er thepollution damage have an informational rent of:

U 2 = t (K d):

The taxpayers who are now distinct from stakeholders and environmentalists have utility:

U 3 = S (1 + )(t + s):

Assuming that each group (environmentalists, stakeholders, taxpayers) represents 13

of the population, utilitarian social welfare is proportional to:

W = U 1 + U 2 + U 3 = S (1 + )

(K d) + V (d)

(U 1 + U 2 + U 3): (7.22)

Under complete information, the optimal pollution is now characterized17 by V 0(d) = .Under incomplete information a revelation mechanism is now a triple fd(; ), t(; ),s(; )g. The relevant incentive compatibility and individual rationality constraints are:

E ft(; ) (K d(; ))g E ft(; ) (K d(; ))g

E ft(; ) (K d(; ))g 0E fs(; ) V (d(; ))g E fs(; ) V (d(; ))g

E fs(; ) V (d(; ))g 0

Assuming Bayesian Nash behavior of stakeholders and environmentalists, the revela-tion mechanism which maximizes expected social welfare

W (!d ) = E ; [S (1 + )((K d) + V (d))] U 1 U 2 (7.23)

under the above incentive and individual rationality constraints is characterized by

V 0

(d(; )) = +

1+

1

V 0(d(; )) =

V 0(d(; )) = + 1+

1

+

1+

1

V 0(d(; )) = + 1+

1

:

(7.24)

Let us assume that the two interest groups use a share of their information rent ascampaign contributions to in‡uence politicians. We consider now a two period model. In

17 Having an individual rationality constraint for the environmentalists amounts to and should beinterpreted as assuming that they are indemni…ed at a social cost of (1 + ). This is why we obtainnow V 0 (d) = instead of V 0 (d) = (1 + ).



7.5. MULTIPLE PRIVATELY INFORMED INTEREST GROUPS 147

period 2, majority 1 is able to favor the interests of environmentalists by maximizing thesum of taxpayers’ utility and environmentalists’ utility,

W 1(!d1) = W (

!d1) U 2 (7.25)

that is, by not including in its objective function the information rent of the stakeholders,

where!d1 =

d1(; ); d1(; ); d1(; ); d1(; )

. Similarly, if elected, majority 2 is able

to favor the interests of the stakeholders of the …rm by maximizing the sum of taxpayers’utility and stakeholders’ utility,

W 2(!d2) = W (

!d2) U 1 (7.26)

that is, by not including the information rent of the environmentalists.Let us assume that each majority makes campaign contributions C 1 and C 2 as a …xedproportion , assumed equal for both majorities, of their average rents: C 1 = U 1 andC 2 = U 2, with U 1 = [V (d(; ))+(1 )V (d(; ))] and U 2 = [(K d(; )) +

(1 )(K d(; ))]. These campaign contributions a¤ect the probability of winning theelection that follows. For majority 1, the probability of winning is assumed to be:

=1

2+

1

2g (U 1 U 2) (7.27)

where g is a parameter representing the importance of campaign contributions in the

electoral process. The stake of winning the election for period 2 is now, for majority1, E 1(

!d1 ;

!d2) = W 1(

!d1) W 1(

!d2) and, for majority 2, E 2(

!d1 ;

!d2) = W 2(

!d2) W 2(

!d1).

Hence, majority 1 maximizes

W 1(!d1) + E 1(

!d1 ;

!d2) (7.28)

leading to

V 0( bd1(; )) =

+

1+

1 1

2

E 1g

(1+)(1)V 0( bd1(; )) =

V 0( bd1(; )) = + 1

+ 12

E 1g (1+)(1 )

+ 1+

1

12

E 1g (1+)(1)

V 0( bd1(; )) = +

1 + 1

2E 1g (1+)(1 )

:

(7.29)

Let! bd1 =

bd1(; ); bd1(; ); bd1(; ); bd1(; )

.18 In comparison with the static case,

the environmentalist majority increases the pollution levels in all cases, except in thecase (; ). The reason is that it now wishes not only to decrease as in the static case the

stakeholders’ rent (with respect to the social optimum) because it undervalues this rent inits objective function, but also to increase its own rent in order to increase its probability

18 One should note that the second period pollution levels can be obtained from (7.29) with = 0.



7.6. CONCLUSION 149

The presence of multiple interest groups may transform valuable reforms toward delegatedincentive mechanisms into undesirable reforms because these powerful mechanisms raise

the stake of political con‡icts generating additional distortions.

Figure 7.2THE DIFFERENTIAL EXPECTED WELFARE

E W ( bd) E c cW (

! bd )as given by (7.33) and (7.30) as a function of

for V (d) = 12

d2; E = 1; var() = 0; = :6; = :6; K = 5; g = 1; = :75

-bb-error = =

7.6 Conclusion

We have interpreted the political economy of environmental policy as an analysis of theeconomic implications of politicians’ discretion in pursuing the private agendas of theirconstituencies: some voters are more concerned than others by pollution, some voters

have stakes in the information rents of the polluting …rms.Sophisticated environmental policy depends on non veri…able variables that cannot be

contracted upon in the Constitution. Consequently it must be delegated to politicians,




thereby creating an incentive problem when politicians’ motivations are to stay in powerby pleasing to a certain degree a majority of voters rather than maximize social welfare.

We have shown that the larger the social cost of public funds i.e., the larger is E andthe greater the variability of economic variables (var(), , ) is, the more valuable‡exibility is and therefore the greater the delegation of authority to politicians should be.However, the thinner majorities are (the lower is) or the larger the information rentsare (the larger and/or the larger are), the more the politicians’ objectives are biasedaway from maximizing social welfare, providing a justi…cation of cruder environmentalpolicies which leave them less discretion.

Reelection considerations lead to con‡icting in‡uences on this basic trade-o¤. If,through reputation e¤ects and a better social control, pursuing excessively private agen-das today is costly for the next election, more sophisticated environmental policies may

emerge as socially optimal. On the other hand, if the campaign contributions favoringreelection are important (large g) and signi…cantly related (large ) to the informationrents of the various interest groups, politicians are led to greater distortions to favor evenmore the interest groups supporting them. When this is added to the waste of campaigncontributions themselves, it favors giving up sophisticated policies which become costlypolitical stakes. Depending on the relative importance of these con‡icting e¤ects of reelec-tion considerations, a longer term view in politics (larger ) may favor (if the reputatione¤ect dominates the combined g-e¤ect and -e¤ect) or not (otherwise) the emergence of sophisticated market based or incentive mechanisms.

The approach developed in this chapter could be extended to other types of social

and economic regulations. It should also be broadened by considering more detailed andrealistic electoral processes and by introducing various institutions (bureaucracy, courts,: : :) which mitigate the incentive problems associated with the delegation of public policyresponsibilities to political majorities.20

20 See in particular Breyer (1992) and Pollak (1995).




where V 0(d0) = (1 + ).Consider now the DPM scheme where the political majorities are restricted to choosing

a single abatement level as a function of . We obtain from (7.11) and (7.12)

dd1

d

=

=1 +

V 00(d0)

anddd2

d

=

=1 +

V 00(d0):

The social welfare, when majority 1 is in power, is given by

W (d1) = W 1

(d1) + (K d1)

and similarly, the social welfare, when majority 2 is in power, is given by

W (d2) =W 2(d2)

+

1

1

(K d2):

Hence,dW (d1)

d= (1 + )(K d1)

dd1

d

and dW (d2)

d= (1 + )(K d2)

1

1

dd2

d:

We therefore obtaind2W (d1)

d2

=

= (1 + 2 )(1 + )

V 00(d0)

andd2W (d2)

d2

=

= (1 + +

2 )(1 +

)

V 00(d0):

Hence the expected second derivative at = in the case of a DPM scheme (assumingagain that each majority is in power half the time) is given by

d2E W (d)

d2

=

=

2

12

2

+ 1 2 + 2(1 )E + (E)2 + var()

V 00(d0):

Therefore, the second derivative of the expected social welfare under the DPM scheme is(1 ) times the second derivative of the expected social welfare under the DIM schemeas given by (7.34). Those derivatives are of the sign of the numerator which is positivei¤ (7.14) holds. If var() > H (), the DIM dominates the DPM for close to andvice-versa if var() < H (). Q.E.D.

A.7.2: Proof of Proposition 7.2



7.6. CONCLUSION 153

We want to compare the expected welfare of each majority under a DPM imposed bythe Constitution and under a DIM to determine the eagerness of each majority to support

the latter constitutional rule. So we want to compare

E W 1(d) E W 1(d; d)

andE W 2(d) E W 2(d; d)

for close to . First note that both di¤erences and their …rst derivatives with respectto vanish at = 0. So we consider second derivatives. Straightforward computations(the proof follows steps similar to those in the proof of proposition 7.1 lead to

E @ 2

W 1

(d)=

@2 E @

2

W 1

(d; d)=

@2 i¤ var() > H 1(; ; E)

and similarly,

E @ 2W 2(d)=

@2 E

@ 2W 2(d; d)=

@2 i¤ var() > H 2(; ; E): Q:E:D:



Part III

Coalition Formation andConstitutional Design

155



157

“Recently David Easton has o¤ered a de…nition that combines all these and,besides, …ts politics into the general scheme of social sciences. Politics, hesaid, is the authoritative allocation of value. . . ”,

Riker (1962), p. 10.

“the greater part of the study of the authoritative allocation of value is reducedto the study of coalitions.”

Riker (1962), p. 12.



158



Chapter 8

Optimal Constitutional Response toCoalition Formation

“It does not follow, because all of the individuals in a group would gain if theyachieved their group objective, that they would act to achieve that objective,even if they were all rational and self interested”

M. Olson (1965), p. 2

8.1 Introduction

Politics is about collective decision making. To understand how interest groups formto in‡uence the political process of collective decision making, one must understand thenature of the transaction costs a¤ecting coalition formation. Olson (1965) has argued thatsmall groups have lower per capita transaction costs for example, and this argument isoften used to explain why taxpayers often do not form an interest group while managersof an industry do. To model Olson’s intuition we need a theory which makes thesetransaction cost endogenous contrary to the modeling of Chapter 2 to 5. We believethat asymmetric information between agents who want to enter collusive agreements isone major force explaining the transaction costs within coalitions.1 In this chapter weexplain a methodology2 to write group incentive constraints when colluding partners have

private information. It provides an important step towards a systematic analysis of groupincentives in organizations such as governments and a framework to model Olson’s ideas.3

The literature on collusion in collective decision mechanisms started with Green andLa¤ont (1979) who proved that Groves mechanisms (which are individually incentivecompatible) are not robust to the formation of coalitions when agents share freely their

1 In his study of political coalitions using cooperative game theory, Riker (1962), p. 77 also insists onthe role of uncertainty but in a di¤erent direction: “The uncertainty of the real world and the bargainingsituation forces coalition members to aim at a subjectively estimated minimum winning coalition ratherthan at an actual minimum. In decision-systems large enough so that participants do not know eachother or what each is doing, the actual size and weight of a coalition may be in doubt, if only because of

lack of communication and because of participants’ inability to estimate each other’s weights”.2 This methodology was …rst developed in La¤ont and Martimort (1997) and (1999).3 However, in this book we will not formalize the dependence of transaction costs on the number of

members in an interest group.

159



160 CHAPTER 8. OPTIMAL CONSTITUTIONAL RESPONSE

private information. Still with dominant strategy mechanisms, for which agents commu-nicate only their own private information, La¤ont and Maskin (1980) show that, with a

continuum of types, only pooling decision rules can be implemented. Cr er (1996) showsthat, even if one takes into account asymmetric information within coalitions, Grovesmechanisms are not collusion-proof.

Maskin (1977) obtained very positive results for Nash implementation (i.e., undercomplete information of the agents) even with no restriction on agents’ characteristics byshowing that any monotonic social choice rule satisfying no veto power was implementablein Nash equilibria. In the same environments and with at least three alternatives, Maskin(1979) showed that any social choice rule satisfying no veto power is not robust to collusion(i.e. is not implementable in strong Nash equilibria).

In this chapter we will study, in a Bayesian setting4, horizontal collusion between two

interest groups who try to manipulate collective decision making de…ned by constitutionalrules.

In Section 2 we present the model which allows for correlation of the private piecesof information for the two interest groups. When the interest groups do not collude,their Bayesian-Nash maximizing behavior in mechanisms proposed by the constitutionallevel does not put any restriction on the set of interim individually rational allocationsthat can be achieved by the Constitution whatever the (non-zero) degree of correlation .Under Bayesian implementation, the ‡exibility of available monetary transfers enables theConstitution to obtain information revelation at no cost. E¢ciency does not con‡ict withincentives. A discontinuity then holds at a correlation coe¢cient of zero. We know that

in this "independent" case, the principal cannot reach the complete information optimumwhereas he can do it for any degree of non zero correlation. Section 2 explains within ourmodel this result due to Cr er-McLean (1988) in a context of auction mechanisms.

Section 3 discusses the various issues raised by the modeling of collusion with softinformation and justi…es the choices made in our analysis. When interest groups canshare costlessly their private information, Section 4 provides a precise framework wherethe characterization of the additional incentive constraints due to collusion follows thetradition of Green and La¤ont (1979) and others. It follows that the complete informationoptimum cannot be reached anymore as the collusion-proof constraints prevent the use of Cr er-McLean mechanisms. When the degree of correlation becomes small, this restores

the continuity of the optimal mechanism at = 0 and calls for distortions even whencorrelation becomes perfect. A second lesson from this section is that the usual approachimplicitly restricts the mechanisms used by the principal to mechanisms for the revelationof only the (original) private information of the agent (before joint disclosure). Section 5considers more general mechanisms which elicit the information obtained by agents aftertheir joint disclosure of private information. Then, the complete information optimumcan in general be reached.

In Section 6 we model collusion under incomplete information, provide a collusion-proof principle with soft information, characterize the collusion-proof constraints and theoptimal constitutional mechanism. Again, this optimal mechanism restores continuity at = 0 through the working of collusion-proof constraints. Furthermore, when correlationbecomes perfect the principal approaches the e¢cient allocation contrary to what is ob-

4 See La¤ont and Maskin (1979) for preliminary work on collusion with Bayesian Nash behavior.



8.2. THE MODEL 161

tained in Section 4. It shows the crucial role of the transaction costs inside the coalitiondue to asymmetric information. As correlation becomes perfect, these transaction costs

turn out to be so e¤ective that collusion-proof constraints become slack. Section 7 con-cludes by outlining the numerous directions for further research opened by the analysisof this chapter.

8.2 The Model

We consider now an extension of Chapter 2 with a benevolent Constitution or principal

and two politicians suppliers of essential inputs necessary to perform a two stage produc-tion process. Each politician is fully integrated or captured by the …rm he controls. Wewill refer to the politician-…rm pairs as the agents for simplicity. When the Constitutionwants to produce a quantity q of …nal good, agent 1 produces a quantity q 1 of an interme-diate good (good 1) which is used by agent 2 to produce a quantity q 2 of …nal good (good2). The production technologies are Leontie¤ and one-to-one, and we denote q = q 1 = q 2.

Each agent has private information about its constant marginal cost i. These marginalcosts (1; 2) are drawn from a joint common knowledge distribution with discrete support = f; g, with = > 0, and we denote

p11 = Pr(1 = and 2 = )

p12 = Pr(1 = and 2 = )

p21 = Pr(1 = and 2 = )

p22 = Pr(1 = and 2 = ):

Let = p11 p22 p12 p21 be the measure of correlation which is assumed to be nonnegative. For simplicity we restrict the analysis to the symmetric case where p12 = p21 6= 0.

As usual, we denote the utility of agent i by:

U i = ti iq; i = 1; 2

where ti is the monetary transfer received from the constitutional level.Social welfare is

W = S (q ) (1 + )(t1 + t2) + U 1 + U 2 = S (q ) (1 + 2)q t1 t2:

We adopt the following notation: the index 1 refers to an e¢cient type and the index2 to an ine¢cient type. Then, tij is the transfer received by a type i agent when the otheragent is of type j; q ij is the production level with a type i agent and a type j agent.

The complete information social optimum is characterized by:

S 0(q 11) = 2(1 + )

S 0(q 12) = S 0(q 21) = (1 + )( + )

S 0(q 22) = 2(1 + )

t11 = q

11 t

12 = q

12 t

21 = q

12 t

22 = q

22:

Note that t12 6= t21 even though q 12 = q 21. The transfer t12 (resp. t21) is received bythe e¢cient (resp. ine¢cient) agent when there is a pair of e¢cient and ine¢cient agents.




Under asymmetric information about the production characteristics (1; 2), the Con-stitution can exploit the correlation of types to design a mechanism with yardstick com-

petition which extracts all the agents’ information rents and achieves the complete infor-mation optimum. Below, we characterize the transfers which implement this solution.

From the revelation principle we can restrict the analysis to revelation mechanismswhich are truthful and interim individually rational in the Bayesian sense. Using symme-try, a revelation mechanism is de…ned by

t11; q 11; t12; t21; q 12 = q 21; t22; q 22:

First we write the incentive constraints. For a agent, it must be the case that heprefers to tells the truth than lying when he anticipates that the other agent is telling thetruth, i.e.

p11 p11 + p12 (t11 q 11) +

p12 p11 + p12 (t12 q 12)

p11

p11 + p12(t21 q 21) +

p12 p11 + p12

(t22 q 22): (8.1)

Indeed p11 p11+ p12

(resp. p12 p11+ p12

) is his belief that the other agent is of type (resp. of

type ) when he is himself of type . Multiplying by p11 + p12 we can rewrite (8.1) as:

p11(t11 q 11) + p12(t12 q 12) p11(t21 q 21) + p12(t22 q 22): (8.2)

Similarly, we obtain for the incentive constraint of type and the individual rationalityconstraints of type and respectively:

p21(t21 q 21) + p22(t22

q 22) p21(t11

q 11) + p22(t12

q 12) (8.3)

p11(t11 q 11) + p12(t12 q 12) 0 (8.4)

p21(t21 q 21) + p22(t22 q 22) 0: (8.5)

The Constitution wishes to maximize under the constraints (8.2) to (8.5) expectedsocial welfare

p11(S (q 11) 2q 11 2t11) + 2 p12(S (q 12) ( + )q 12 (t12 + t21))

p22(S (q 22) 2q 22 2t22): (8.6)

We obtain a special case of the Cr er-McLean (1988) theorem.5

For 6= 0, the Constitution achieves the complete information optimum.Proof: We can …nd transfers which saturate the four constraints, i.e., which satisfyincentive compatibility without leaving any expected rent at the interim stage to anyagent. Indeed, for 6= 0, the following system is invertible because the determinant is2. 26666

66664

0 0 p11 p12

p21 p22 0 0

p11 p12 0 0

0 0 p21 p22

3777777775

2666666664

t11

t12

t21

t22

3777777775

=

2666666664

( p11q 21 + p12q 22)

( p21q 11 + p22q 12)

( p11q 11 + p12q 12)

( p21q 21 + p22q 22)

3777777775

: (8.7)

5 See also McAfee and Reny (1991), Riordan and Sappington (1988).



8.2. THE MODEL 163

The transfers that implement the complete information solution are obtained by solv-

ing (8.7) for 6= 0.

t11 =p22( p11q 11 + p12q 12) p12( p21q 11 + p22q 12)

t12 =p11( p21q 11 + p22q 12) p21( p11q 11 + p12q 12)

t21 =p22( p11q 21 + p12q 22) p12( p21q 21 + p22q 22)

t22 = p11( p21q 21 + p22q 22) p21( p11q 21 + p12q 22)

We observe that as p12 goes to zero, all ex post rents uij = tij iq ij go to zero. Withpenalties and rewards which converge to zero one can achieve the optimum.

At the opposite, if goes to zero, then t11 and t21 go to 1 and t12 and t22 go to+1.

It may not be surprising that, when agents are very similar, it is relatively simpleto extract their rents by yardstick competition. The more intriguing result is that theresult remains true for any degree of correlation of types, even if it is in…nitesimal. Themechanism exploits the risk neutrality of the agents by specifying extreme rewards and

penalties. A agent faces, when he tells the truth, an extreme reward if the other agentis a agent and an extreme penalty if the other agent is a agent. And similarly for a agent when he is associated with a agent and a large reward if he is associated with a agent. Those numbers can be arranged in such a way that he always wants to tell thetruth.

The result raises two concerns. First, it is not realistic to think that unbounded penal-ties (or even unbounded rewards) can be implemented because of the limited resources of the agents (or the principal). Second, a striking discontinuity occurs at = 0. Indeed forindependent types, the Constitution cannot achieve the complete information optimum(while it can for any in…nitesimal degree of correlation).

For the independent case, de…ne

= Pr(1 = ) = Pr(2 = ):

Then

p11 = 2; p12 = p21 = (1 ); p22 = (1 )2:

Following the methods of Chapter 2, we obtain the optimal mechanism characterizedas follows:

S 0(q I 11) = 2(1 + )

S 0(q I 12) = (1 + )( + ) +

1

S 0(q I 22) = 2(1 + ) +2

1 :




The Constitution gives up information rents to the -agents and, to decrease thoserents, distorts production downward (q I 12 < q 12; q I 22 < q 22).

Continuity at = 0 can be restored by imposing exogenous limited liability constraintsfor the agents

tij k for any i;j;

or limited resources constraints for the principal

tij k for any i;j:

In this chapter, we will explore a di¤erent solution. The ability to extract all the rentsfrom agents through yardstick competition is susceptible of triggering collusive behavior.The principal will have to take into account not only individual incentive constraints but

also coalitional incentive constraints. A by-product of the analysis will be to restore thecontinuity of the optimal mechanism at = 0.

8.3 Modeling Collusion

Modeling collusion requires a large number of choices. What is the timing of informa-tion ‡ows and of contracting: do agents learn their private information before or aftercontracting with the principal or the ringmaster, do colluding partners contract with theringmaster before or after contracting with the principal? Does collusion entail sharinginformation or not and, if it is possible to share information, does it happen also without

collusion? Do the colluding parties have access to an uninformed third party, the ringmas-ter, to organize their collective response to the mechanism proposed by the Constitution,or does the o¤er of collusion comes from an informed partner? Is the colluding contractbinding, can it use monetary transfers or should it be self enforcing because colludingcontracts are illegal? Are there transaction costs in these illegal contracts?

In this chapter we will o¤er two examples of such modeling, bearing in mind that eachparticular problem requires careful attention to the details of this modeling.

In the two cases the timing will be as follows:

Agents

obtain theirprivate

information

Constitution

o¤ers

mechanism

G

Agents

accept or

reject

G

Agents

share

or not

information

An uninformedringmaster

o¤ers a

collusion

contract S

G S is played

First, each agent i, i = 1; 2 learns its type i. Then the Constitution (principal) o¤ersa revelation mechanism6 G that we write as q (~1; ~2), t1(~1; ~2), t2(~1; ~2) where ~1 and

6 One can show (La¤ont-Martimort (1999)) that, in the case of no sharing of information betweenagents there is no gain to expect from a more general mechanism (see also Section 8.5). However, weassume that G cannot be conditional on an announcement by the agents of the collusion contract S



8.4. COLLUSION UNDER COMPLETE INFORMATION 165

~2 are the announcements of agent 1 and agent 2 respectively. If one agent rejects G thegame stops and all players get a payo¤ of zero. If both agents accept G, we will consider

two cases: in the …rst, we assume that agents have a technology enabling them to sharetheir private information; in the second case this step does not exist. Then, an uninformedthird party o¤ers to agents a collusive contract S which entails a manipulation of reportsand side-transfers maximizing the expected sum of utilities of the agents under incentiveconstraints and individual rationality constraints ensuring to agents at least as much aswhat they obtain by playing non cooperatively G. If one agent rejects S , G is played noncooperatively. Otherwise G S is played.

The most debatable assumption here is the access to a ringmaster who can enforcea contract. Using an uninformed third party as a ringmaster weakens the power of acoalition when agents share their private information because the informed parties could

commit to an informational alliance which eliminates the individual incentive constraints.On the contrary, when the colluding partners are uninformed about each other, the useof an uninformed party avoids informed principal ine¢ciencies and increases the powerof the coalition. What is more problematic in all these cases is that a binding contractis postulated, despite the fact that it is illegal. Either one must appeal to a third partylike the ma…a or to reputation in which case it should be viewed as a shortcut to a trulydynamic analysis.

The main virtue of our modeling is to allow for a collusion-proofness principle which,as the revelation principle, leads to a characterization of implementable allocations andtherefore of the optimal constitutional response to individual and group incentives.

8.4 Collusion Under Complete Information

For a given mechanism G; (q (); t1(); t2()), the ringmaster o¤ers the manipulation of reports (1; 2) and side-transfers y1(1; 2), y2(1; 2) which maximize the expected sumof the agents’ utilities under the incentive, individual rationality and balanced transfersconstraints.7 Since agents share their private information, the constraints are writtenunder complete information, so that the ringmaster’s program can be decomposed in amaximization program for each pro…le (1; 2).

(I ) max(:);y1(:;);y2(:) t1((1; 2)) + t2((1; 2)) (1 + 2)q ((1; 2))

s.t.y1(1; 2) + y2(1; 2) = 0 (8.8)

t1((1; 2)) 1q ((1; 2)) + y1(1; 2)

t1((~1; 2)) 1q ((~1; 2)) + y1(~1; 2) for ~1 6= 1 (8.9)

t2((1; 2)) 2q ((1; 2)) + y2(1; 2)

t2((1; ~2)) 2q ((1; ~2)) + y2(1; ~2) for ~2 6= 2 (8.10)

because agents coordinate their response to G. Implicitely the ringmaster is assumed to be always ableto undo mechanisms designed for inducing agents to reveal their common information S .

7 Through this assumption we consider the case most favorable to collusive behavior organized by anuninformed third party.




t1((1; 2)) 1q ((1; 2)) + y1(1; 2) U G1 (1; 2) (8.11)

t2((1; 2)) 2q ((1; 2)) + y2(1; 2) U G2 (1; 2) (8.12)

where U Gi (1; 2) denotes the utility of agent i when G is played non cooperatively undercomplete information.

Note that here the restriction to revelation mechanisms for the principal and the third-party is a strong restriction, because both know that the agents are informed and coulduse Maskin games asking each agent to reveal all his information (1; 2). We explorethese more general mechanisms in Section 8.5.

Under the above restrictions, one obtains immediately a generalization of the revelationprinciple.

The collusion-proofness principle: any Bayesian perfect equilibrium of the twostage game of contract o¤er and collusion contract o¤er, GS , can be achievedby a truthtelling revelation mechanism o¤ered by the principal such that thebest response of the third party is to o¤er no manipulation of reports and noside-transfers.

Proof: Consider ~G = GS for the optimal collusion contract S o¤ered by the third partywhen the principal o¤ers G. Then, ~G is a truthtelling revelation mechanism such that thenull-collusion contract (no manipulation of reports; no side-transfers) is the best responseof the third party. Suppose it is not the case. ~G is truthtelling by construction. Suppose

then that the third party can o¤er a new contract ~S which is better for the coalition for atleast some pro…le (1; 2). But then ~S S is better than S for the coalition, a contradictionof the optimality of S .

It remains to write the implications that () = i(); y1 = y2 = 0 is the optimalcontract o¤er in (I ) to describe the collusion-proof constraints.

A revelation mechanism G is collusion-proof if and only if

2(t11 q 11) t12 + t21 2q 12

2(t22 q 22)

t12 + t21 ( + )q 12 2t22 ( + )q 22

2t11 ( + )q 11

2(t22 q 22) t12 + t21 2q 12

2(t11 q 11)

Proof: Call ; 1; 2; 1; 2 the multipliers of (8.8), (8.9), (8.10), (8.11), (8.12) respectively

in (I ).Maximizing with respect to y1(1; 2) and y2(1; 2) gives

+ 1 + 1 = 0 = + 2 + 2 or 1 + 1 = 2 + 2 + :



8.4. COLLUSION UNDER COMPLETE INFORMATION 167

Maximizing with respect to (1; 2) gives

(1; 2) 2 arg max~nt1(~) + t2(~) (1 + 2)q (~)

+ 1(t1(~) 1q (~)) + 2(t2(~) 2q (~))

+ 1(t1(~) 2q (~)) + 2(t2(~) 2q (~))o

or(1; 2) 2 arg max

~(1 + + )(t1(~) + t2(~) (1 + 2)q (~))

hence the result.

It is as if the incentive constraints of the agents were not binding for the third partyand the collusion-proof constraints are identical to the incentive constraints of a mergerof the two agents. However individual incentive constraints remain in the principal’sproblem since an agent could reject the null side contract o¤ered by the third party anddeviate if the contract o¤ered by the principal was not truthtelling.8

Substituting these transfers into the principal’s objective function (8.6) we maximizewith respect to quantities and we get:

The optimal collusion-proof Constitution is characterized by:

S 0(q 11) = 2(1 + )

S 0(q 12) = (1 + )( + ) + p11 p21

S 0(q 22) = 2(1 + ) + 2 p21 p22

:

For the timing we have chosen, we must take into account interim individual ra-tionality constraints (because agents accept G before sharing information) and ex postindividual and collective incentive constraints. As usual, we can expect the ine¢cienttype’s participation constraint and the upward incentive constraints to be binding, i.e.:

t11 q 11 = t21 q 12 (8.13)

t12 q 12 = t22 q 22 (8.14)

t12 + t21 ( + )q 12 = 2t22 ( + )q 22 (8.15)

p21(t21 q 21) + p22(t22 q 22) = 0 (8.16)

From (8.13) to (8.16) we obtain:

t11 = q 11 + q 12 (8.17)

t21 = q 12 (8.18)

t22 = q 22 (8.19)

t12 = q 12 + q 22: (8.20)8 Writing dominant strategy individual and collective incentive constraints is the approach followed by

Green and La¤ont (1979).




If agents refuse the collusive contract S , they play G non cooperatively11 and obtainan expected utility U Gi (i).

The interim individual rationality constraints of -agents and -agents write:

p11[t1(11) + y1(; ) q (11)] + p12[t1(12) + y1(; ) q (12)]

( p11 + p12)U G1 () (8.29)

p11[t2(11) + y2(; ) q (11)] + p12[t2(21) + y2(; ) q (21)]

( p11 + p12)U G2 () (8.30)

p21[t1(21) + y1(; ) q (21)] + p22[t1(22) + y1(; ) q (22)]

( p21 + p22)U G1 () (8.31)

p12[t2(12) + y2(; ) q (12)] + p22[t2(22) + y2(; ) q (22)]

( p21 + p22)U G2 () (8.32)

For any mechanism G : q (); t1(); t2() that the Constitution o¤ers the (uninformed)ringmaster o¤ers the collusion contract S which maximizes the expected welfare of theagents under the above constraints, i.e. solves

(II ) maxij

i; j = 1; 2

Xij

pij[t1(ij) + t2(ij) (i + j)q (ij)]

s.t. (8.26) to (8.32).We can then follow the same reasoning as in Section 8.4: Establish a collusion-

proofness principle and characterize the collusion-proof constraints by the …rst orderconditions of the concave problem (II ) in which we state that the null collusion con-tract is the best contract that the third party can o¤er (see Appendix 8 for details). Weobtain:

A mechanism G is collusion-proof if there exists " 2 [0; 1) such that:

2t11 2q 11 t1(1; 2) + t2(1; 2) 2q (1; 2) for any (1; 2) (8.33)

t12 + t21

+ +p11 p12

"

q 12 t1(1; 2) + t2(1; 2)

+ +

p11 p12

"

q (1; 2) for any (1; 2) (8.34)

2t22 2

+

p12"

p22 + " p12

!q 22 t1(1; 2) + t2(1; 2)

2 + p12"

p22 +"

p12! q (1; 2) for any (1; 2): (8.35)

11 We assume here that following the refusal of contract S agents do not change their beliefs (see La¤ontand Martimort (1999) for a discussion of other out-of-equilibrium beliefs and a more general analysis).



8.6. COLLUSION UNDER INCOMPLETE INFORMATION 171

The optimal mechanism G maximizes expected social welfare under the individualrationality and incentive constraints and under these group incentive constraints. The

di¢culty, as usual, is to guess which are the relevant constraints.Note …rst that (8.33) and (8.34) imply the monotonicity condition

q 11 q 12: (8.36)

Similarly (8.34) and (8.35) imply

(")(q 12 q 22) 0 (8.37)

with

(") = 1 + 2 p2

12" p12 p22 + "( p11 p22 p212)

p11" p12

:

For small, (") is positive for any " in [0; 1) and we have the usual monotonicitycondition q 12 q 22. But, for large (") may be negative for " close to one. AsProposition 8.5 shows, " is a free variable in the principal’s optimization problem. So(8.37) opens the possibility of implementing production decisions with q 12 < q 22, i.e.enables the principal to violate monotonicity. This new possibility created by Bayesianincentive compatibility, rather than dominant strategy incentive compatibility we had inthe previous section, turns out to be very valuable for high correlation as we see below.

We distinguish the cases of low and high correlation.

CASE 1: Low correlation.We can expect the upward incentive constraint of the e¢cient type, the individual

rationality constraint of the ine¢cient type and the upward group incentive constraintsto be binding. Then, the optimization program of the principal can be written:

maxq ij; tij

i; j = 1; 2

p11(S (q 11) 2q 11 2t11) + 2 p12(S (q 12) ( + )q 12 (t12 + t21))

+ p22(S (q 22) 2q 22 2t22)

s.t.

p11[t11 q 11] + p12[t12 q 12] p11[t21 q 12] + p12[t22 q 22] (8.38)

2t11 2q 11 t12 + t21 2q 12 (8.39)

t21 + t12

+ +

p11"

p12

q 12 2t22

+ +

p11"

p12

q 22 (8.40)

p12[t21 q 12] + p22[t22 q 22] 0 (8.41)

q 11 q 12 q 22 (8.42)

Since q 22 q 12, " = 0 is the best choice to weaken constraint (8.40). Solving fortransfers, substituting in the objective function and maximizing with respect to quantitiesyields.




For low correlation, the optimal Constitution is characterized by:

S 0(q 11) = 2(1 + )

S 0(q 12) = (1 + )( + ) +p11

2 p12

1 +

p12 + p12

S 0(q 22) = 2(1 + ) +

p22

p11 + 2 p12

p12 p11 p12 +

:

Note that, as goes to zero,

S 0(q 12) goes to (1 + )( + ) +p11

p12

S 0(q 22) goes to 2(1 + ) +2p12

p22

i.e. we restore the continuity at = 0 with the case of independent types since then

p11 p12

=p12 p22

=

1 :

Again the collusion-proof constraints prevent the use of the Cr er-McLean mechanisms.

CASE 2: High correlation.

With high correlation, the principal can achieve a higher payo¤ than above, by ex-ploiting the (possible) non monotonicity of production. When p12 is small, the probabilityof a pair of (; ) agents is low and the principal can a¤ord a low production level in thisunlikely event. This enables him, by choosing " = 1, to weaken considerably the collusion-proof constraint (8.40) which becomes

t12 + t21

+ +

p11

p12

q 12 2t22

+ +

p11 p12

q 22: (8.43)

Since q 12 is now very low, the collusion-proof constraint

2t11 2q 11 2t22 2q 22 (8.44)

replaces (8.39).

Maximizing expected social welfare under the constraints (8.38), (8.44), (8.43), (8.41)and q 11 q 22 q 12 we obtain now

For high correlation, the optimal Constitution is characterized by:

S 0(q 11) = 2(1 + )

S 0(q 12) = (1 + )( + ) + p11

p12:

S 0(q 22) = 2(1 + ) +2p12 p22

:



8.7. CONCLUSION 173

Note that when p12 goes to zero, q 12 goes to zero12, and q 22 approaches the completeinformation optimum q 22.

So, as p12 goes to zero we approach in probability the complete information optimum.We can also check that the expected rent converges to zero. Indeed for p12 close enoughto zero

t11 q 11 goes to q 22t12 q 12 goes to q 22(1 p11

p12)

and p11(t11 q 11) + p12(t12 q 12) goes to p12q 22 which goes to zero as p12 goes tozero.

The result here is strikingly di¤erent from the case of collusion under complete infor-mation of Section 8.4. As p12 goes to zero, the cost of eliminating production when themessages are and goes to zero, since the case (; ) occurs with a probability going tozero, and the gain is that it eliminates the stake of collusion. The fear of the event (; )remains very large because the ex post rent t12 q 12 goes to minus in…nity when p12 goesto zero and such a fear is necessary for the third party to be able to induce truthtelling13.The transaction costs within the coalition become so high that the collusion constraintsbecome ine¤ective. With complete information within the coalition, this fear is eliminatedby a perfect coordination of reports.

The main conclusion here is that the transaction costs within collusion contracts due toasymmetric information can be extremely favorable for the principal. Even if a principalcould provide costlessly technologies enabling agents to learn their types, it is clear that

he should not do it for weakening collusion incentive constraints. In general there willbe a trade-o¤ between improving communication within the organization for e¢ciencypurposes and maintaining agents under incomplete information to eliminate more easilyincentives for collusion.

8.7 Conclusion

We have modeled the transaction costs existing when colluding partners want to organizean interest group. They are based on asymmetric information within the coalition andwe believe that they can provide the foundations of Olson’s theory of group behavior.Indeed, Olson (1965) stressed the free rider problem existing within groups. From therecent theory of public goods we know that the real explanation of the free rider problemlies in the combination of asymmetric information and participation constraints. La¤ontand Maskin (1979) and Myerson and Satterthwaite (1983) have shown that completeinformation e¢ciency cannot then be achieved within a group in general, and Mailathand Postlewaite (1990) proved that the ine¢ciency grows with the size of the group.Organizing the best response of a group to a mechanism o¤ered by a principal is a publicgood to be provided under incomplete information and it is not surprising that transactioncosts decrease the e¢ciency of collusion for the bene…t of the principal. It remains toextend the analysis to multiagent situations, to model the behavior of subcoalitions, to

12 q 12 0 becomes binding if S 0(0) is …nite.13 Note that even a weak limited liability constraint would prevent such a mechanism and would recreate

ine¢ciencies when p12 goes to zero.




prove that small groups may be more powerful interest groups (i.e. groups who a¤ect morethe collective decision) than larger groups because of their lower internal transaction costs.

We have stressed in this chapter the methodology enabling to extend incentive theoryto group incentive theory in a model with soft information. In so doing we have mademany assumptions, but we have provided a solid starting point for further analysis.

One major assumption is that we have assumed that colluding partners were alwaysable to coordinate their answers about their collusion contract in such a way that theprincipal was unable to elicit that information. Following the general approach of Nashimplementation, one could attempt to elicit this information with extended mechanisms.One would have to model collusion for such mechanisms and one might be able to designuniversal mechanisms which implement again the complete information optimum. Even if this were true, it would be quite unrealistic, to push so far the logic of the principal-agent

model. Either at the cost of some slight departure of the principal-agent model or with aparticular assumption of incompleteness for the principal’s contract, we are able to o¤era modeling of the transaction costs due to the possibility of collusion which is attractive.

This approach is particularly attractive for our purpose of normative political econ-omy because it enables us to extend the revelation principle. We can then characterizeimplementable allocations and consequently the optimal constitutional response to theactivity of interest groups made possible by informational asymmetries.

We can distinguish three lines of further research.The …rst one would maintain the basic framework and study the same model with

more types, more agents (raising the issue of subcoalitions), ine¢ciencies in the collusion

contract (due to the lack of a third party and particular extensive forms of bargaining)etc.The second one would model collusion with more general mechanisms used by the

principal to elicit information about collusive activities.The third one would relax the assumption of enforceable collusion contracts and look

for a self enforcement by reputation in dynamic models (see Tirole (1992) and Martimort(1997) for a start).

With this new methodology we have made available a theory of endogenous transactioncosts in the formation of coalitions. It o¤ers one line of attack for understanding whysome coalitions form and others do not, and therefore a theory of interest groups and someelements for designing institutions able to cope with these interest groups. It is by now

well understood that contracts a¤ect the performance of institutions. We can push thisinsight one step further. The side-contracts that agents can design within an institution,which themselves depend on the information structures, a¤ect also their performance,even if it is only indirectly because of the collusion-proofness principle. There are manytestable implications of this theory that we hope to investigate.14

14 A related stylized fact is that the occurrence of wars in Africa is known to depend on the distributionof tribes as represented by an index of ethnolinguistic fractionalisation (see Collier and Hoeer (1998)).



8.7. CONCLUSION 175

Appendix 8

A.8.1: Proof of Proposition 8.6The game tree of the game induced by the contracts G and S is as follows:

Nature chooses 1; 2

Principal o¤ers G

Agent 1

Agent 2

@ @ @ @ @ @

rejectsaccepts

Accepts Rejects Accepts Rejects

Ringmaster o¤ers S

A A A A A

T T T T T

(0; 0) (0; 0) (0; 0)

Agent 1

Agent 2

@ @ @

@ @

RejectsAccepts

A A A A A A

A A A A A A

Accepts Rejects Accepts Rejects

G S G G Gplayed played played played

We are interested in characterizing the perfect Bayesian equilibria (PBE) GS of thewhole game described above. G maps M 1 M 2 into the space of allocations (productionlevel and transfers). G maximizes the principal’s expected welfare taking into account the




continuation equilibrium of the game of coalition formation. We assume that the out-of-equilibrium beliefs remain the original beliefs. S maps the space of characteristics

(where = f; g) into the space of message spaces and side-transfers. S maximizes thesum of agents’ expected utilities under Bayesian incentive constraints, budget balance andindividual rationality constraints which ask for expected utility levels higher than thoseobtained in the truthful Nash equilibrium play of G.

The mechanism ~G = G S is a truthful revelation mechanism which implementstruthfully the PBE of G S and for which the optimal strategy of the ringmaster is too¤er the null side contract (with no manipulation of reports and no side-transfers). If itwas not the case, the ringmaster could o¤er ~S achieving higher utility levels than thoseobtained with G S which are themselves higher than those obtained playing G. Thiswould contradict the optimality of S .

Therefore to characterize all the PBE achievable by the principal, it is enough to char-acterize the revelation mechanisms which are interim individually incentive compatibleand interim individually rational and for which the best strategy of the third party is too¤er the null collusion contract. This last requirement is achieved by writing the …rstorder conditions of problem II and inserting that truthful behavior and no side transfersare optimal.

In problem II, call (1; 2); 1; 2; 1; 2; 1; 2 the multipliers associated with con-straints (8.22) to (8.32) respectively. Maximizing with respect to y1(; ) and y2(; ) weobtain:

(; ) + p11( 1 + 1) = 0 (8.45)

(; ) + p11( 2 + 2) = 0 (8.46)

(; ) + p12( 1 + 1) = 0 (8.47)

(; ) p11 2 + p12 2 = 0 (8.48)

(; ) p11 1 + p12 1 = 0 (8.49)

(; ) + p12( 2 + 2) = 0: (8.50)

Note that from (8.41) (8.42)

1 + 1 = 2 + 2 (8.51)

from (8.43) (8.44)

1 + 1 = p11 p12

2 + 2 (8.52)

from (8.45) (8.46)

2 + 2 = p11 p12

1 + 1: (8.53)

Maximizing with respect to 11; 12; 21; 22

11 2 arg max

11

n p11(t1(11) + t2(11) 2q (11)) + ( 1 + 1) p11(t1(11) q (11))



8.7. CONCLUSION 177

+( 2 + 2) p11(t2(11) q (11)

oor using (8.47)11 2 arg max

11

ft1(11) + t2(11) q (11)g (8.54)

12 2 arg max

12

n p12(t1(12) + t2(12) ( + )q (12)) + ( 1 + 1) p12(t1(12) q (12))

p11 2(t2(12) q (12)) + p12 2(t2(12) q (12))o

or using (8.48)

12 2 arg max12nt1(12) + t2(12) + + p11 p12

"1q (12)o (8.55)

with

"1 = 2

1 + 1 + 1:

Symmetrically

21 2 arg max

21

nt1(21) + t2(21)

+ +

p11 p12

"2

q (21)o

with

"2 = 11 + 2 + 2

:

22 2 arg max

22

p22(t1(22) + t2(22) 2q (22))

p12 1(t1(22) q (22))

p12 2(t2(22) q (22))

+ p22 1(t1(22) q (22))

+ p22

2(t

2(

22) q (

22)):

We rewrite the objective function as:

( p22 p12 1 + p22 1)(t1(22) q (22) p12 1q (22))

+( p22 p12 2 + p22 2)(t2(22) q (22) p12 2q (22)) (8.56)

Noting that at a symmetric equilibrium 1 = 2 = ; 1 = 2 = and "1 = "2 = "(8.47) (8.48) (8.49):

p22 p12 + p22 = p22(1 + + ) + p221 +

p11

p12 ( p22 + p21)

= p22(1 + + ) +

p12:




Dividing (8.53) by 1 + + we obtain:

p22 + " p12 (t1(22) + t2(22) 2) 2p12"q (22)

hence

22 2 arg max

22

t1(22) + t2(22) 2

+

p12"

p22 + " p12

q (22)

!: (8.57)

(8.50) (8.51) (8.52) (8.54) summarize the collusion-proof constraints where " is a freevariable in [0; 1).



Chapter 9

Collusion and Decentralization

“Certainly, the bene…ts derived from delegation come at a price. The principalsu¤ers welfare losses caused by opportunistic behavior on the part of his orher agents. Even under the best of circumstances, agency losses cannot beeliminated.”

Kiewiet and McCubbins (1991), p. 37.

9.1 Introduction

A major debate in the theory of government concerns its proper degree of decentraliza-tion.1 A large part of the information relevant for decision-making is dispersed amongthe members of society. The goal of organizational design is to set up the communicationchannels and to allocate authority in order to use this information in the least costly way. 2

Under delegation , the agents of the periphery have no direct communication with the cen-ter. Reports on their information must ‡ow up a hierarchy and then recommendationsfrom the center ‡ow down leaving some decision making authority at several levels of the hierarchy. In contrast, under centralization , the agents of the periphery communicatedirectly with the center which centralizes all decision-making. What are the costs andbene…ts of each of these di¤erent organizations? How are incentive problems solved un-

der each of those arrangements? What is the exact impact of communication constraintsin each case? For a given distribution of asymmetric information, what should be theoptimal form of organization?

In Section 9.2 we consider the issue of delegation when the Constitution —the principal—faces two privately informed agents who may collude. We show that, for independentprivate pieces of information and risk neutral agents, delegation entails no cost for theprincipal. Section 9.3 even shows that for a principal with bounded rationality, delega-tion may even be preferable because of the interaction of collusion constraints and limitedcommunication. Section 9.4 extends the analysis to a particular case of correlated privateinformation between the two agents. This enables us to return to the supervision model

1

See CEPR (1993) for a discussion of the related notion of subsidiarity and Kiewiet and McCubbins(1991) for an analysis of delegation in the US Congress.

2 See Baiman (1982), Baron and Besanko (1992), (1995), Cr er and Riordan (1987), McAfee andMcMillan (1995).

179



180 CHAPTER 9. COLLUSION AND DECENTRALIZATION

of Chapter 2 which is generalized to the case of soft information. Risk aversion of theagent to whom contracting is delegated (the delegated agent) creates new transaction

costs which may become a building block of a general theory of delegation. Section 9.5concludes.

9.2 The Independent Case

The model is the same as in Chapter 8, but with independent types. We show thatdelegation entails no cost.

9.2.1 The Optimal Centralized Constitution

The Constitution maximizes expected social welfare under the interim incentive constraintof a -agent and the interim participation constraint of a -agent, i.e.:

(I ) max(q ij; tij)

i; j = 1; 2

2[S (q 11) 2q 11 2t11] + 2 (1 )[S (q 12) ( + )q 12 (t12 + t21)]

+(1 )2[S (q 22) 2q 22 2t22]

s.t.

(t11 q 11) + (1 )(t12 q 12) (t21 q 12) + (1 )(t22 q 22) (9.1)

(t21 q 12) + (1 )(t22 q 22) 0: (9.2)

We note that program (I ) can be rewritten with only expected transfers:

T 1 = t11 + (1 )t12

T 2 = t21 + (1 )t22:

(II ) max(q ij; tij)

i; j = 1; 2

2[S (q 11)2q 11]+2 (1 )[S (q 12)(+)q 12]+(1 )2[S (q 22)2q 22]

2T 1 2(1 )T 2

T 1 (q 11 + (1 )q 12) T 2 (q 12 + (1 )q 22) (9.3)

T 2 (q 12 + (1 )q 22) 0: (9.4)

Solving (9.3) and (9.4) for T 1 and T 2 and substituting in (II ), we obtain:

(III ) maxq ij

i; j = 1; 2

2[S (q 11)2q 11]+2 (1 )[S (q 12)(+)q 12]+(1 )2[S (q 22)2q 22]

2(q 11 + (1 )q 12) 2(1 )(q 12 + (1 )q 22)



9.2. THE INDEPENDENT CASE 181

2 (q 12 + (1 )q 22)

hence the solutions (as in Section 8.2):

S 0(q I 11) = 2(1 + ) (9.5)

S 0(q II 12) = (1 + )( + ) +

1 (9.6)

S 0(q II I 22 ) = 2(1 + ) +2

1 : (9.7)

We observe that only the expected transfers T 1 and T 2 are determined. Therefore,we have two degrees of freedom in determining transfers. They can be used to obtainadditional properties.

a) Dominant strategy implementation and ex post individual rationality constraints3.

We can choose

t21 = q 12 t22 = q 22:

Then, dominant strategy implementation requires:

t11 q 11 t21 q 12 = q 12

t12 q 12 t22 q 22 = q 22:

We can choose:

t11 = q 11 + q 12 ; t12 = q 12 + q 22:

It implies of course Bayesian strategy implementation.

b) Collusion-proof implementation.

Reasoning as in Section 8.5 (for = 0), we know that collusion-proofness requires twoadditional constraints

2t11 2q 11 t12 + t21 2q 12 (9.8)

t21 + t12 ( + )q 12 2t22 ( + )q 22: (9.9)

Therefore, under Bayesian strategy implementation we can use the two degrees of freedom to ensure collusion-proofness.

The optimal centralized collusion-proof Constitution is characterized by (9.5),(9.6), (9.7) with associated transfers obtained from (9.1), (9.2), (9.8), (9.9).

We want to evaluate now the cost of the loss of control involved in delegating con-tracting to one agent.

3

This result is a special case of a theorem in Mookherjee and Reichelstein (1992) which gives generalconditions under which Bayesian strategy implementation implies dominant strategy implementation.This theorem is itself a generalization of a result in La¤ont and Tirole (1987) where a dominant strategyVickrey auction is shown to be equivalent to the optimal Bayesian auction.




9.2.2 Optimal Delegation

The Constitution has now no relationship with agent 2 and contracts only with agent1 who himself contracts with agent 2. We assume that agent 1 accepts or rejects theprincipal’s o¤er before contracting with agent 2. Solving the game backward, there isno loss of generality in assuming in stage 2 that agent 1 uses a revelation mechanism tocontract with agent 2.

However, it is an informed principal agent problem with private values. From Propo-sition 11 in Maskin and Tirole (1990), the principal neither gains nor loses if his type isrevealed to the agent before the game is played. So, we assume that agent 1 maximizes hisown expected utility under the participation and incentive constraints of agent 2 awareof agent 1’s type.

Let s(m); q (m) be the mechanism o¤ered by the principal to agent 1 where the messagem asked from agent 2 maps all the information he has acquired, i.e., (1; 2) 2 ,into M .

Let (1; 2) 2 M denote the message agent 1 commits to transmit to the principaland y(1; 2) the compensatory payment to agent 2. Agent 1 looks for the optimal in-ternal contract by maximizing his expected utility under the incentive and participationconstraints of agent 2, i.e. solves the program:

(IV ) max();y()

[s((1; )) y(1; ) 1q ((1; ))]

+(1 )[s((1; )) y(1; ) 1q ((1; ))]

s.t.

y(1; ) q ((1; )) y(1; ) q ((1; )) (9.10)

y(1; ) q ((1; )) 0: (9.11)

As usual we have written only the incentive constraint of the -agent 2 and the indi-vidual rationality constraint of the -agent 2.

Solving (9.10), (9.11) and inserting in (IV ) we get:

(V ) max(:)

[s((1; )) (1 + )q ((1; )) q ((1; ))]

+(1 )[s((1; )) (1 + )q ((1; ))]:

Applying again the revelation principle, we know that the Constitution can restrictitself to revelation mechanisms (s(); q ()) from into R R+ which are truthful.Writing that

(1; 2) = (1; 2)

is optimal in program (V ), we have immediately:

s11 2q 11 s(1; 2) 2q (1; 2) for any (1; 2)

s12 + + 1

q 12 s(1; 2) + + 1

q (1; 2)

for any (1; 2)



9.2. THE INDEPENDENT CASE 183

s21 ( + )q 12 s(1; 2) ( + )q (1; 2) for any (1; 2)

s22

2 +

1

q 22 s(1; 2)

2 +

1

q (1; 2)

for any (1; 2).

To these constraints, the Constitution must also add the interim participation con-straint of agent 1 before he knows agent 2’s type. Only the -agent 1’s constraint isexpected to bind, as well as the upward incentive constraints obtained above. Taking intoaccount the symmetry of the problem,4 we obtain the following optimization program for

the Constitution:

(V I ) maxq ij; sij

i; j = 1; 2

2[S (q 11) 2q 11 s11] + 2 (1 )[S (q 12) ( + )q 12 s12]

+(1 )2[S (q 22) 2q 22 s22]

s.t.

s11 2q 11 = s12 2q 12

s12

+ +

1

q 12 = s22

+ +

1

q 22

(s12 ( + )q 12 q 22) + (1 )(s22 2q 22) = 0:

Solving (V I ), we get (9.5), (9.6), (9.7) again.

The optimal Constitution with delegation is equivalent to the optimal central-

ized collusion-proof Constitution.

This proposition generalizes (trivially) the result proved in Melumad, Mookherjee andReichelstein (1995) according to which centralization (without considering the possibilityof collusion) is equivalent to delegation.5 The loss of control is costless for the principal. Indelegation, the choice of a contract by agent 1 becomes a moral hazard variable. However,it is fully anticipated by the principal, and because agent 1 is risk neutral and uninformedabout agent 2’s type, the principal achieves the same allocation as if he was controllingthis variable.6

4

One can easily show that the symmetry q 12 = q 21 and s12 = s21 is not a restriction of generality.5 See Itoh (1993), Balliga and Sjostrom (1996) for studies of delegation and collusion with moral hazard.6 It is well known that, for utility functions separable in e¤ort and risk neutral, moral hazard is

innocuous.




9.3 The Independent Case with Limits on Commu-

nicationLimits on communication is a fundamental structuring feature of organizations whichwas the main center of attention of the theory of organizations until the emergence of incentive theory. Very little research has been done to integrate those two lines of research.Green and La¤ont (1982) put constraints on the dimensionality of the messages thatcan be transmitted, while Green and La¤ont (1986) use Shannon’s information theoryto model these constraints, and study the interaction of these constraints with incentiveconstraints. One can model the processing of each signal reported as involving a …xed cost(Dye (1985)). Melumad, Mookherjee and Reichelstein (1995) model the incompleteness of communication as the possibility for the agents to report only a …nite number of messages

on their types even if these types are continuously distributed. All these approaches aredebatable, as they are imperfect shorcuts for a missing theory of bounded rationality.

We will assume (the limited communication assumption) that because of bounded ra-tionality of the principal the whole vector of types cannot be transmitted to the principal.Only the sum of the reports can be received by the principal who does not obtain theidentity of the reports.

The optimal Constitution with delegation is una¤ected by limited communi-cation.

We observed that the symmetry constraints (foonote 4) do not restrict the delegationcontract. The asymmetry of transfers is reconstructed within the agents’ relationshipsince the incentive contract o¤ered by agent 1 to agent 2 yields outcomes which vary withagent 2’s type.

The optimal Constitution with centralization (without collusion) is not af-fected by limited communication.

Proof: The optimal contract entails from the symmetry of the problem q 12 = q 21 andfurthermore we have two degrees of freedom in the choice of contracts. We can use onesuch degree of freedom to impose t12 = t21.

Limited communication alone or collusion-proofness alone do no invalidate the equiv-alence of centralization and delegation. However, when both constraints are imposeddelegation dominates centralization.

The optimal collusion-proof Constitution with centralization is a¤ected by theconstraint of limited communication. It entails:

S 0(q 11) = 2(1 + )

S 0(q 12) = (1 + )( + ) +(1 + )

2(1 )

S 0(q 22) = 2(1 + ) +

(1 ):




centralization does not. Delegation is a type of collusion in which all the bargaining powerbelongs to agent 1, while in centralization the bargaining power is split between the two

agents. If the principal can manage to create the asymmetric distribution of bargainingpowers that delegation entails, he bene…ts. The limited communication constraint betweenthe principal and the agents imposes an equal treatment under the centralization regimebetween a -agent and a -agent when there is a pair of and agents. The asymmetryof delegation eliminates this equal treatment constraint to the bene…t of the principal. 7

Because of the revelation principle delegation can only be valuable for a principal in asecond best framework. We have given here an example of such a framework by postulat-ing constraints on communication. A more general theory of the bene…ts of delegation willexplore additional second best constraints. The most traditional constraint considered isa limit of commitment for the principal.8 The literature relies then on the availability

of third parties with given preferences to present delegation as a partial solution to thecommitment problem (see Rogo¤ (1985), Spulber and Besanko (1992), Fershtmann, Judd,and Kalai (1991)). The question remains of the origin of these preferences.

An alternative is to recognize the non benevolence of the principal as we have done inPart II. Delegation can then play the same role as above (Seabright (1996)). Within thesame framework Faure-Grimaud and Martimort (1999) compare two timings of delegation(before and after elections) that they interpret as (politically) independent or dependentbureaucracies.

9.4 Risk AversionDelegation of the choice of a contract creates a moral hazard problem as we saw in theprevious section. To deal with asymmetric information agent 1 o¤ers to agent 2 a contractwhich is incentive compatible. Agent 1 is obliged to give up a rent to agent 2 and thisrent depends on the type of agent 2: it is risky from the point of view of agent 1 whoaccepts the contract with the principal before knowing agent 2’s type. If agent 1 is riskaverse a risk premium must be provided to agent 1 for him to bear this risk. This riskpremium is a new transaction cost of delegation for the principal.

We could develop this idea in the model of the previous sections. Instead, we go back tothe supervision model of Chapter 2 with two major changes in the hypotheses: the signal

obtained by the supervisor is soft as is private information in this chapter. Furthermore,we consider a noisy signal to remain close to the notations of previous sections. We willobtain a new theory of supervision with soft information.9

9.4.1 The Benchmark Model

Agent 2 is now the …rm producing the public good with a marginal cost 2 f; g wherewe also denote 1 = , 2 = . The information technology of the politician-supervisor

7 See La¤ont and Martimort (1998) for further developments.8

This constraint itself is often imposed by the Constitution. It is another example of contractuallimitation of the Constitution, which settles for a limit on the length of delegation rather than using amore complete contract.

9 See Faure-Grimaud, La¤ont and Martimort (1998) for a more detailed exposition.



9.4. RISK AVERSION 187

consists of two signal 1 and 2 with the following stochastic structure:

pij

= Pr( = i; =

j) and = p

11 p22

p12

p21

> 0:

ThenPr( = i= = j) =

pij

p1 j + p2 jfor any i; j

and we note that, from > 0,

Pr( = 1= = 1) =p11

p11 + p21>

p12 p12 + p22

= Pr( = 1= = 2):

So 1 (resp. 2) is a signal favorable to 1 (resp. 2). For simplicity we assume thatthe signal is also observed by the agent.

We assume that the politician-supervisor (agent 1) has an utility function with con-

stant absolute risk aversion V (s) = 1 ers:

The timing is like in Chapter 2. In the absence of collusion between the politicianand the …rm, the principal learns 2 f 1; 2g with zero payments to the politician whois indi¤erent between all reports.

For each value of , the principal maximizes expected social welfare under the incentiveand individual rationality constraints of the …rm, i.e.:

max(q ij; tij)

i; j = 1; 2

Pr( = 1= = j)(S (q 1 j) 1q 1 j t1 j)

+Pr( = 2= = j)(S (q 2 j) 2q 2 j t2 j)

s.t.

t1 j 1q 1 j t2 j 1q 2 j

t2 j 2q 2 j t1 j 2q 1 j

t1 j 1q 1 j 0

t2 j 2q 2 j 0:

As usual, the incentive constraint of the -agent and the participation constraint of the -agent are binding, leading to:

maxq ij

i; j = 1; 2

Pr( = 1= = j)(S (q 1 j) (1 + )q 1 j q 2 j)

+Pr( = 2= = j)(S (q 2 j) (1 + )q 2 j)

hence

S 0(q 1 j) = (1 + )

S 0(q 2 j) = (1 + ) +p1 j p2 j

j = 1; 2:

Because of the positive correlation p11 p21

> p12 p22

and q 22 > q 12. The production level when

the signal 1 is transmitted is smaller than for 2 because the posterior probability thatthe principal is facing an e¢cient type (to whom a costly information rent will have tobe given up) is higher.




9.4.2 Collusion with Complete Information

If the politician and the …rm can share their private information, and if we continueto consider revelation mechanisms s(i; j), t(i; j), q (i; j) = q ij the individual andcollective incentive constraints write:

t(1; 1) 1q 11 t(2; 1) 1q 21

t(1; 2) 1q 12 t(2; 2) 1q 22

s(1; 1) s(1; 2)

s(1; 2) s(1; 1)

s(2; 1) s(2; 2)

s(2; 2) s(2; 1)

for all i; j

V (s(i; j)) + t(i; j) iq ij V (s(i0; j0)) + t(i0; j0) iq i0 j0

for all i0; j0The fact that the supervisor has a ‡at utility function (i.e. not depending on the

production level) implies a constant payment for him and therefore from the collusionconstraints

t(1; 1) = t(1; 2)

t(2; 1) = t(2; 2):

The principal is therefore restricted to the unconditional optimum which does not usethe message about . It is characterized by

S 0(q u11) = S 0(q u12) = (1 + )

S 0(q u21) = S 0(q u22) = (1 + ) + p11 + p12 p21 + p22

:

In this informational context, if the contract is delegated to the politician, since no

rent is given up to the …rm, the politician’s utility function is

V [s(; ) q (; )]

and the function V () is irrelevant for writing incentive and participation constraints.We obtain again the non-conditional optimum, and similarly of course if we delegate thecontract to the …rm (which simply ignores the signal ).

9.4.3 Collusion under Incomplete Information

The characterization of the optimal centralization contract with collusion under incom-

plete information would follow the methodology of Chapter 8. It leads to formidablecalculations because of the asymmetry of the agents and because of risk aversion. Here,we simply compare the two types of delegation.



9.4. RISK AVERSION 189

Delegation to the Agent

Clearly, as above, there is no way to elicit the signal from the agent if he observes it, andno way for the agent to elicit the politician’s signal, if he does not observe it. We stillobtain the unconditional optimum.

Delegation to the Politician

Following Section 9.2, the politician commits to a manipulation of reports (i; j) andtransfers to the agent y(i; j), which maximize his expected utility (conditional to hisinformation j) under the incentive and participation constraints of the agent (who isassumed to have observed j).

The politician’s optimization program can be reduced to:

max(())

Pr(1j j)V [s((1; j)) 1q ((1; j)) q ((2; j))]

+Pr(2j j)V [s((2; j)) 2q ((2; j))]:

Applying the revelation principle we know that the principal can restrict himself torevelation mechanisms s(); q () which induce truthful revelation by the politician of hisinformation (i; j). Expressing the fact that the optimal () is the identity function(and using the fact that V is exponential) we obtain the incentive constraints faced bythe principal.

s11 1q 11 s21 2q 21 + q 21 (9.15)

s12 1q 12 s22 2q 22 + q 22: (9.16)

s11 1q 11 q 21 1

rlog

p11

p11 + p21+

p21 p11 + p21

er[s211q21s11+1q11+q21]

s11 1q 11 q 22 1

rlog

p11

p11 + p21+

p21 p11 + p21

er(s222q22s11+1q11+q21]

: (9.17)

The participation constraints of the politician are:

s11 1q 11 q 21

1

rlog

p11

p11 + p21+

p21 p11 + p21

er[s212q21s11+1q11+q21]

0 (9.18)

s12 1q 12 q 22

1

rlog

p12

p12 + p22+

p22 p12 + p22

er[s222q22s12+1q12+q22]

0: (9.19)

The principal maximizes, under (9.16) to (9.20), his expected utilityXij

pij(S (q ij) iq ij sij):




Expressing the solution as a function of the index of risk aversion r we obtain:

S 0(q 11(r)) = S 0(q 12(r) = (1 + ) (9.20)

S 0(q 21(r)) = (1 + ) + p11er(q22(r)q21(r))

p21 + p11(1 er(q22(r)q21(r)))(9.21)

S 0(q 22(r)) = (1 + ) +

p22

p11 + p12

p21 p11er(q22(r)q21(r))

p21 + p11(1 er(q22(r)q21(r)))

:(9.22)

We summarize the above discussion in:

a) The optimal Constitution with delegation to the politician entails (9.20), (9.21),(9.22).

b) q 21(r) (resp. q 22(r)) is an increasing (resp. decreasing) function of r. Moreover, forall r, q 21(r) < q 22(r).

c) limr!1 q 21(r) = limr!1 q 22(r) = q u22.

Figure 9.1 describes the behavior of the solution. 6

-

0

r

q 22

q sb2

q 21

Figure 9.1

When risk aversion goes to zero, we obtain the conditional optimum. Indeed, since thepolitician is risk neutral there is no need to give him a risk premium for bearing the riskassociated with the contract to the agent. The principal obtains the signal at no cost. As

risk aversion increases, a costly risk premium must be given to the politician. To mitigatethis cost the principal decreases the riskiness of the incentive payments to be made to the…rm by decreasing the spread between q 22 and q 21 i.e., by making the production level less



9.5. CONCLUSION 191

responsive to the politician’s information. In the limit as risk aversion goes to in…nity, weget the unconditional optimum. The politician observing soft signals becomes useless.

To see the sensitivity of the solution with respect to the informativeness of the signalsconsider the special case where

Pr( = 1j = 1) = Pr( = 2j = 2) = " " 1=2:

When " goes to 1/2 (uninformative signal) the solution converges to the unconditionaloptimum. There is continuity at " = 1=2 with the independent case.

When " goes to 1 (complete information) we again converge to the unconditionaloptimum (as in section 9.4). It is as if collusion is perfect.

This suggests that, if the principal can control the information structure of the politi-cian, he will provide an information structure with an intermediary level of correlation.This reminds us of Proposition 4.1.b.

Furthermore, we can observe that incomplete information between the politician andthe agent is a way to endogeneize the transaction cost of collusion that was taken exoge-nous in Chapter 2. Indeed, one can identify10 the two models with a transaction cost

k r

2

1 +

"

(1 )(1 ")

q

for ; q small. This provides a building block for a theory of organizational designwhich takes into account these transaction costs. For example, when it comes to select

who should be the supervisor among two agents, this theory favors the choice of the lessrisk averse agent to minimize the risk premium required.Finally, we note that delegation to the politician is better than delegation to the agent

in this model. More generally, governmental design will have to solve for the optimalallocation of delegation.

9.5 Conclusion

Delegation does two things. But cutting communication between the principal and one of the two agents, it makes impossible the use of Maskin games through which the principal

extracts common information by relying on the possibility of con‡icting reports. It basi-cally restricts the principal to the use of revelation mechanisms designed to elicit all theinformation of the delegated agent, both his own private information and the informationhe acquires on the other agent.

Secondly, delegation introduces a moral hazard problem since the choice of the contractbetween the delegated agent and the agent becomes non observable, and therefore nondirectly controllable. With risk neutral agents, this loss of control is irrelevant.

The combination of risk neutrality and of our way of modeling collusion under cen-tralization lead then to the absence of any e¢ciency loss in delegation. Decentralizationappears costless.

When the principal has bounded rationality and can absorb only a limited amount of information it is clear that decentralization which uses all the information may dominate

10 See Faure-Grimaud, La¤ont and Martimort (1998).




centralization which will use a limited amount of information despite the con‡icting objec-tives of the principal and the agents. Section 9.3 gives a more subtile result to the extent

that it is the combination of the collusion-proof constraints and the limited communica-tion constraints which triggers the superiority of delegation (while limited communicationalone is not enough).

When the delegated agent has risk aversion, delegation introduces a new transactioncost with respect to centralization with a risk neutral principal since the risk associatedwith the incentive compatible contract of the bottom agent must be borne by the delegatedagent who requests a risk premium.

These insights clarify the problem of delegation in government when interest groupscan form. They open an avenue of research about the optimal structuring of delegation inmore complex environments than those considered here. In particular, all the questions

we have explored in part I can be revisited with this new notion of transaction costsadapted to soft information. Beyond, these questions can be imbedded in a model of partisan politics as in Part II.



Chapter 10

Concluding Remarks

“Without commitment to a paradigm, there could be no normal science.”

Thomas Kuhn (1962), p. 100.

Economic activities as described in the Arrow-Debreu world require a political and judicial system with are left outside economic analysis. However, when public goodsare introduced, the need for collective decision making , which is more than de…ning andenforcing a judicial system, becomes blatantly clear. We have argued that such a collectivedecision process needs intermediaries which are agents of the people, either for learningabout the issues more that what ordinary people can do, or for deciding in the case of

unanticipated circumstances.The people must delegate to these intermediaries, called politicians, the dual roles of

supervision and residual decision making. This delegation raises incentive issues whichcan be analyzed at two levels.

Assuming …rst that the Constitution attempts to maximize a well de…ned notion of social welfare, the …rst di¢culty comes from the private information of politicians whichenable them to further their own private interests and to be captured by interest groups.Information is here the determinant of their power and one must study the design of governmental institutions including the selection of politicians to mitigate the costs of delegation.

Part I and Part III of the book followed this line of research. Chapter 2 showedhow the Constitution must distort economic activities to avoid the capture of politiciansby the economic interest groups they control. Incentives for politicians and bureaucratsmust be put in place and decision making must be bureaucratized to limit the stakes of collusion at levels compatible with those incentives. Chapter 3 explored to which extentthe separation of powers can raise the transaction costs of collusion and thereby facilitatethe …ght against capture. Chapter 4 studied how the design of communication channelsbetween governmental bodies must be structured and contributed to an analysis of checksand balances which stresses the dangers of reciprocal favors. All along, the modeling of collusion itself was a central question. Part I was based on Tirole’s collusion model withveri…able (hard) information which can cover only a limited set of circumstances. This

is why in Part III we returned to the central question of group incentives by proposingin Chapter 8 a new methodology for characterizing the optimal constitutional responsesto the activities of interest groups when their private information is soft and cannot be

193

d-incentives and political economy

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