Financing Organizations

Rocco Macchiavello∗

First Version: January 2005Very Preliminary and Incomplete: Comments Welcome !

Abstract

Firms are financially constrained in developed and developing coun-tries as well. The consequences of these constraints on the organizationof firms are however poorly understood. We study the financing andallocation of control rights of two linked projects when agents have noinitial cash. Because of limited liability, the optimal contract can notimprove upon simple allocations of control rights such as centralized,decentralized and external control. We emphasize that the allocation ofcontrol rights within an organization affects the financial constraintsof the organization itself and deliver comparative statics linking theoptimal allocation of control rights and pleadgeable income to the sta-bility of the environment and the degree of alignment of interest withinthe organization: these critically depend on the relative level of privatebenefits and cash flows. As an application we consider the boundariesof the firm under financial constraints, and we discuss how the frame-work can be applied to the analysis of business groups, the financingof non profit organizations and the practice of microfinance.

Keywords: Control Rights, Limited Liability, Mechanism Design,Theory of the Firm, Corporate Finance, Group Lending.

JEL Codes: D23, G32, K12, L22, O10.

∗London School of Economics, Sticerd and PSE (Joint Research Unit CNRS-EHESS-ENPC-ENS). This paper is a substantially revised version of a previous paper that circu-lated under the title ’Investor Protection and the Boundaries of the Firm’. The projectwas started during a period of visit spent at the MIT Economics Department, and hasbeen completed at IDEI: the hospitality of both institutions is gratefully acknowledged.I am especially indebted with my advisor Maitreesh Ghatak for invaluable support andwith Abhijiit Banerjee and Jean Tirole for many helpful advice. I also benefited from con-versations with Bob Gibbons, Patrick Legros, Bengt Holmstrom and Patrick Rey. E-Mail:R.Macchiavello@lse.ac.uk

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1 Introduction

There is now a substantial amount of evidence that firms are constrainedin their investment decisions in developed and developing countries as well(see e.g. Banerjee and Munshi (2004), Banerjee and Duflo (2004), Banerjee,Duflo and Munshi (2004) for firms in India, Fazzari et al. (1998) for theU.S. and Hubbard (1998) for a review of the literature1). The consequencesof financial constraints on the organization of firms in general and on firmboundaries in particular are however poorly understood.

To some extent it is obvious that the organization of a firm, through itseffects on firm activities and performance, affects how much external financecan be raised by a firm. If this was the only channel linking the financialand the organizational aspects of a firm, the two issues could profitably beanalyzed separately: for a given level of external finance it would be possibleto establish the optimal organizational form, since the organizational formwould be chosen to maximize efficiency.

There are two lines of reasonings suggesting that the financial and or-ganizational dimensions of economic activities are not orthogonal. First ofall, if parties are not cash constrained they will choose the organizationalform that maximizes ex-ante surplus. When parties are cash constrainedinstead the organizational form will in general be ex-post twisted in favorof the party that has ex-ante bargaining power, and may therefore distortinvestments and reduce social surplus2. One problem with this view is thatthe predictions of those kind of model depends on which party is assumedto have ex-ante bargaining power, a dimension which may be highly contextspecific.

This work instead focuses on a second line of arguments. We emphasizethat the organizational form itself (i.e. the distribution of control rights

1Most of the empirical literature on internal capital markets finds evidence which isconsistent with firms being constrained in the first place, although both empirically andtheoretically the main focus of this literature is on allocative efficiency within the firm.

2This is the argument in Aghion and Tirole (1994) and Legros and Newman (2004).The first paper considers a vertical relationship in which parties initially face liquidityconstraints and introduces some of the issues considered here. However it does not focuson the implications for the optimal organizational form of credit market imperfectionsand do not consider the relationship between financial structure and organizational form.Legros and Newman (2000, 2004) have a different setting in which the two parties have afixed amount of resources, and finance is needed only to transfer ex-ante rents. In theirsetting however external finance is an inefficient tool to transfer surplus and it is thereforenever used. A variant of this general argument has been proposed in the corpoate financeliterature with the idea that (contingent) allocations of control rights substitute for cash(see e.g. Aghion and Bolton (1992)).

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within an organization) affects how much money can be raised from externalinvestors. In particular we ask how two linked projects should be financedand control rights over the two projects distributed in a setting in whichthe two agents have no initial cash. We analyze a case in which the actionyielding high cash flow is perfectly observed by the two agents, but it is notobserved by any other third party (external investors and courts) and agentsmay derive private benefits from another action that yields lower cash flows.

We analyze the model taking a mechanism design approach. The firstmain result is that because of limited liability the optimal mechanism oftencannot improve over a simple allocation of ex-post control rights. Insteadof restricting attention to exogenously given allocations of control rights,we endogenously provide microfoundations for when a simple allocation ofcontrol rights replicates the optimal contract given non verifiability of thestate and limited cash of the agents. Our framework accounts for the possi-bility of collusion within the organization. The model rationalizes a varietyof allocations of control rights as optimal contracts (such as centralized anddecentralized allocations of control rights and external control).

Our second main result (a direct implication of the first one) is thatthe allocation of control rights within an organization affects the financialconstraints of the organization itself in systematic ways. The model deliv-ers comparative statics linking the optimal allocation of control rights withthe degree of stability of the environment and the degree of alignment ofinterest within the organization. The comparative statics critically dependon the relative level of private benefits and cash flows. When private ben-efits are low with respect to cash flows rents should be left using money.When money is easily transferrable within the organization the pleadgeableincome is higher if rents and control rights are distributed in a centralizedway. Centralization becomes more attractive the higher is the congruenceof interest within the organization. When private benefits are high withrespect to cash flows instead rents tend to be given distorting the courseof action followed by the organization. When this is the case it is in theinterest of external investor to maximize conflict within the organization,and decentralization more often emerges as the optimal allocation of con-trol rights and may be preferred when congruence within the organization ishigher. We emphasize that in most of the existing corporate finance modelsin which the corporation is treated as a single economic agent the effectsof the alignment of interests within an organization on financial constraintscan not even be asked. We believe instead that this may be a crucial element

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of organizational design3.As an application of our framework we consider the question of firm

boundaries under financial constraints. We show that the allocation of con-trol rights (namely putting the two projects under the umbrella of a cen-tralized firm or keeping them as two separate stand alone units) within theorganization affects the pleadgeable income of the entire organization. Whenprivate benefits mostly arise from internal trade a firm tend to pledge lowercash flows than two stand alone firms. The application sheds some newlight on the links between firm boundaries and financial structure: a firmis defined as an organization with centralized allocation of control rightsand joint liability of the financed investments (centralized finance). Cen-tralized financial structures and allocations of control rights, while possiblycorrelated, do not need to always appear together.

There are several strand of the literature to which this work is linked4. Arecent literature on internal capital markets makes a complementary point:the organizational form (e.g. conglomerates versus stand alone firms) affectshow efficiently is a given amount of resources allocated across projects. Anecessary condition for this literature to be meaningful is that the firmis financially constrained in the first place. In this recent literature thetwo papers that are closest in spirit to the present work are Inderst andMueller (2003) and Faure-Grimaud and Inderst (2005)5. There are twomain differences with respect to our approach. First of all we consider asetting in which the two projects are (economically) interdependent: in thissense our focus is especially about organizations as opposed to financial linksbetween projects. Most importantly we take a mechanism design approachin which the organizational form is endogenously derived6.

This work also contributes to the literature on the (complete contracts)foundations of control rights7. Since limited cash substantially limit the

3One can think, for instance, central trade off between coordination and incentiveswithin organizations.

4The paper mainly bridges across three recent literatures on organizational economics,on corporate finance and on the theoretical foundations for control rights.

5 Inderst Mueller (2003) building on Bolton and Sharfstein (1990) formalizes the fol-lowing intuition: financing two projects together may raise pleadgeable income since it ispossible to use cash flows from one project to buy continuation rights for the other project.However, the extra cash flows may reduce the disciplinatry role of the credit market overa centralized firm. For an excellent survey of this literature see Stein (2003).

6They also follow a mechanism design approach to determine the optimal financial con-tract. However the set of agents playing the mechanism changes with the (two exogenouslygiven) organizational forms.

7Tirole (1999) building on Aghion and Tirole (1997) presents a similar exercise ina different context in which agents do not respond to monetary incentives. This non

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power of (the optimal) complete contract, simple allocations of control rightsachieve the same pleadgeable income of the optimal contract.

This work is also linked to a recent literature on collusion in organiza-tions (Baliga and Sjostrom (1998), Laffont and Martimort (1997, 2000)). Inline with this literature we find that the possibility of collusion may push to-wards decentralization when incentives can not be given through monetarytransfers. However this result is reversed when incentives are given throughmonetary transfers.

For lack of space we only focus on an application of the present frame-work to the theory of the firm. We do not discuss in detail a list of possibleapplications. We feel however that this paper is closely related to the theo-retical literature on micro finance and to a recent literature on non profitsorganizations8.

The rest of the paper is organized as follows. In section 2 the settingis introduced and a simplified version of the model is analyzed in order tointroduce the main themes of the paper. Incidentally the example shedssome interesting lights on the question of firm boundaries. Section 3 com-pletely solves for the model using a mechanism design approach. The mainresults are presented and some example and implications discussed. Section4 provides some concluding remarks and discuss directions for future work.All the proofs are in the Appendix.

2 The Model

2.1 The setting

We consider two projects managed by two agents j ∈ {1, 2}. The two projectscan be (jointly) managed in (essentially) two ways. Ex-post one of twoactions can be taken, ai ∈ A ={a1, a2}. With probability π action a1 yieldscash flows V while action a2 yields cash flows V , with V > V . With thecomplementary probability action a2 yields higher cash flows. In order tofix ideas it is useful, but not essential, to think about these two actionsas ex-post trade taking place between the two units, or each unit tradingseparately.

responsiveness is however not essential to its argument. Rey and Tirole (2001) presents amodel in which the optimal mechanism to provide monitoring incentives can not improveover a simple allocation of control rights.

8For microfinance the closest work is Laffont and Rey (2001), while Holmstrom (1999)how insights gained in the microfinance literature can be applied to the theory of the firm.For non profit organization see Besley and Ghatak (2005).

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Ex-post trade brings private benefits. Without loss of generality I assumethat each agent j may derive private benefits b from the low cash flowaction. Conditional on action a yielding higher cash flows, four state ofnature σ ∈ B = {0, 1, 2, θ} can be realized, depending on which set ofagents derives private benefits from taking action a0 6= a. State 0 is realizedwhen none of the two parties derives private benefits from action a0. Statej ∈ {1, 2} is realized when only party j drives private benefits from actiona0. Finally, state θ is realized when both parties have private benefits fromaction a0. I allow the realization of b to be correlated across units and withthe realization of the return from trade V.

To summarize, eight state of nature s ∈ S = A × B are in principlepossible: this is the minimum amount of states required to describe anenvironment in which the state not being observable has some bite, and inwhich each of the two agents may have conflicting or aligned preferenceswith respect to the action preferred by external investors. The realized s isperfectly and exclusively observed by the two agents. A state s is representedas aσ. The ex-ante probability of realization of state s is denoted πs.

None of the two agents has initial wealth. Each project needs an initialsunk investment I = 1. I assume that external investors are on the short sideof the market, so that the mechanism maximizes the pleadgeable income. Iassume that V < 2 < V . The timing of the model is formally introduced inthe next session, where we follow a mechanism design approach.

As pointed out before, the interpretation in terms of trade taking placeseparately or between the two units, while not essential, can help in fixingthe ideas for the kind of private benefits we have in mind. In designing aproduct, the two units may find ex-post profitable (e.g. a reduction in nonmonetary costs) to tailor the good on the needs of an alternative party withrespect to the use that maximizes revenues. This can be due to a better fitof the capabilities of a unit to produce a good which is complementary tothe one produced by the other unit. As an illustration, one can think abouttwo researchers deciding wether to write a joint paper or not. While it maybe efficient for the two researcher to invest their time in alternative projects,they may find easier, or more pleasant, to work jointly. Either because ofpersonal affinity, or because they share interests or view over the subject.

Private benefits may be completely unspecific to a relationship, or tothe organization. This is the case when the realization of agent j privatebenefits is independent with respect to the action affecting agent j09.

9For now we keep the level and realization of private benefits as exogenous. We discusslater on how to think in terms of external investor protection and organizational design

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2.2 An application to the Boundaries of the Firm

Organizational form, Control Rights and Ex-Post TradeIn order to fix ideas let interpret the model as follows. Trade can (ba-

sically) take place in two forms t ∈ {i, o}: internally, i.e. between the twounits (−i) or outside, when each unit trades with a third party (−o). Giventhe interpretation that we have in mind, it is natural to index the two unitsas downstream (D) and upstream (U).

In this section we look at two basic organizational forms (allocations ofcontrol rights): vertical integration and two stand alone firms10. In the nextsession I introduce other (simple) allocations of control rights.

An integrated firm is a firm in which one party has exclusive controlrights over trade. The owner of the firm decide how trade takes place. Eachstand alone firm instead has a veto power over internal trade, i.e. each firmcan unilaterally decide to trade with another partner.

I assume that the value from trade takes two values Vt ∈ {V , V }, andV > V . With probability π, Vi = V and Vo = V . With the complementaryprobability 1 − π instead Vo = V and Vi = V . Finally, when the two unitstrade outside I assume that the (net of costs) profits of the D unit are 1

2Voand 1

2Vo for the U unit. Each of the two units can derive private benefitsfrom the low cash flows action, as described in the previous subsection.

When two stand alone firms trade separately they do not bargain. Ifthey trade internally, the price is determined through an efficient ex-postbargaining process. We follow the literature assuming that the outcomeof the ex-post negotiation process is determined according to a symmetricNash Bargaining.

In an integrated firm instead there is no bargaining since one party uni-laterally decides which action should be taken. There are two differencesbetween a vertically integrated firm and two stand alone firms. Since undera centralized structure there is no bargaining, i) the trade decision is takenunilaterally, and ii) the financial returns are entirely appropriated by the

as affecting the level and distribution of private benefits. It is also useful to keep in mindthat, since private benefits are to some extent specific to the organization, agents will notbe randomly allocated to organizations. This may have consequences for the working andthe optimal allocation of control rights in the organization.10Given our assumptions, when parties have deep pockets, the ex-post organizational

form does not matter. In fact under the assumption of ex-post efficient bargaining partiesalways agree in choosing the trade action that maximize joint surplus, taking into accountthe realization of private benefits. A simple option contract would achieve ex-post effi-ciency. Unit j set a price p, and unit j0 decide wheter to buy or sell at price p the rightto decide the action.

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party with control. In principle one could assume that not all the finan-cial returns can be appropriated. Since, at this stage, the model does nothave ex-ante non contractible investments, this simplification does not haveconsequences.

External investors and financial contractsI analyze the case in which there is a single external investor (a bank,

say) involved in the process of financing both projects. I also focus on simplefinancial contracts. In particular I assume that the bank holds a debt likeclaim Bj over the profits of unit j. In principle the repayment of Bj coulddepend on the repayment of Bj0 , i.e. joint liability should be allowed.

I assume that money is completely fungible. The bank in particular cannot holds claims which are contingent on the identity of the trading partners.Let Bj,jj be the claim the bank holds over transfers from jj ∈ {1, 2} to j,and without loss of generality let Bj,1 > Bj,2. Suppose 1 has to make atransfer. I assume that j, 1 and 2 can costlessly agree in having 1 transfermoney to 2 which than transfer money to j. This allows the coalition to savethe difference Bj,1 − Bj,2. I assume that there is a competitive supply ofparties 2, so that the difference Bj,1−Bj,2 can be shared between 1 and j11.Let us denote with ΣjBj the total claim that the bank has on the profits ofthe two units.

2.2.1 An Example

In order to keep the exposition short in this session I focus on describing howto determine the pleadgeable income for the case in which private benefitsarise only from internal trade. In the appendix we report a table illustratingthe pleadgeable income of the two organizational form for the general setting.I assume that the realization of b is independent across units.

IntegrationLet us, without loss of generality (the model is at this stage completely

symmetric), consider downstream integration. Since we assumed that V <2 the financial contract must have V < ΣjBj < V , where ΣjBj is the debtof the firm. Since private benefits are realized only for the case of internaltrade, when Vi > Vo there is no conflict between the ex-post incentives of

11 In the next session I introduce a transaction cost associated with this kind of transfersmanipulation.

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the two units and the investors. Therefore ΣjBj is repaid12. The interestingcase therefore is the one in which Vi < Vo.With probability (1−δ)2 howeverno private benefits are realized, and therefore trade occurs externally. Wenow turn to the other cases.

Case 1 With probability δ(1− δ) we have d > 0, u = 0Under this configuration if the firm trade outside cash flows are equal to

V , and D is able to retain financial benefits equal to V −ΣjBj . If instead thefirm trade inside, since cash flows are equal to V < ΣjBj financial returnswill be equal to zero, but D enjoys private benefits b. Internal trade thereforeoccurs if and only if

b > V −ΣjBj

We conclude that the bank is repaid ΣjBj if V −b > ΣjBj and V otherwise.Case 2 With probability δ(1− δ) we have d = 0, u > 0Under this configuration instead U would prefer to trade internally. The

question is to know wether U can bribeD to convince him to trade internally.This is clearly not possible since internal trade would lead to zero financialearnings and U has no wealth to compensate D for the loss V − ΣjBj . Inthis case therefore the bank is always repaid ΣjBj .

Case 3 With probability δ2 we have d > 0, u > 0Under this configuration both U and D prefers to trade inside. However

D in taking the decision only compares her private benefits b to the financialreturns V −ΣjBj .We conclude that the bank is repaid ΣjBj if V −b > ΣjBjand V otherwise.

We conclude this discussion with

Lemma 1 The maximum pleadgeable income under vertical integration isgiven by

Pint = max{V − b, V − (1− π)δ∆V }

Non Integration - Independent liabilitiesThings are here slightly more subtle. The two firms could be willing

to use third parties in order to transfer money between the two units and

12Note that we stick to this notation even if an integrated firm as a unique debt Bint =ΣBj . This is because we assume that centralized control involves joint responsabilty fordebt repayment. This need not to be the case however, as discussed in greater detail lateron.

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save the repayment of one debt Bj13. This distorsions introduced in thebargaining process geopardize the pleadgeable income that can be postedby the two firms. We have

Lemma 2 The maximum pleadgeable income under decentralization is givenby

Pdec =

(V − (1− π)(1− (1− δ)2)V2 if V >

V2

V − (1− π)δ2∆V if V < V2

Proof. In the Appendix.

When only one firm has private benefit from internal trade, this unit maytry to ”bribe” the other firm in order to trade internally. The independentfinancing here is critical. The problem for the firm with private benefits isthat as soon as some financial flows are recorded in the accounts the bankwill takeBj of it. This firm could however propose the following ”accountingtrick”: she could ask a third party (e.g. her customers) to directly pay theother firm U. This strategy is profitable for firm the first firm if b > V

2 −Bjand for the second one if V2 −Bj < V −Bj .

Corollary 3 When private benefits only arise from internal trade an inte-grated firm has higher pleadgeable income than two independent firms inde-

pendently financed if V > V2 or if V ≤ V

2 and δ ≥q

b∆V (1−π)

Proof. We have Pint ≥ V −(1−π)δ∆V. Moreover when V > V2 we have

(1 − (1 − δ)2)V2 > δ∆V since V2∆V > 1 >

δ(1−(1−δ)2) . When V < V

2 instead

δ2∆V < δ∆V and therefore integration has higher pleadgeable income if andonly if V − b > V − (1− π)δ2∆V.

Non Integration - Joint LiabilityThe problem with decentralized firms is that, since they are not jointly

responsible for the debt repayment, they may use third parties in order toavoid the repayment of a debt. In principle however firms could be ableto sign joint liability contracts. Under these contracts, if firm j does not

13The possibility of transfers through third parties also makes clear why it is legitimateto focus on symmetrc debt contracts. Firms could otherwise find jointly profitable toalways repay the debt Bj = min{Bd, Bu}.

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repay, firm j0 is responsible for repaying firm j debt. We now introduce jointliability contracts.

Since private benefits are realized only for the case of internal trade,when Vi > Vo there is no conflict between the ex-post incentives of thetwo units and the investor. Without loss of generality for any vector Bj ,the amount ΣjBj is repaid. The interesting case therefore is the one inwhich Vi < Vo. With probability (1 − δ)2 however no private benefits arerealized, and therefore trade occurs externally. When only one unit hasprivate benefits, joint liability implies that it is impossible to bribe the otherunit to chose the low cash flows action. Because of joint liability the unitwithout private benefits is left without cash flows, since ΣjBj > V . Weconclude that ΣjBj is repaid. With probability δ2 instead both units realizeprivate benefits and repay ΣjBj if and only if ΣjBj < V −2b. Note howeverthat an asymmetric contract Bj 6= Bj0 , would achieve a pleadgeable incomeiqual to ΣjBj = V − b.

Lemma 4 The maximum pleadgeable income under decentralization andjoint liability is given by

Pdec,jl = max{V − b, V − (1− π)δ2∆V }

We thus have

Corollary 5 When private benefits only arise from internal trade two standalone firms signing a joint liability contract with the bank have higher plead-geable income than an integrated firm

2.3 Discussion

The example discussed above highlights a couple of general points and havesome other implications more specific to the analysis of firm boundaries.A first general theme is that the distribution of control rights within theorganization (in the example integration versus non integration) affects thepleadgeable income of the firm. The existing literature noted that whenparties are limited in the amount of money that can be transferred thedistribution of control rights will reflect ex-ante bargaining power. In mostof the applications the resulting distribution of control rights is not efficient,i.e. does not give appropriate incentives to take actions that maximize jointsurplus. We provide a second argument for why the organizational andfinancial aspects of a firm can not be treated independently. We feel that

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since our approach de-emphasize the importance of ex-ante bargaining powerit is better suited to deliver systematic implications.

A similar exercise, but in a quite different context, is performed in In-derst and Mueller (2004). In their paper however the distribution of controlrights is exogenously given. In the next session we take a mechanism designperspective, and show that simple allocations of control rights endogenouslyarise as optimal mechanism in our environment.

In the example the divergence in interest between the investors and thetwo productive units arises from action that need bargaining, and in prin-ciple agreement, of the two units (trading inside). In a centralized firm aunit is able to impose the trade inside action relatively more often. Theadvantage of the centralized form stems from the fact that an integratedfirm can not easily ”move” money across units avoiding to repay the bank.The two units of a firm are jointly responsible for debt repayment. In somesense the model defines a firm as an organization with (some degree of)centralization in the distribution of (formal) control rights and centralized(i.e. joint) financial liabilities.

This correlation of centralized control rights and joint liability need tobe the case. In fact the two units could in principle be jointly owned andstill not being jointly financed (as it may be the case, to some extent forbusiness groups and pyramids, at least for that part of external finance thatcomes from external, possibly non voting, equity). Conversely two unitscould be separately controlled, but jointly financed. This is for instancethe case in which a firm provide some warranty for another firm, a sup-plier, for instance14. Joint financing removes the inefficiencies associatedwith decentralized firms, namely the opportunistic behavior associated withtransferring money across financially independent units.

A vertically integrated firm also has jointly responsible projects. Becauseof centralization in decisions rights the wrong action from the point of viewof investors is taken relatively more often15. The model can be extendedin order to introduce costs of joint liability. Joint liability creates an exter-nality across the two units: opportunistic behavior of one unit compromisethe financial returns of the other units. The interesting insights that canbe gained from this exercise refer to the possibility that a particular form

14Another interesting example is given by micro-finance arrangements, in which howeverthe joint liability aspect is often much more amphasized than the distribution of controlrights.15 In the next session we will introduce the possibility of private benefits arising from

both actions, so that a centralized allocation of control rights could, in principle be optimalagain.

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of allocation of control rights can be systematically associated with jointliability.

We conclude this session providing an informal definition of other allo-cations of control rights. We define

• Under J-Integration the manager of unit j has the right to implementthe action he prefers.

• Under De-Centralization each manager can refuse to trade internallywith the other unit. This is equivalent to assume that action a1 re-quires unanimity.

• Under Joint-Ownership each manager can refuse trade outside. Thisis equivalent to assume that action a2 requires unanimity.

• Under External Control an uninformed party has the right to decidethe action. Since this party is uninformed she selects the action thatis most likely to yield high cash flows.

3 Optimal Mechanism and Foundations for Con-trol Rights

In th previous section we compared the pleadgeable income of two differentallocations of control rights: decentralization and centralization. We as-sumed that cash flows are ex-post verifiable, so that it is possible for partiesto make transfers to the bank contingent on the realization of cash flows,but we did not allow the bank to write contracts contingent on the identityof the trading parties.

On the ground that the state is not verifiable by third parties, we as-sumed that agents are restricted to contracts that allocates decisions rightsover the optimal action to be taken, i.e. we assumed that the feasible con-tracts are highly incomplete. In principle however parties could design anex-ante mechanism in which they report to a third party messages on therealization of the state of the world, and actions are taken accordingly tothe reported messages.

In this section we solve the previous model allowing the informed partiesj (the agents in charge of the two units) to send messages about the realizedstate of the world (the optimal action as that delivers higher cash flows andthe distribution of private benefits bj). Investors chose ex-ante a mechanismthat specifies the (probability with whom a particular) action (has) to be

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taken, and transfers from the investors to the party j which are contingenton the realization of cash flows, as function of the messages sent by the twoinformed parties. The natural interpretation for these transfers is that thebank has a claim over profits.

Since parties do not have money we restrict attention to the case of nonnegative transfers. The bank cannot extract monetary payments beyond therealized cash flows, but can in principle leave some extra money to (some)of the two agents in order to provide incentives and improve the pleadgeableincome. We assume that the bank has all the bargaining power, and thatthe mechanism is designed to maximize pleadgeable income16.

As it is well known, the set of choice function that can be implementedheavily depends on the equilibrium concept used to solve the mechanism.We make the following assumption about the environment.

Assumptions

1. Nash implementation. In each realized state of nature the mecha-nism must be individually incentive compatible, i.e. truthtelling mustbe a Nash Equilibrium.

2. Collusion Proofness. On top of individual incentive compatibilityconstraints we impose coalitional incentive compatibility constraints.That is, for a candidate message report to be an equilibrium, it mustbe impossible for the two parties to achieve a (Strictly) Pareto Su-perior allocation by coordinating their reports. When the mechanismspecifies that some money is left on the table to provide incentives, par-ties can transfer to one another this money, possibly incurring sometransaction cost.

3. Commitment. We rule out mutually profitable ex-post renegotiation,and we assume that the bank is committed to the mechanism.

DiscussionIn contrast with most of the implementation literature, I do not re-

quire the desired outcome to be the unique Nash equilibrium of the message

16The two units will also try to maximize the money that they can raise from externalinvestors in order to use this money to transfer rents according to the initial distributionof bargaining power.

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game17. The spirit of our exercise if however quite different from the clas-sic work in implementation theory: we are not so interested in determin-ing which choice function can be implemented, but rather finding an upperbound on the pleadgeable income that parties can credibly deliver to out-side investors. The classic literature in implementation required uniquenessof the equilibrium on the ground that the mechanism could admit Paretosuperior equilibria, from the point of view of the sending agents. Since weindeed allow parties to coordinate reports, i.e. to collude, the existence ofPareto superior equilibria in which parties do not truthfully report the stateof nature, is already accounted for in our framework. Finally, uniquenesshas also been required noting that implementing a choice function seemedto be, in some sense, too easy. Consider any mechanism in which partiessending contradictory reports are heavily punished. Clearly, truthtelling isa Nash Equilibrium of such a mechanism. However coordinating reportsin any other way may as well constitute Nash equilibria of the mechanism.In our framework it is however not possible to heavily punish parties whenthey contradict because of limited liability. Limited liability, as we will see,already give a certain bite to the state of nature being non observable18. Forthese same reasons we do not look at sequential mechanisms.

In this section we deal with only two parties. As it is well known imple-mentation is generally a lot harder when only two agents observe the stateof nature. This is so since it is impossible to tell who is lying, should thetwo parties send contradictory messages. The analysis of the case of n ≥ 3agents is left for future research.

The precise application we are considering (the financing of an economicorganization), suggests that collusion may be an important problem. Indeedthe two agents are likely to be involved in a long term relationship, sharethe same kind of knowledge of the environment, and may derive substantialprivate benefits from trading with each other. For these reasons we allow thetwo parties to collude. Collusion is modeled here as black box: we assumethat parties can agree (and enforce agreements) on two dimensions. Theymay agree on coordinating their reports and they are able to commit tohidden transfers ex-post.

In most of the cases, truthful revelation is implemented through IC

17The issue of uniqueness is further discussed below, when I describe the collusiongame. In our setting, when the mechanism designer does not leave rents through monetarytransfers, the mechanism uniquely implements states which are pay-off equivalent for themechanism designer.18Since we assume that cash flows are verifiable, if parties have deep pockets it is trivial

to implement the high cash flows action in any state of nature.

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satisfied with weak inequality at equilibrium. We introduce the assumptionthat, ceteris paribus, parties always prefer the high cash flow action to betaken19, i.e. ties are resolved in favor of external investors.

Finally we assume that all the parties are committed to the mechanism.Even if we are considering a setting in which there is a planner, renegotiationcould still have some bite. Once the state of the world has been truthfullyreported, parties may have incentives to renegotiate the mechanism20. Aseparate issue concerns the possibility for the bank of unilaterally violatingthe mechanism. The mechanism may specify that the action with lower cashflows has to be taken. We assume that the bank has no possibility, aftermessages have been sent, to impose the action with the highest cash flows21.

The timing of the game is illustrated in figure 1.

INSERT FIGURE 1

3.1 Nash Implementation

We can now formally state the implementation problem. We want to findthe mechanism that maximizes the pleadgeable income. A mechanism spec-ifies (without loss of generality) the probability x(m1,m2) that the actionrecommended by party 1 is taken, and transfers Tj(V,m1,m2) to party j, asfunction of messages mj sent by each agent j. Each agent j sends a messagemj ∈ S, the space of all possible state of the world. A message is composedof two parts: a recommendation a about the action that gives high cashflows, and a description of the distribution of private benefits σ.

Formally, let πs be the probability of occurrence of state s, the mecha-nism solves

max{x(s,s0),Tj(s,s0)}s×s0×j

V − Σsπs [(1− x(s, s))∆V +ΣjTj(V, s, s)]

subject to

for any j ∈ {1, 2} and s ∈ STj(V, s, s) ≥ 0, ICj and CIC

19The idea is that in these cases, parties derives a small private benefits ε from theaction that yields higher cash flows.20 In our setting, renegotiation may only occurs when none of the parties derive private

benefits from the low cash flow action and the bank committ not to listen the reports sentby the players.21As it will become clear, simple allocations of control rights achieve the same plead-

geable income as the optimal mechanism. In the real world agents could seek externalfinance from an investor, and than have incentives to reorganize (i.e. redistributing controlrights) within the organization.

16

where ICj is the set of individual truthtelling constraints for agent jand CIC is the set of coalitional truthtelling constraints. These sets ofconstraints are reported in Appendix B.

There are two relevant cases depending on wether b ≶ ∆V. Intuitively,there are two ways to provide incentives for truthtelling. The mechanismdesigner can try to bribe agents with a monetary transfer, or can insteadcommit to take the low cash flow action in some state of the world. Whenb > ∆V this second option tends to be preferable, since it is too expensiveto bribe an agent with monetary transfers. When b < ∆V instead it maybe more profitable to leave rents with the use of monetary transfers. Thepossibility of collusion however makes this approach relatively less conve-nient. While private benefits associated with low cash flows actions are nottransferrable across agents, money in principle is. We look at the two casesseparately.

We first consider the case in which the mechanism designer does not usemonetary transfers to provide incentives. In order to solve the problem weproceed in steps. We first state

Lemma 6 (1) Any mechanism implements the high cash flows action in atmost four states of nature

Proof. In the Appendix

Let us denote with ICj(s, s0) the individual incentive compatibility con-straint of agent j not reporting state s0 in state s. When the mechanismdesigner does not use monetary transfers, the problem is that there are”cross ” IC: satisfying ICj(s, s0) requires a violation of ICj0(s, s0), wheres ∈ {a1, a2} × {1, 2, θ}. The following table illustrate which states of theworld are not ”compatible” because of Individual IC. The dotted cases rep-resent the trade-off. A dot in case s, s0 implies that it is not possible topledge income V in both states s and s0. For future reference, crosses repre-sent trade-off arising from Coalitional IC.

states a10 a11 a12 a1θa20 ×a21 · ·a22 · ·a2θ × · · ·

The intuition is quite simple. Suppose agent 1 claims that action a1 shouldbe taken, and says that agent 2 derives private benefits from action a2.

17

Suppose agent 2 says the exact contrary. If the bank follows the recom-mendation of agent 1, than should the state of the world be the one agent2 claims the low cash flow action will be taken, and viceversa if the bankfollows the recommendation of agent 2.

Similarly suppose, for instance, that the mechanism implements the highcash flows action in state aθ. This immediately rule out the possibility ofimplementing the high cash flow action in state a0θ, since than the two agentswould always find individually profitable to report aθ. In general when thereis no conflict within the organization, it is impossible for external parties toextract surplus.

The possibility of collusion, which in this setting is limited to coordinatereports, rules out the possibility of implementing the high cash flows actionin state a0 and a0θ. This is so since both parties would coordinate to reporta0 when they both derive private benefits from it. So that trying to extractcash flows in at least one of the states in which both agents has privatebenefit, say aθ, is extremely costly, since it requires abandoning the highcash flow in every state a0.

The mechanism designer gets some more flexibility by renouncing toimplement the high cash flows action in state aθ. In this case the mechanismdesigner can implement the high cash flow action in any state a0. The firstimportant insight is that alignment of interest within the organization is badnews for the external investor.

Leaving apart the possibility of implementing the high cash flow actionin states aθ, the right decision can be implemented in states a0, i.e. whenthere is no conflict of interest between the organization as a whole and theinvestors, and in one of the following pairs of states:

S/0,θ = {12, 11}, {12, 22}, {21, 11}, {21, 22}

The economic intuition for these pairs is quite simple: they exclude thepossibility of getting the high cash flow action contingent on the state and onthe identity of the agent with private benefits. It is not possible to implementhigh cash flows actions in state aj and a0j0 : when agents have conflictinginterests the mechanism designer can exploit these conflicts and implementthe high cash flows action, but since it is in general impossible to tell who isnot reporting truthfully, rents can not be provided in a fully contingent way(i.e. in states {aσ, a0σ0} , a 6= a0 and σ 6= σ0). Rents have to be providedeither with respect to one agent, or with respect to one action. Using thedefinitions introduced at the of the previous session, it is easy to check thatthe first pair of states in S/0,θ replicates the allocation of a partnership, the

18

second is type 1−Integration, the third is type 2−Integration and the lastone is decentralization. We conclude this discussion with

Proposition 7 (2) When b > ∆V, the optimal mechanism can not do bet-ter than one of the following simple allocation of control rights: j-Integration,Decentralization, Joint Ownership, External ownership.

The proposition confirm the intuition that limited liability, i.e. the factthat agents can not be punished arbitrarily for their opportunistic behavior,provides a microfoundation for control rights.

The terminology used in the previous proposition refers to the examplediscussed in the previous section, and it is appropriate to think in terms oftrading between the two units or externally. More generally we have seenthat the control rights can be awarded to an external (uninformed) party, toan agent (J−Centralization) or with respect to an action (Veto power overaction a). In the remaining part of this session we stick to this more generalclassification.

The model only consider two agents. It is well known that the exerciseof implementation is much easier when there are n ≥ 3 agents. It is possiblethat a combination of limited liability and collusion is needed to microfounda simple allocation of control rights as an optimal mechanism. This topic isleft for future research.

3.2 Discussion and Examples

The previous proposition established that the optimal mechanism can notdo better than a simple allocation of control rights. Since we allow for anypossible level of correlation in the realization of private benefits across units,we have in principle 6 = 2ס22 − 1¢ parameters describing the environmentin terms of realization of private benefits. The next proposition tries tocharacterize under which kind of configurations each allocation of controlrights is optimal.

Proposition 8 (3) When b > ∆V,

• External control is optimal whenever ¯̄12 − Σσπaσ¯̄ → 1

2 , or πaθ →Σσπaσ.

• J−centralization is optimal whenever πa0j0 − πa0θ ≥ πaj − πaθ andπaj0 − πaθ ≥ πa0j − πa0θ. If both these inequalities are not satisfiedJ 0−centralization is optimal. If the first (second) inequality is violatedveto power over action a0 (a) should be awarded.

19

Proof. In the Appendix

Quite obviously the higher are πaj the less likely is j−integration: ex-clusive control should not be given to the agent that has a bigger conflict ofinterest with the external investor.

A quite subtle comparative statics emerges with respect to Σσπaσ. Startwith Σσπaσ <

12 . In this case awarding veto power with respect to action a

0

is the optimal allocation of control . If Σσπaσ increases we should observe j-centralization, where j is the units with lower average conflicts with respectto the external investors. As Σσπaσ further increases, the optimal organi-zational form may award veto power with respect to action a. Eventually,however when Σσπaσ is very high the bank should take control.

Because of the large numbers of parameters it is difficult to completelycharacterize the optimal organizational form. It is however instructive todiscuss a couple of examples. We are interested in exploring how the optimalallocation of control rights changes along three dimensions: the (average)level of rents, the stability of the environment, and congruence ofinterest within the organization. This last dimension is the main focusof our analysis and one of the main novelty of our approach to financingorganization with respect to the existing literature in corporate finance onfinancing entrepreneurs.

Let the probabilities of occurrence of each state s ∈ S be represented bythe following table.

0 1 2 θ

a1 π 18 +

18k +

β2

58 − 1

8k − β2

14 − β

2β2

a2 1− π 316 +

β2

38 − β

214 +

18k − β

218 − 1

8k +β2

We can easily compute the probabilities that each optimal allocation ofcontrol implements the high cash flows action. Expected rents for this case:

R =7

8− 18k

Since R does not depend on β and on π, we can use these two parametersto perform an analysis of the effects of the stability in the environment andcongruence of interests within the organization on the optimal allocation ofcontrol rights. The two figures represent the case k = 1 and k = 2, all thecalculations needed to derive the two figures are reported in Appendix B.

INSERT FIGURE 2AND 3

20

There are two forces that leads to external control being the optimalownership structure. The first is stability in the environment. When¯̄12 − π

¯̄→ 12 an uninformed party take most of the time the good action in

terms of cash flows. However as π get closer to 12 it becomes critical to matchthe action with the state of the world. The bank needs to delegate controlin order to exploit the information held by the units managers. Letting(some of the) agents some control has advantages if and only if there is areasonable amount of conflict within the organization. A second force forexternal ownership, therefore, is congruence of interest. When β is veryhigh the two agents almost always derive private benefits in a coordinatedway. In this case it is very difficult for the bank to exploit within organizationconflicts in order to extract information.

The table reported above is constructed in order to avoid symmetrywith respect to actions and agents, in order to gain a richer configurationof allocation of control rights. Considering symmetric cases helps in gainingsome intuition about the optimal allocation of control rights, from the pointof view of external investors, in an organization.

If units (agents) are completely symmetric, centralization is never opti-mal. There is no gain in concentrating control rights in the hands of oneagent instead of the other, while there would possibly be an action thathas, on average lower conflicts between members of the organization andexternal investors. The intuition is that giving power on actions (insteadof giving power to agents) achieve a more contingent allocation of control.Conversely when the environment is very unstable (π → 1

2), and the likeli-hood of agreement within the organization is balanced across the two actionsai, i.e. actions tend to be symmetric, the model produces a strong tendencytowards integration. This is so because, properly choosing the agent thathas (slightly) less conflict on average, enables to select the high cash flowsaction exploiting his information. The intuition is that giving power on ac-tions (instead of giving power to agents) achieve a less contingent allocationof control. To summarize, allocation of control rights exploits asymmetries:when actions are symmetric control is given to agents (centralization), whilewhen agents are symmetric control is awarded with respect to actions (”vetopower” allocations of control, i.e. joint ownership and decentralization).

”Veto Power ” allocations of control rights only can arise when collusionis allowed for. Intuitively, when parties can collude it is optimal to establishsome form of veto power in the organization in order to increase partiesconflict over the optimal course of action. It is the possibility of collusionwithin the organization that create scope for allocations of control rightsthat empower multiple agents. This is done in order to gain information

21

from the conflict of interest between the two parties22. In other words, thepossibility of collusion within the organization push towards a fragmentationin the distribution of control rights. This prediction is reminiscent of recentresults in the collusion literature (see e.g. Baliga and Sjostrom (2000)).This prediction may be reversed when rents are provided with monetarytransfers.

3.3 Monetary Transfers

We now turn to the case b ≤ ∆V. When this is the case the bank couldbe willing to give rents in order to achieve truthtelling by leaving money to(at least one of) the two players. The mechanism design problem is nowmore complex than before for at least two reasons: first, optimal transfersTj(s, s

0) have to be determined. Secondly, there is an important differencebetween paying rents with private benefits and with money. Money is trans-ferrable, and therefore coalition proof incentive compatibility constraintsbecome harder to be satisfied.

We make the following

AssumptionMonetary transfers can be made contingent on the realization of cash

flows V, i.e. cash flows are ex-post verifiable. However the realization ofprivate benefits is not ex-post verifiable.

When cash flows are verifiable transfers from the bank to the agents caneasily be interpreted as standard debt contract (possibly contingent on theaction taken). As before, we first look at Individual IC constraints.

Lemma 9 (4) Because of Individual Incentive Compatibility Constraints,to implement the high cash flow action in all possible states, a transfer b hasto be paid (at least) four times in (at least) three different states. Dependingon the likelihood of occurrence of each of the following combinations of states.Always pays player j in states {aσ}, where a ∈ {a1, a2} and σ : Ij,σ(b) = 1,one of player j and j0 in states a· and a0· whenever player j has privatebenefits in state a · .

Proof. In the Appendix C.

Because of Individual IC, transfers have to be paid either with respect toplayers or with respect to actions. With respect to individual IC the setting22Since we are looking at an environment with only two players, power can be given

only with respect to one action.

22

with monetary transfers is completely analogous to the one when rents areprovided distorting the ex-post action. Either transfers are unconditionallyleft to players with private benefits in action a, or transfers are paid to playerj every time that he has private benefits.

We now turn to Coalition IC constraints. Collusion within the organiza-tion can now potentially take two forms: coordinating messages and hiddentransfers of money. In particular we assume that players can commit in thecollusion contract to transfers, i.e. they can redistribute the money that isleft on the table. We make the following assumptions

AssumptionIn order to transfer x dollars from player j to player j0, λx dollars are

lost in the transaction.Transfers in the collusion game are negotiated ex-post according to a

Nash Bargaining game in which the relevant status quo is given by truthtelling

The first part of the assumption is introduced in order to analyze envi-ronments in which the institutional framework shapes how effectively canparties collude. We think that the parameter λ can be associated with thedegree of investor protection. When λ → 0, parties are free to redistributethe money that is left on the table. This limit case is the equivalent ofthe assumption made in the previous section according to which the bankcan not hold claims that are contingent on the identity of the player thatpays and receive money. When λ → 0 only the sum of money left on thetable is relevant for the two agents, as perfect transferability and efficientbargaining ensure that any profitable colaitional deviation is exploited. Ingeneral instead the bank can try to influence the bargaining process and theeasiness of collusion by manipulating the distribution of rents left to the twoagents.

The second part of the assumption is needed to pin down the (endoge-nous) distribution of bargaining power in the collusion stage. We assumean efficient bargaining. This seems to be a sensible assumption in our en-vironnement in which agents share symetric information. The bank, byappropriately structuring financial claims among the two parties can, inprinciple affect how difficult is to reach a collusive agreement within theorganization23. The use of truthelling as the relevant status quo point ofthe bargaining game is discussed in more detail below.23A similar intuition is at work in other paper on collusion as Laffont and Martimort

(1996) and Baliga and Sjostrom (2000). The first paper analyze a context of asymmetricinformation so that the collusive agreement is potentially subject to endogenous inefficien-cies. In the second paper instead limited liability induces a failure of the Coase theorem

23

In order to analyze the effects of the Coalitional IC, we first note thatthey are again independent of the Individual IC: if transfers that are neces-sary in order to provide Individual IC are not lowered, this set of constraintsis still satisfied.

We have seen that the set of .Individual IC implies that transfers willbe left either to one agent or with respect to one action. These two config-urations have radically different implications when Coalition IC are takeninto account.

When rents are left to agent j each time that the state of the worldis such that he derives private benefits from the low cash flows action, theonly relevant coalitional deviations are from states in which no money is lefton the table, i.e. states aσ such that I(σ)j = 0. When this is the case thetwo agents would rather coordinate their reports, to extract money from thebank. In order to do that however, agent j has to bribe agent j0. Since thistransfer implies some transaction cost, the bank can in principle design amechanism that would make it too costly to bribe agent j0.

Lemma 10 (5) When monetary transfers are used to provide rents with re-spect to agent j the pleadgeable income is equal to PIj = V−b+ λ

1+λbΣa¡πaφ + πaj0

¢Proof. In the Appendix

Because of the possibility of collusion the bank has to provide somemoney also to those agents that could be bribed. Two remarks are particu-larly useful here. As λ → ∞ collusion becomes extremely difficult, and nomoney should be left to player j0. As λ → 0 instead collusion is extremelysimple and µ→ b.

When rents are instead left according to the action that is taken inequilibrium coalitional IC have substantially more bite on the problem.First it becomes impossible to implement both states aθ and a0θ: whenmoney is left in state aθ parties would like to coordinate their reports in statea0θ so that they can both reap the private benefits. This can be avoidedonly at the cost of paying at least b to one agent in state a0θ. Howeverleaving money on the table in state a0θ triggers joint deviations from all theother states a0σ, that can only be prevented at monetary cost b

1+λ . This isso since coordinated deviations with respect to the recommended action areonly profitable if both agents derive private benefits from the low cash flowsaction.

within the coalition, and it is therefore closer in spirit to our framework. Under bothapproaches the mechanism designer can manipulate the mechanism in order to induceinefficiencies in the bargaining process.

24

Secondly, the set of ”intra-action” coalition IC is now more complexwith respect to action a. In principle agents could coordinate to deviate fromany state in which the sum of transfer left on the table is lower to one thatis higher.

Lemma 11 (6) When monetary transfers are used to provide rents withrespect to action a the pleadgeable income is equal to PIa = V − 2bΣσπaσ −[πa0θb+

11+λb(Σσπa0σ − πa0θ)]

Proof. In the Appendix

Essentially, even when λ→∞, in every state a it must be that transfers2b have to be paid. We conclude this discussion with the following

Proposition 12 (7) When cash flows, but not private benefits, are ex-postverifiable, b < ∆V, and λ → 0, the optimal mechanism can not do betterthan j-centralization.

Proof. Simply note that when λ → 0 the two pleadgeable income aregiven by PIj = V − b and PIa = V − 2bΣσπaσ − bΣσπa0σ and thereforePIj > PIa. Finally, note that V −b is the same pleadgeable income achievedby giving control rights to one agent j.

When individual IC are satisfied paying rents with respect to one agentj, when λ → 0 the bank could essentially leave an unconditional monetarytransfer b to the same player j. This strategy has essentially the same mon-etary cost than leaving µ → b to player j0, but uniquely implements thedesired outcome24.

It is a general message of this section that the possibility of collusionshifts the optimal allocation of control rights towards centralization. Thisis the contrary of the results of the previous section when rents were paiddistorting the optimal decision, but without paying monetary transfers. The

24The problem with leaving asymmetric transfers is that, when these reports do notchange the action taken, reporting state aj and aj0 are both Nash Equilibria of the messagegame. When no money is left on the table this is not a big problem for the bank, since thetwo states are perfectly equivalent. When money is left on the table the multiplicity ofequilibria is disturbing since the associated monetary costs for the bank are different, andthe two equilibria are not Pareto ranked from the point of view of the two agents. Onepossibility would be for each of them to report aj, this would not change the allocation,but would automatically set transfers equal to 0 in the outside option. In this case thebank can not influence at all the bargaining game and in each case b should be paid (thebribe goes to zero).

25

intuition for the results in this section is that when money is left on thetable, in a decenralized structure it is necessary to provide rents to twoagents instead of one.

It is instructive to re-examine the example we analyzed in the previoussection for the case k = 0 (Computations for the derivation of Figures 3 and4 are reported in the Appendix)

INSERT FIGURE 3 AND 4

It is clear that in an unstable environnement (π → 12) it is not profitable

to pay rents with respect to actions since, once again it will not be possi-ble to pay rents in a contingent way. For a given level of stability of theenvironnement paying rents with respect to agents becomes more profitableas β increases. The figure therefore ilustrate the point that when rentsare paid using monetary transfers centralized organization tend to deliverhigher pleadgeable income since only one agent has to be given (most of the)monetary rents.

Figure 4 makes a similar point. Even when collusion becomes extremelycostly (λ → ∞), if the alignement of interests within the organization issufficiently high, it is better to provide incentives paying (most of the) rentsto one agent, sugesting once again that some form of centralization has tobe preferred.

4 Conclusion

In this paper we introduced a simple model to analyze how two (econom-ically) linked projects should be financed. In particular we ask how twolinked projects should be financed and control rights over the two projectsdistributed in a setting in which the two agents have no initial cash. Weemphasize that the organizational form itself (i.e. the distribution of controlrights within an organization) affects how much money can be raised fromexternal investors.

We first analyzed an application of our framework we consider the ques-tion of firm boundaries under financial constraints. We show that the alloca-tion of control rights (namely putting the two projects under the umbrella ofa centralized firm or keeping them as two separate stand alone units) withinthe organization affects the pleadgeable income of the entire organization.When private benefits mostly arise from internal trade a firm tend to pledgelower cash flows than two stand alone firms. The application sheds somenew light on the links between firm boundaries and financial structure: a

26

firm is defined as an organization with centralized allocation of control rightsand joint liability of the financed investments (centralized finance).

To analyze the general model we took a mechanism design approach.The first main result is that because of limited liability the optimal mecha-nism often cannot improve over a simple allocation of ex-post control rights.Instead of restricting attention to exogenously given allocations of controlrights, we endogenously provide microfoundations for when a simple alloca-tion of control rights replicates the optimal contract given non verifiabilityof the state and limited cash of the agents. Our framework accounts for thepossibility of collusion within the organization. The model rationalizes a va-riety of allocations of control rights as optimal contracts (such as centralizedand decentralized allocations of control rights and external control).

The model delivers comparative statics linking the optimal allocation ofcontrol rights with the degree of stability of the environment and the degreeof alignment of interest within the organization. The comparative staticscritically depend on the relative level of private benefits and cash flows.When private benefits are low with respect to cash flows rents should be leftusing money. When money is easily transferrable within the organizationthe pleadgeable income is higher if rents and control rights are distributed ina centralized way. Centralization becomes more attractive the higher is thecongruence of interest within the organization. When private benefits arehigh with respect to cash flows instead rents tend to be given distorting thecourse of action followed by the organization. When this is the case it is inthe interest of external investor to maximize conflict within the organization,and decentralization more often emerges as the optimal allocation of controlrights and may be preferred when congruence within the organization ishigher.

The framework that we developed can be applied to the analysis of otherforms of organizations25. As an example it would be possible to link pri-vate benefits to variables related to the degree of investor protection andthe quality of corporate governance. It would than be possible to deliver aboundaries of the firm approach to business groups and other hybrid cor-porate structures that are commonly observed (especially in the developingworld).

A second promising application is with respect to the financing non profitorganizations. There may be an inherent trade off in the process of financ-

25The model does not embed costs associated with joint liability. It is possible toextend the present model to introduce these costs under the form of moral hazard. It isthen possible to show that centralized control rights and joint liability tend to go together.

27

ing non profit organizations if their agents are not randomly selected. Ithas been noted that most of the incentives that agents respond to in theseorganizations are not monetary in nature (they could come, e.g. from per-sonal motivation or from the interaction with ideologically similar agents).It is than likely that small non profit organization in which agents tend tobe more homogenous display higher congruence of interest within the orga-nization. This is however bad from the point of view of external investors.Those small organizations that manage to attract homogeneously motivatedagents, and are therefore the most efficient in the delivery of services sincethey economize on the internal costs of providing incentive, may turn out tobe the most difficult to finance since they can not guarantees that those de-cision that are appropriate from the point of view of external supporters aretaken on a regular basis. Bigger organizations may suffer the opposite prob-lem: because of lower congruence of interest within the organization theymay be less effective in providing services and they need heavier and costlybureaucracies but may be better suited in taking actions in the interest ofexternal supporters.

In a more normative spirit, a last application is related to microfinance.We have analyzed a context in which joint liability and the distribution ofcontrol rights are endogeneized. Most of group lending practice (and theo-retical literature on the subject) focus only on the joint liability dimension.Two remarks are useful here. First of all, even if there are many rationalefor group lending, most of them boil down to exploit some form of superiorinformation within the group. Under symmetric information (complete)contracts are very powerful, but collusion is also easier. It is therefore likelythat work in micro-finance not taking into account collusion overstates theefficiency of group lending practices (on this see for instance Laffont and Rey(2001)). If symmetric information is somewhat correlated with congruenceof interest across the two projects some further trade off has to be taken intoaccount. It may be the case that not enough attention has been paid to thecontrol right dimension as a potential instrument to improve the improvethe practice of microfinance26.

This work can be extended in many directions. We mention here someof those that we consider more promising. It would be interesting to gen-eralize the model to the case of n ≥ 3 agents and a ≥ 3 actions / projects.It is well known that implementation is easier when there are more than

26More broadly the model suggest that the financial structure may have importantconsequences in terms of evolution of the organization, and conversely organizationaldesign is an important variable in the hands of investors to secure appropriate financialreturns.

28

two agents. However in our setting, in which collusion is allowed for, thesame considerations that hold for individual IC could potentially hold forany coalition of agents. One can than hope to gain some insight over thestructure of the optimal allocation of control rights in terms of hierarchiesand core activities.

A second crucial aspect is monitoring. We assumed that agents com-monly observe the state of the world. Monitoring activities could be per-formed by the mechanism designer, or by (some set of) agents. With respectto the theory of the firm, a firm could be created to maximize the incentivesof monitoring inputs. However this very deep nature of a firm, by facilitatingcollusion within the firm, would jeopardize the financing of firms.

Finally we believe that exploring the connections between organizationaldesign and financial structure is a general theme that deserves much furtherwork.

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[18] Moore, J. (1992) ”Implementation in Environements with CompleteInformation”, in Advances in Economic Theory, ed. by J.J. Laffont.Cambridge: Cambridge University Press.

[19] Rey, P. and J. Tirole (2001) ”Alignement of Interests and the Gover-nance of Joint Ventures ”, mimeo IDEI

[20] Tirole, J. (1999) ”Incomplete Contracts: where do we stand?”, Econo-metrica 67-4: 741-781.

30

5 Appendix A

5.1 Proof of Lemma 0

Proof. We restrict attention to symmeric contracts Bj0 = Bj , and lim-

ited liability implies Bj < V2 . Since private benefits are realized only from

internal trade, when Vi > Vo there is in principle no conflict between theex-post incentives of the two units and the investor. Without loss of gen-erality for any vector Bj , the amount ΣjBj is repaid. The interesting casetherefore is the one in which Vi < Vo. With probability (1− δ)2 however noprivate benefits are realized, trade occurs externally and firms repay ΣBj .With probability δ2 both parties have private benefits and jointly reimboursemax{V,Bj}, since it is profitable to switch all the cash flows into a singlefirm. With probability 2(1 − δ)δ only one firm has private benefits. Thisunit can bribe the unit with no private benefits by shfting al the cash flowsif and only if V − Bj > V

2 − Bj . The bank is repaid Bj V > V2 and ΣjBj

otherwise. Note that for the unit with private benefits b > V2 − Bj since

ΣjBj > V and 2b > ∆V. Summing up, we conclude that if V > V2 pleadge-

able income is V − (1−π)(1− (1−δ)2)V2 while if V < V2 pleadgeable income

is V − (1− π)δ2∆V.

The following table summarize the pleadgeable income that can be re-alized from integration and non integration, when private benefits can arisefrom intenral and external trade, and joint liability contracts are considered.

Reaizationsz }| {πi0πiDπiUπiθπo0πoDπoUπoθ

D−Integrationz }| {Repayment ConditionΣjBj \

ΣjBj or V if ΣjBj < V − bΣjBj \

ΣjBj or V if ΣjBj < V − bΣjBj \

ΣjBj or V if ΣjBj < V − bΣjBj \

ΣjBj or V if ΣjBj < V − b

Non Integrationz }| {Repayment ConditionΣjBj \

ΣjBj or V if ΣjBj < V − bΣjBj or V if ΣjBj < V − bΣjBj or V if ΣjBj < V − 2bΣjBj \ΣjBj \ΣjBj \

ΣjBj or V if ΣjBj < V − 2b

31

6 Appendix B

6.1 Individual Truthtelling Constraints

For each s = aσ ∈ S, it must be the case that for player 1

[1− x(aσ, aσ)] · I1,σ(b) + T1(aσ, aσ)≥ £¡

1− x(a0σ0, aσ)¢ ¡1− I(a0)¢+ x(a0σ0, aσ)I(a0)¤ · I1,σ(b) + T1(a0σ0, aσ)where I1,σ(b) = b if player 1 derive private benefits from action a0 in stateaσ, and I(a0) = 1 if a0 6= a. Similarly for player 2 we have

[1− x(aσ, aσ)] · I2,σ(b) + T2(aσ, aσ) ≥£1− x(aσ, a0σ0)¤ · I2,σ(b) + T2(aσ, a0σ0)

Coalitional Truthtelling constraints are introduced below.

6.2 Proof of Lemma 1

Proof.

Remark 13 We first look at IC constraints, to see if they imply that theimplementation of the high cash flow action in some state s is inconsis-tent with the implementation of the high cash flow action in state s0. Wethen derive a table with all the possible combinations of states that can beimplemented respecting IC. We apply the same procedure to coalition IC27.

The Lemma is prooved combining the following Lemmas.

LemmaWhen b > ∆V we have Tj(V, s, s0) = 0 for any {s, s0} ∈ S2 andj ∈ {1, 2}.

Proof. (Heuristic) First, it is clear that transfer Tj(s, s0) = 0, whens 6= s0. This is the case since these trasnfers never appear on the RHS of anyIC, and do not appear in the objective function of the mechanism designer.Suppose Tj(s, s0) > 0, then it is possible to lower Tj(s, s0) and either reduceTj(s, s) or Tj(s0, s0) (depending on which IC is under consideration) or in-crease x(s, s) or x(s0, s0), increasing the mechanism designer profits. Supposeinstead that rents R have to be given to player j in state of the world s.There are two ways of providing these rents, either leaving x(s, s) · b ≥ R or27There are 8 states of nature, and therefore for each player there are 7 × 8 incentive

compatibilities constraints: this amount to 112 individual IC for the two players.

32

Tj(s, s) ≥ R. The cost of providing these rents is equal to R if transfers areused and to ∆V

b R if the probability are used. If b > ∆V distorting actionsis more efficient than compensating with monetary transfers.

Lemma The set of incentives compatibility constraints in which playerj lies only with respect to the distribution of private benefits may be omitted.

Proof. (Heuristic) When a0 = a, i.e. the action relevant part of themessage is reported truthfully, we have that the IC for player 1 becomes

[1− x(aσ, aσ)] · I1,σ(b) ≥£¡1− x(aσ0, aσ)¢¤ · I1,σ(b)

On the other hand it must also be the case that£1− x(aσ0, aσ0)¤ · I2,σ(b) ≥ £¡1− x(aσ0, aσ)¢¤ · I2,σ(b)

Setting x(aσ0, aσ) = 1 discourages such deviations.

Lemma Player j never has incentives to lie in states in which he doesnot get private benefits from action a0 6= a.

Proof. (Heuristic) In such a state the IC for player j is authomaticallysatisfied since 0 ≥ 0 regardless of the message sent, and action taken.

Lemma Incentive constraints in which player j claims that the state σis such that player j0 has no private benefits should not bind.

Proof. (Heuristic) The IC for player j in these states takes the form

[1− x(aσ, aσ)] · Ij,σ(b) ≥£¡1− x(a0σ0, aσ)¢¤ · Ij,σ(b)

and σ ∈ {j, θ} while σ0 ∈ {0, j}. Conversely we have to check that£1− x(a0σ0, a0σ0)¤ · Ij0,σ0(b) ≥ £¡1− x(a0σ0, aσ)¢¤ · Ij0,σ0(b)

but in states σ0 ∈ {0, j} we have Ij0,σ0 = 0, and therefore the ICj is au-thomatically satisfied. We can then set x(a0σ0, aσ) = 1.

The problem can not be semplified further. We are still left with 8×2 =16 out of the original 112 individual IC. This constraints can be paired,illustrating the trade offs arising. In general giving incentives to agent j toreport trutfully in state s may be incompatible with also having the highcash flow action implemented in state s0. The set of incompatible states isillustrated with a table in the text.

We now turn to the coalition truth-telling constraints. First note thatnone of this constraints can be relevant for assymetric states of the world s =

33

aj, with a ∈ {1, 2} and j ∈ {1, 2}. Suppose truthtelling leads to the actionpreferred by player j. This action can either entails private benefits for playerj, in which case pay offs are b and 0 respectively, or this action can entailsa payoff ε for each player. Coordinating on the opposite action can clearlynot represent a Pareto improvement for the coalition. Similarly in states inwhich σ = 0, parties can not gain from coordinating towards the adoptionof the wrong action. The only coalition-incentive compatibility constrantsthus come from the states s = aθ. The following Lemma introduces the costof coalition IC.

Lemma It is impossible to implement state s = aθ and s = a00.Proof. Suppose not. Than it must be that

(1− x(aθ, aθ)) · b ≥ x(a00, a00) · b and(1− x(aθ, aθ)) · b ≥ (1− x(a0, a0)) · b

In order to have x(aθ, aθ) = 1, it is necessary to have x(a00, a00) = 0.

Proof. Combining the previous Lemmas completes the proof.

6.3 Proof of Proposition 3 (to be completed)

Lemma 1 established that in at most four states of nature the high cash flowsaction can be implemented. The high cash flows action can be implementedin any of the wollowing six sets of four states: a) Ai = {aiσ}i=1,2; b) Bj ={aij, a10, a20}i=1,2; c) ABi = {aij, a10, a20}j=1,2. The optimal mechanismchooses among these sets of states the one that is more likley to occurr. StateAi occurrs with probability πi, and it is optimal selected if πi → 1.Moreoverif βa → minj δa,j → maxj δa,j → 1 state aiθ occurrs with probability πi, itis therefore optimal to chose Ai.

6.4 Proof of Lemma 4

The proof of this lemma is actually very close to the proof of Lemma 1. Itproceeds through steps.

Lemma Whenever mj 6= mj0 it must be that Tj(m,m0) = 0.Proof. (Heuristic) These transfers only appear on the RHS of individual

IC. They should always be set to zero.

34

Lemma The set of incentives compatibility constraints in which playerj lies only with respect to the distribution of private benefits may be omitted.

Proof. (Heuristic) Identycal to the one provided above.

Lemma In states s = aσ such that Ij,s(b) = 0 it must be Tj(s, s) = 0.Player j has no incentives to lie in these states.

Proof. No money should be left to players in states in which they donot have private benefits.

Lemma Incentive constraints in which player j claims that the state σis such that player j0 has no private benefits should not bind

Proof. (Heuristic) Analogous to the one presented above.These lemmas brings the case under consideration very close to the one

explored above. We now explore the consequences (in terms of costs andbenefits) of using transfers. In particular by inspection of the remaining16 individual IC cosntraints we can draw a table in which all th mutuallyexclusive states with transfers are depicted. This is done in the next table

1φ 11 12 1θ 2φ 21 22 2θ1φ1112 · ·1θ · ·2φ2122 · ·2θ · ·

On the vertical axis are reported transfers to player 2, on the horizontal axisto player 1. Dotted cases describe the states of the world in which eitherplayer 1 or player 2 has to be paid a transfer equal to b.

6.5 Proof of Lemma 5

Proof. Formally, let us call m and µ the transfers left to agent j andj0 respectively in the states in which the coalition IC is binding. Clearlythere is no gain in raising above b the transfer left to player j in states ofthe world in which rents should be provided. Let t(aeσ0, aeσ) represent thetransfer from player j to player j0 when the realized state of the world is aeσ0and agents coordinate their reports towards state aeσ, and the states are such

35

that Ijaeσ0(b) = 0 and Ijaeσ(b) = b. Because of Nash Bargaining the transferfrom agent j to agent j0 when the relevant outside option is truthtelling,that is m and m0 is given by

t(aj0, aj) =b−m+ (1 + λ)µ

2(1 + λ)

In order for m and µ to make the bribe too high it must be that

b−m+ (1 + λ)µ

2(1 + λ)≤ µ and b−

·b−m+ (1 + λ)µ

2

¸≤ m

i.e.

m+ µ ≥ b− λµ

Since the bank wants to minimize m + µ, the optimal solution is givenby m = 0 and µ = b

1+λ . Summing up, b is left in states occurring withprobability Σaπaj + πaθ = 1 − (Σaπaj + πaθ) and µ = b

1+λ is left withthe complementary probability. Pleadgeable income is therefore given byV − b+ λ

1+λbΣa¡πaφ + πaj0

¢.

6.6 Proof of Lemma 6

Proof. There are three levels of rents, depending on the state: 0, b and 2b.Let us call µj(σ) the monetary transfer left to agent j in state aσ. Taking intoaccount Nash Bargaining for the determination of the monetary transfer, theset of ”intra-action” coalitional IC is then given by

1) Σjµj(φ) ≥ µj(j) + (1 + λ)µj0(j)− λµj0(φ) for any j ∈ {1, 2}2) Σjµj(φ) ≥ µj(θ) + (1 + λ)µj0(θ)− λµj0(φ)

for µj(θ)− µj(j) ≥ µj0(θ)− µj0(j)3) Σjµj(j) ≥ µj(θ) + (1 + λ)µj0(θ)− λµj0(j) for any j ∈ {1, 2}

Lemma The optimal mechanism does not depend on λ.Proof. First note that, for each j, combining 1) and 3) constraint

2) is automatically satisfied. Constraint 1) can be rewritten as µj(φ) ≥µj(j

0)+ µj0(j0)−µj0(φ)1+λ , while constraint 3) can be rewritten as µj(j

0) ≥ µj(θ)+

36

µj0(θ)−µj0(j0)1+λ implying µj(φ) − µj(θ) ≥ µj0(θ)−µj0(φ)

1+λ . We are therefore leftwith a linear program with eight endogenous variables, µj(σ) and eight con-straints (for each j ∈ {1, 2} constraints 1) and 3) and the four Individual ICµj(θ) ≥ b and µj(j) ≥ b). Since the objective function is decreasing in allits arguments, it is clear that constraint 3) are binding. Suppose not, thanone can lower µj(j

0) without violating any other constraints. Substituting3) into the respective constraint 1) we are left with six constraints in six un-known. It is then clear from this set of constraints that the four IndividualIC are binding. Substituting the appropriate values into 1) we are left withtwo constraints in µj(φ). It is easy to show that the unique solution to theproblem

max−π(aφ)Σjµj(φ)

s.t. µj(φ) ≥ b+b− µj0(φ)1 + λ

for each j ∈ {1, 2}, and j 6= j0

has a unique solution µj(φ) = b. From this we also conclude that µj(j0) = b.

Proof. Summing up with respect to all the possible realizations of sates,we obtain the expression for the pleadgeable income.

7 Appendix C: derivation of figures 1 to 4

The following table represents the probabilities of occurrence of each states ∈ S.

0 1 2 θ

a1 π 18 +

18k +

β2

58 − 1

8k − β2

14 − β

2β2

a2 1− π 316 +

β2

38 − β

214 +

18k − β

218 − 1

8k +β2

We can easily compute the probabilities that each optimal allocation ofcontrol implements the high cash flows action. Excpected rents for thiscase:

R =7

8− 18k

Since expected rents do not depend on π and β, movements along π and βexclusively represent changes in the stability of the environnement and in

37

the alignement of inerest within the organization. The pleadgeable incomecorresponding to the allocation of control rights is given by

1-CENTR = − 116

π +7

16+1

8k

2-CENTR =3

16π +

9

16

a1-VP =13

16π − πβ +

3

16+1

2β

a2-VP = −1116

π + πβ +13

16− 12β +

1

8k

where ai-VP means that veto power is given with respect to action ai. Let-ting ECi be the pleadgeable income of external control when the uninformedparty chooses action ai, we can compare the allocations of control rights ob-taining the following table in which each case gives the condition underwhich the element in the column gives higher pleadgeable income than theelement in the line.

EC1 EC2 1-CENTREC2 π > 1

2 −1-CENTR 2k+7

17 < π 9−2k15 > π −

2-CENTR π > 913

719 > π π < k−1

2

a1-VP 381−π2π−1 < β 1

813−29π1−2π < β 1

47π−2−k2π−1 < β

a2-VP β < 1827π−13−2k2π−1 β < 1

85π−3+2k1−2π β < 1

45π−32π−1

EC21-CENTR2-CENTRa1-VPa2-VP

2-CENTR a1-VP

−145π−32π−1 < β −

β < 147π−2−k2π−1 β < 1

812π−5−k2π−1

The two figures represent the case k = 1 (and therefore β < 12) and k = 2

(and therefore 18 < β < 1

2).Figure 3 and 4 are instead derived from the same table when k = 0.

It is then possible to compare the pleadgeable income associated with pay-ing rents to agent j, for j ∈ {1, 2} and the pleadgeable income associatedwith paying rents with respect to action a ∈ {a1, a2}. These magnitude are

38

respectively given by

Pla1 = V − b½2π + (1− π) [

1

8+

β

2+

1

1 + λ(7

8− β

2)]

¾Pla2 = V − b

½2(1− π) + π[

β

2+

1

1 + λ(1− β

2)]

¾Plj=1 = V − b+ λ

1 + λb(3

8π + (1− π)

7

16) and

Plj=2 = V − b+ λ

1 + λb(3

4π + (1− π)

9

16)

It is clear that Plj=2 > Plj=1 for any {π,λ} ∈ [0, 1]× (0,∞). We have

Pla1 < Plj=2 if β <1

8

5λ− 33λπ − 16π(1− π)λ

Pla1 < Pla2 if β <1

4

¯̄̄̄−8− 15λ+ 16π + 31λπλ (2π − 1)

¯̄̄̄and

Pla2 < Plj=2 if β >1

8

−16− 25λ+ 29λπ + 16πλπ

Figure 3 is obtained setting λ = 1 while figure 4 is obtained settingπ = 15

16 . In fugure 4 only the comparison between Pla2 and Plj=2 is relevant,and the corresponding boundary is given by β > 1

2 − 2151λ .

39