1 chapter 21 political economics copyright ©2005 by south-western, a division of thomson learning....
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Chapter 21
POLITICAL ECONOMICS
Copyright ©2005 by South-Western, a division of Thomson Learning. All rights reserved.
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Social Welfare Criteria
• Analyzing the choice among feasible allocations of resources is difficult– it involves making choices about the utility
levels of different individuals– in choosing between two allocations (A and
B) the problem arises that some individuals prefer A while others prefer B
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Social Welfare Criteria• We can use the Edgeworth box diagram
to show the problems involved in establishing social welfare criteria– only points on the contract curve are
considered as possible candidates for a social optimum
– along the contract curve, the utilities of the two individuals vary, and these utilities are directly competitive
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Social Welfare CriteriaOJ
OS
UJ4
UJ3
UJ2
UJ1
US4
US3
US2
US1
Contract curve
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Social Welfare Criteria
• If we are willing to assume that utility can be compared among individuals, we can use the contract curve to construct the utility possibility frontier
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Social Welfare Criteria
Smith’s utility
Jones’s utility
OJ
OS
The utility possibility frontier shows those utility levels for Smith and Jones that are obtainable from the fixed quantity of goods available
Any point inside the curve is Pareto-inefficient
C
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Equality Criterion
Smith’s utility
Jones’s utility
OJ
OS
One possible criterion could require complete equity giving Smith and Jones the same level of welfare
45°
Utility is equal in this case, but the quantities of x and y may not be
This occurs at UJA and US
A
USA
UJA
A
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Contract curve
Equality CriterionOJ
OS
UJ2
UJA
UJ1
US2
USA
US1
A
XSA
XJA
YSA
YSA
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Utilitarian Criterion
• A similar criterion would be to choose the allocation on the utility possibility frontier so that the sum of Smith’s and Jones’s utilities is the greatest– this point would imply a certain allocation
of x and y between Smith and Jones
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The Rawls Criterion• This was first posed by philosopher
John Rawls
• Suppose that each individual begins in an initial position in which no one knows what his final position will be– individuals are risk averse– society will only move away from perfect
equality when the worst off person would be better off under inequality than equality
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The Rawls Criterion
Smith’s utility
Jones’s utility
OJ
OS
Unequal distributions such as B would be permitted when the only attainable equal distributions are below D
45°
D
B
A Equal distributions that lie between D and A are superior to B because the worse-off individual is better off there than at B
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Social Welfare Functions
• A social welfare function may depend on Smith’s and Jones’s utility levels such as
social welfare = w(US,UJ)
• The social problem is to allocate x and y between Smith and Jones as to maximize w
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The optimal point of social welfare is where w is maximized given the utility possibility frontier
w1
w2
Social Welfare Functions
Smith’s utility
Jones’s utility
OJ
OS
E This occurs at UJE and US
E
USE
UJE
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w1
w2
Social Welfare Functions
Smith’s utility
Jones’s utility
OJ
OSEven though point F is Pareto-inefficient, it is still preferred to point D
Note the tradeoff between equity and efficiency
D
F
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Equitable Sharing
• A father arrives home with an 8-piece pizza and must decide how to share it between his two sons
• Teen 1 has a utility function of the form
11 2 xU
• Teen 2 has a utility function of the form
22 xU
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Equitable Sharing• The least resistance option would be to
give each teen 4 slices– U1 = 4, U2 = 2
• The father may want to make sure the teens have equal utility– x1 = 1.6, x2 = 6.4, U1 = U2 = 2.53
• The father may want to maximize the sum of his sons utility– x1 = 6.4, x2 = 1.6, U1 = 5.06, U2 = 1.26
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Equitable Sharing• Suppose the father suggests that he will
flip a coin to determine who gets which portion listed under the three allocations
• The expected utilities of the two teens from a coin flip that yields either 1.6 or 6.4 slices is
E(U1) = 0.5(2.53) + 0.5(5.06) = 3.80
E(U2) = 0.5(2.53) + 0.5(1.26) = 1.90
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Equitable Sharing
• Given this choice, the teens will opt for the equal distribution because each gets higher expected utility from it than from the coin flip
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Equitable Sharing
• If the father could subject the teens to a “veil of ignorance” so that neither would know his identity until the pizza is served, the voting might still be different– if each teen focuses on a worst-case
scenario, he will opt for the equal utility allocation
• insures that utility will not fall below 2.53
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Equitable Sharing• Suppose that each teen believes that he has
a 50-50 chance of being labeled as “teen 1” or “teen 2”
• Expected utilities are
x1 = x2 = 4 E(U1) = 0.5(4) + 0.5(2) = 3
x1 = 1.6, x2 = 6.4 E(U1) = 0.5(2.53) + 0.5(2.53) = 2.53
x1 = 6.4, x2 = 1.6 E(U1) = 0.5(5.06) + 0.5(1.26) = 3.16
• The teens will opt for the utilitarian solution
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The Arrow Impossibility Theorem
• Arrow views the general social welfare problem as one of choosing among several feasible “social states”– it is assumed that each individual can rank
these states according to their desirability
• Arrow raises the following question:– does there exist a ranking on a society-wide
scale that fairly records these preferences?
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The Arrow Impossibility Theorem
• Assume that there are 3 social states (A, B, and C) and 2 individuals (Smith and Jones)– Smith prefers A to B and B to C
• A PS B and B PS C and A PS C
– Jones prefers C to A and A to B• C PJ A and A PJ B and C PJ B
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The Arrow Impossibility Theorem
• Arrow’s impossibility theorem consists of showing that a reasonable social ranking of these three states cannot exist
• Arrow assumes that any social ranking should obey six seemingly unobjectionable axioms– “P” should be read “is socially preferred to”
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The Arrow Axioms• It must rank all social states
– either A P B, B P A, or A and B are equally desirable (A I B) for any two states A and B
• The ranking must be transitive– if A P B and B P C (or B I C), then A P C
• The ranking must be positively related to individual preferences– if A is unanimously preferred by Smith and
Jones, then A P B
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The Arrow Axioms• If new social states become feasible, this
fact should not affect the ranking of the original states– If A P B, then this will remain true if some
new state (D) becomes feasible
• The social preference function should not be imposed by custom– it should not be the case that A P B
regardless of the tastes of individuals in society
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The Arrow Axioms
• The relationship should be nondictatorial– one person’s preferences should not
determine society’s preferences
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Arrow’s Proof• Arrow was able to show that these six
conditions are not compatible with one another– because B PS C and C PJ B, it must be the
case that B I C• one person’s preferences cannot dominate
– both A PS B and A PJ B, so A P B
– transitivity implies that A P C
– this cannot be true because A PS C but C PJ A
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Significance of theArrow Theorem
• In general, Arrow’s result appears to be robust to even modest changes in the set of basic postulates
• Thus, economists have moved away from the normative question of how choices can be made in a socially optimal way and have focused on the positive analysis of how social choices are actually made
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Direct Voting
• Voting is used as a social decision process in many institutions– direct voting is used in many cases from
statewide referenda to smaller groups and clubs
– in other cases, societies have found it more convenient to use a representative form of government
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Majority Rule
• Throughout our discussion of voting, we will assume that decisions will be made by majority rule– there is nothing particularly sacred about a
rule requiring that a policy obtain 50 percent of the vote to be adopted
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The Paradox of Voting
• In the 1780s, social theorist M. de Condorcet noted that majority rule voting systems may not arrive at an equilibrium– instead, they may cycle among alternative
options
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The Paradox of Voting
• Suppose there are three voters (Smith, Jones, and Fudd) choosing among three policy options– we can assume that these policy options
represent three levels of spending on a particular public good [(A) low, (B) medium, and (C) high]
– Condorcet’s paradox would arise even without this ordering
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The Paradox of Voting
Smith Jones Fudd
A B C
B C A
C A B
• Preferences among the three policy options for the three voters are:
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The Paradox of Voting
• Consider a vote between A and B– A would win
• In a vote between A and C– C would win
• In a vote between B and C– B would win
• No equilibrium will ever be reached
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Single-Peaked Preferences
• Equilibrium voting outcomes always occur in cases where the issue being voted upon is one-dimensional and where voter preferences are “single-peaked”
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Single-Peaked Preferences
Quantity ofpublic good
Utility
A B C
Smith
We can show each voters preferences in terms of utility levels
Jones
Fudd
For Smith and Jones, preferences are single-peaked
Fudd’s preferences have two local maxima
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Single-Peaked Preferences
Quantity ofpublic good
Utility
A B C
Smith
Jones
Option B will be chosen because it will defeat both A and C by votes 2 to 1
If Fudd had alternative preferences with a single peak, there would be no paradox
Fudd
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The Median Voter Theorem
• With the altered preferences of Fudd, B will be chosen because it is the preferred choice of the median voter (Jones)– Jones’s preferences are between the
preferences of Smith and the revised preferences of Fudd
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The Median Voter Theorem
• If choices are unidimensional and preferences are single-peaked, majority rule will result in the selection of the project that is most favored by the median voter– that voter’s preferences will determine
what public choices are made
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A Simple Political Model• Suppose a community is characterized
by a large number of voters (n) each with income of yi
• The utility of each voter depends on his consumption of a private good (ci) and of a public good (g) according to
utility of person i = Ui = ci + f(g)
where fg > 0 and fgg < 0
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A Simple Political Model
• Each voter must pay taxes to finance g• Taxes are proportional to income and
are imposed at a rate of t• Each person’s budget constraint is
ci = (1-t)yi
• The government also faces a budget constraint
An
ii tnytyg
1
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A Simple Political Model
• Given these constraints, the utility function of individual i is
Ui(g) = [yA - (g/n)]yi /yA + f(g)
• Utility maximization occurs when
dUi /dg = -yi /(nyA) + fg(g) = 0
g = fg-1[yi /(nyA)]
• Desired spending on g is inversely related to income
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A Simple Political Model
• If G is determined through majority rule, its level will be that level favored by the median voter– since voters’ preferences are determined
solely by income, g will be set at the level preferred by the voter with the median level of income (ym)
g* = fg-1[ym/(nyA)] = fg
-1[(1/n)(ym/yA)]
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A Simple Political Model• Under a utilitarian social welfare
criterion, g would be chosen so as to maximize the sum of utilities:
n
i
AAi
Ai gnfgnygfyyngyUSW
1
)()](/)/[(
• The optimal choice for g then is
g* = fg-1(1/n) = fg
-1[(1/n)(yA/yA)]
– the level of g favored by the voter with average income
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Voting for Redistributive Taxation
• Suppose voters are considering a lump-sum transfer to be paid to every person and financed through proportional taxation
• If we denote the per-person transfer b, each individual’s utility is now given by
Ui = ci + b
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Voting for Redistributive Taxation
• The government’s budget constraint is
nb = tnyA
b = tyA
• For a voter with yi > yA, utility is maximized by choosing b = 0
• Any voter with yi < yA will choose t = 1 and b = yA
– would fully equalize incomes
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Voting for Redistributive Taxation
• Note that a 100 percent tax rate would lower average income
• Assume that each individual’s income has two components, one responsive to tax rates [yi (t)] and one not responsive (ni)
– also assume that the average of ni is zero, but its distribution is skewed right so nm < 0
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Voting for Redistributive Taxation
• Now, utility is given byUi = (1-t)[yi (t) + ni] + b
• The individual’s first-order condition for a maximum in his choice of t and g is now
dUi /dt = -ni + t(dyA/dt) = 0
ti = ni /(dyA/dt)
• Under majority rule, the equilibrium condition will be
t* = nm /(dyA/dt)
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Representative Government• In representative governments, people
vote for candidates, not policies
• Politicians’ policy preferences are affected by a variety of factors– their perceptions of what their constituents
want– their view of the “public good”– the forcefulness of “special interests”– their desire for reelection
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Probabilistic Voting• Assume there are only two candidates
for a political office– each candidiate announces his platform (1
and 2)
– also assume that the candidate, once elected, will actually seek to implement the platform he has stated
• Each of the n voters observe the two platforms and choose how to vote
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Probabilistic Voting
• The probability that voter i will vote for candidate 1 is
i = fi [Ui(1) - Ui(2)]
where f’ > 0 and Ui(j) is the utility that
voter i expects to receive from platform j
• The probability that voter i will vote for candidate 1 is 1 - i
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The Candidate Game
• Candidate 1 chooses 1 to maximize the probability of his election
n
i
n
iiiii UUfEV
1 1211 )]()([ vote expected
• Candidate 2 chooses 2 to maximize his expected votes
n
ii EVnEV
112 )1( vote expected
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The Candidate Game• Our voting game is a zero-sum game
with continuous strategies (1 and 2)
• Thus, this game will have a Nash equilibrium set of strategies for which
EV1(1,2*) EV1(1*,2*) EV1(1*,2)
– Candidate 1 does best against 2* by
choosing 1*
– Candidate 2 does best against 1* by choosing 2*
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Net Value Platforms
• A “net value” platform is one under which a candidate promises a unique dollar benefit to each voter
• Suppose candidate 1 promises a net dollar benefit of 1i to each voter
• The candidate is bound by a government budget constraint:
n
ii
11 0
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Net Value Platforms
• The candidates’ goal is to choose 1i that maximizes EV1 against 2*
• Setting up the Lagrangian yields
n
iiEV
111L
n
iiii UUf
1121 )]*()([L
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Net Value Platforms
• The first-order condition for the net benefit promised to voter i is given by
L/1i = fi’Ui’ + = 0
• If the function fi is the same for all voters, this means that the candidate should choose 1i so that Ui’ is the same for all voters– a utilitarian outcome
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Rent-Seeking Behavior
• Elected politicians perform the role of agents– choose policies favored by principals
(voters)
• A perfect agent would choose policies that the fully informed median voter would choose– are politicians so selfless?
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Rent-Seeking Behavior
• Politicians might engage in rent-seeking activities– activities that seek to enhance their own
welfare
• This would create an implicit tax wedge between the value of public goods received by voters and taxes paid
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Rent-Seeking Behavior
• Extraction of political rent r would require that the government budget constraint be rewritten as
g = tnyA - r
• Voters would take such rent-seeking activities into account when deciding on public policies– would likely reduce g and t
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Rent-Seeking Behavior• Whether political rents can persist in an
environment of open electoral competition is questionable– Candidate A announces policy (g,t)A – Candidate B can always choose a policy
(g,t)B that is more attractive to the median voter by accepting a smaller rent
• Only with barriers to entry or imperfect information can positive rents persist
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Rent-Seeking Behavior
• Private citizens may also seek rents for themselves by asking politicians to grant them favors
• Thus, economic agents engage in rent-seeking activities when they use the political process to generate economic rents that would not ordinarily occur in market transactions
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Rent Dissipation
• If a number of actors compete in the same rent-seeking activity, it is possible that all available rent will be dissipated into rent seekers’ costs
• Suppose a monopoly might earn profits of m and a franchise for the monopoly can be obtained from the government for a bribe of B (B < m)
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Rent Dissipation
• Risk-neutral entrepreneurs will offer bribes as long as the expected gain exceeds the cost of the bribe
• If each rent seeker has the same chance of winning the franchise, the number of bribers (n) will expand to the point at which
B = m /n
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Important Points to Note:
• Choosing equitable allocations of resources is an ambiguous process because many potential welfare criteria might be used– in some cases, achieving equity
(appropriately defined) may require some efficiency sacrifices
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Important Points to Note:
• Arrow’s impossibility theorem shows that, given fairly general assumptions, there is no completely satisfactory social choice mechanism– the problem of social choice theory is
therefore to assess the performance of relatively imperfect mechanisms
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Important Points to Note:
• Direct voting and majority rule may not always yield an equilibrium– if preferences are single-peaked,
however, majority rule voting on one-dimensional public questions will result in choosing policies most favored by the median voter
• such policies are not necessarily efficient
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Important Points to Note:
• Voting in representative governments may be analyzed using the tools of game theory– in some cases, candidates’ choices of
strategies will yield Nash equilibria that have desirable normative consequences
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Important Points to Note:
• Politicians may engage in opportunistic rent seeking, but this will be constrained by electoral competition