1. BASIC PRINCIPLES AND EXTENSIONS
Chapter 25
POLITICAL ECONOMICS
MICROECONOMIC THEORY
BASIC PRINCIPLES AND EXTENSIONS
EIGHTH EDITION
WALTER NICHOLSON
Copyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.

2. 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

3. 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

4. Social Welfare CriteriaOJ
Contract curve
UJ1
US4
US3
US2
US1
UJ2
UJ3
UJ4 OS

5. 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

6. Social Welfare Criteria
The utility possibility frontier shows those utility levels for Smith and Jones that are obtainable from the fixed quantity of goods available
Jones’s utility OS
Any point inside the curve is Pareto-inefficient  C
Smith’s utility OJ

7. Equality Criterion
One possible criterion could require complete equity giving Smith and Jones the same level of welfare
45°
Jones’s utility OS
This occurs at UJA and USA
USA
UJA  A
Utility is equal in this case, but the quantities of X and Y may not be
Smith’s utility OJ

8. Equality Criterion OJ OS XJA UJ1 UJA US2 A  UJ2 USA YSA US1
XSA
XJA OJ
YSA A 
Contract curve
UJ1
UJA
US2
UJ2
USA
US1 OS

9. 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

10. 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

11. The Rawls Criterion
Unequal distributions such as B would be permitted when the only attainable equal distributions are below D
Jones’s utility OS B 
Equal distributions that lie between D and A are superior to B because the worse-off individual is better off there than at B A   D
45°
Smith’s utility OJ

12. 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

13. Social Welfare Functions
The optimal point of social welfare is where W is maximized given the utility possibility frontier W1 W2
Jones’s utility OS E
This occurs at UJE and USE
USE
UJE 
Smith’s utility OJ

14. Social Welfare Functions
Note the tradeoff between equity and efficiency D  F
Jones’s utility
Even though point F is Pareto-inefficient, it is still preferred to point D OS W2 W1
Smith’s utility OJ

15. 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
Teen 2 has a utility function of the form

16. 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

17. 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

18. 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

19. 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

20. Equitable Sharing
Suppose that each teen believes that he has a chance of being labeled as “teen 1” or “teen 2”
Expected utilities are
X1 = X2 = E(U1) = 0.5(4) + 0.5(2) = 3
X1 = 1.6, X2 = E(U1) = 0.5(2.53) + 0.5(2.53) = 2.53
X1 = 6.4, X2 = E(U1) = 0.5(5.06) + 0.5(1.26) = 3.16
The teens will opt for the utilitarian solution

21. 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 societywide scale that fairly records these preferences?

22. 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

23. 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”

24. 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

25. 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

26. The Arrow Axioms The relationship should be nondictatorial
one person’s preferences should not determine society’s preferences

27. 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

28. Significance of the Arrow 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

29. Direct Voting
Voting is used as a decision process in many social 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

30. Majority Rule
Throughout our discussion of voting, we will assume that decisions will be made by majority rule
Keep in mind though, that there is nothing particularly sacred about a rule requiring that a policy obtain 50 percent of the vote to be adopted

31. 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

32. 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 without this ordering

33. The Paradox of Voting
Preferences among the three policy options for the three voters are:

34. 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

35. 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”

36. Single-Peaked Preferences
We can show each voters preferences in terms of utility levels
Utility
For Smith and Jones, preferences are single-peaked 
Smith 
Fudd 
Jones
Fudd’s preferences have two local maxima
Quantity of
public good A B C

37. Single-Peaked Preferences
If Fudd had alternative preferences with a single peak, there would be no paradox 
Fudd
Utility
Option B will be chosen because it will defeat both A and C by votes 2 to 1 
Smith 
Jones
Quantity of
public good A B C

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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)]

44. A Simple Political Model
Under a utilitarian social welfare criterion, G would be chosen so as to maximize the sum of utilities:
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

45. 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 g, each individual’s utility is now given by
Ui = Ci + g

46. Voting for Redistributive Taxation
The government’s budget constraint is
ng = tnYA
g = tYA
For a voter with Yi > YA, utility is maximized by choosing g = 0
Any voter with Yi < YA will choose t = 1 and g = YA
would fully equalize incomes

47. 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

48. Voting for Redistributive Taxation
Now, utility is given by
Ui = (1-t)[Yi (t) + Ni] + g
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)

49. 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

50. 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

51. Probabilistic Voting
The probability that voter i will vote for candidate 1 is
i = fi [Ui(1) - Ui(2)]
where f’ > 0 and f’’< 0
The probability that voter i will vote for candidate 1 is 1 - i

52. The Candidate Game
Candidate 1 chooses 1 so as to maximize the probability of his election
Candidate 2 chooses 2 so as to maximize his expected votes

53. EV1(1,2*)  EV1(1*,2*)  EV1(1*,2)
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*

54. Net Value Platforms
A “net value” platform is one in which a candidate promises a unique dollar benefit to each voter
Suppose candidate 1 promises a net dollar benefit of 1 to each voter
The candidate is bound by a government budget constraint:

55. Net Value Platforms
The candidates’ goal is to choose 1 that maximizes EV1 against 2*
Setting up the Lagrangian yields

56. 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

57. 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?

58. 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

59. 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

60. Rent-Seeking Behavior
Whether political rents can exist 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

61. 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

62. 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

63. Rent Dissipation
Risk-neutral entrepreneurs will offer bribes as long as the expected net gain is positive
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

64. 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

65. 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

66. 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

67. 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
Politicians may engage in opportunistic rent seeking, but this will be constrained by electoral competition