Chapter 25 POLITICAL ECONOMICS MICROECONOMIC THEORY BASIC PRINCIPLES

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.

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

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

Social Welfare Criteria OJ UJ 1 UJ 2 US 4 UJ 3 US 3 UJ 4 US 2 Contract curve OS US 1

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

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

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

Equality Criterion X JA OJ UJ 1 UJ YSA A US 2 A UJ 2 USA YSA Contract curve OS XSA US 1

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

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

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° OJ Smith’s utility

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

Social Welfare Functions The optimal point of social welfare is where W is maximized given the utility possibility frontier Jones’s utility OS UJ E E This occurs at UJE and USE W 2 W 1 USE OJ Smith’s utility

Social Welfare Functions Note the tradeoff between equity and efficiency Jones’s utility OS Even though point F is Pareto-inefficient, it is still preferred to point D D F W 2 W 1 OJ Smith’s utility

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

Equitable Sharing • The least resistance option would be to give each teen 4 slices – U 1 = 4, U 2 = 2 • The father may want to make sure the teens have equal utility – X 1 = 1. 6, X 2 = 6. 4, U 1 = U 2 = 2. 53 • The father may want to maximize the sum of his sons utility – X 1 = 6. 4, X 2 = 1. 6, U 1 = 5. 06, U 2 = 1. 26

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(U 1) = 0. 5(2. 53) + 0. 5(5. 06) = 3. 80 E(U 2) = 0. 5(2. 53) + 0. 5(1. 26) = 1. 90

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

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

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 X 1 = X 2 = 4 E(U 1) = 0. 5(4) + 0. 5(2) = 3 X 1 = 1. 6, X 2 = 6. 4 E(U 1) = 0. 5(2. 53) + 0. 5(2. 53) = 2. 53 X 1 = 6. 4, X 2 = 1. 6 E(U 1) = 0. 5(5. 06) + 0. 5(1. 26) = 3. 16 • The teens will opt for the utilitarian solution

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?

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

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”

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

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

The Arrow Axioms • The relationship should be nondictatorial – one person’s preferences should not determine society’s preferences

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

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

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

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

The Paradox of Voting • In the 1780 s, social theorist M. de Condorcet noted that majority rule voting systems may not arrive at an equilibrium – instead, they may cycle among alternative options

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

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

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

Single-Peaked Preferences • Equilibrium voting outcomes always occur in cases where the issue being voted upon is one-dimensional and where voter preferences are “singlepeaked”

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

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

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

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

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 f. G > 0 and f. GG < 0

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

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 d. Ui /d. G = -Yi /(n. YA) + f. G(G) = 0 G = f. G-1[Yi /(n. YA)] • Desired spending on G is inversely related to income

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* = f. G-1[Ym/(n. YA)] = f. G-1[(1/n)(Ym/YA)]

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* = f. G-1(1/n) = f. G-1[(1/n)(YA/YA)] – the level of G favored by the voter with average income

Voting for Redistributive Taxation • Suppose voters are considering a lumpsum 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

Voting for Redistributive Taxation • The government’s budget constraint is ng = tn. YA g = t. YA • 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

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

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 d. Ui /dt = -Ni + t(d. YA/dt) = 0 ti = Ni /(d. YA/dt) • Under majority rule, the equilibrium condition will be t* = Nm /(d. YA/dt)

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

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

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

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

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 EV 1( 1, 2*) EV 1( 1*, 2) – Candidate 1 does best against 2* by choosing 1* – Candidate 2 does best against 1* by choosing 2*

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:

Net Value Platforms • The candidates’ goal is to choose 1 that maximizes EV 1 against 2* • Setting up the Lagrangian yields

Net Value Platforms • The first-order condition for the net benefit promised to voter i is given by L/ 1 i = fi’Ui’ + = 0 • If the function fi is the same for all voters, this means that the candidate should choose 1 i so that Ui’ is the same for all voters – a utilitarian outcome

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?

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

Rent-Seeking Behavior • Extraction of political rent r would require that the government budget constraint be rewritten as G = tn. YA - r • Voters would take such rent-seeking activities into account when deciding on public policies – would likely reduce G and t

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

Rent-Seeking Behavior • Private citizens may also seek rents for themselves by asking politicians to grant them favors • Thus, economic agents engage in rentseeking activities when they use the political process to generate economic rents that would not ordinarily occur in market transactions

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

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

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

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

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 onedimensional public questions will result in choosing policies most favored by the median voter • such policies are not necessarily efficient

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