Chapter 25Social Welfare CriteriaSlide 3Slide 4Slide 5Slide 6Equality CriterionSlide 8Utilitarian CriterionThe Rawls CriterionSlide 11Social Welfare FunctionsSlide 13Slide 14Equitable SharingSlide 16Slide 17Slide 18Slide 19Slide 20The Arrow Impossibility TheoremSlide 22Slide 23The Arrow AxiomsSlide 25Slide 26Arrow’s ProofSignificance of the Arrow TheoremDirect VotingMajority RuleThe Paradox of VotingSlide 32Slide 33Slide 34Single-Peaked PreferencesSlide 36Slide 37The Median Voter TheoremSlide 39A Simple Political ModelSlide 41Slide 42Slide 43Slide 44Voting for Redistributive TaxationSlide 46Slide 47Slide 48Representative GovernmentProbabilistic VotingSlide 51The Candidate GameSlide 53Net Value PlatformsSlide 55Slide 56Rent-Seeking BehaviorSlide 58Slide 59Slide 60Slide 61Rent DissipationSlide 63Important Points to Note:Slide 65Slide 66Slide 67Chapter 25POLITICAL ECONOMICSCopyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.MICROECONOMIC THEORYBASIC PRINCIPLES AND EXTENSIONSEIGHTH EDITIONWALTER NICHOLSONSocial 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 BSocial 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 competitiveSocial Welfare CriteriaOJOSUJ4UJ3UJ2UJ1US4US3US2US1Contract curveSocial 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 frontierSocial Welfare CriteriaSmith’s utilityJones’s utilityOJOSThe utility possibility frontier shows those utility levels for Smith and Jones that are obtainable from the fixed quantity of goods availableAny point inside the curve is Pareto-inefficient-CEquality CriterionSmith’s utilityJones’s utilityOJOSOne possible criterion could require complete equity giving Smith and Jones the same level of welfare45°Utility is equal in this case, but the quantities of X and Y may not be This occurs at UJA and USAUSAUJA-AContract curveEquality CriterionOJOSUJ2UJAUJ1US2USAUS1A-XSAXJAYSAYSAUtilitarian 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 JonesThe 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 equalityThe Rawls CriterionSmith’s utilityJones’s utilityOJOSUnequal distributions such as B would be permitted when the only attainable equal distributions are below D45°DBAEqual distributions that lie between D and A are superior to B because the worse-off individual is better off there than at B---Social Welfare Functions•A social welfare function may depend on Smith’s and Jones’s utility levels such associal welfare = W(US,UJ)•The social problem is to allocate X and Y between Smith and Jones as to maximize WThe optimal point of social welfare is where W is maximized given the utility possibility frontierW1W2Social Welfare FunctionsSmith’s utilityJones’s utilityOJOSEThis occurs at UJE and USEUSEUJE-W1W2Social Welfare FunctionsSmith’s utilityJones’s utilityOJOSEven though point F is Pareto-inefficient, it is still preferred to point DNote the tradeoff between equity and efficiencyD--FEquitable 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 form112 XU •Teen 2 has a utility function of the form22XU 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 = 1.26Equitable 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 isE(U1) = 0.5(2.53) + 0.5(5.06) = 3.80E(U2) = 0.5(2.53) + 0.5(1.26) = 1.90Equitable Sharing•Given this choice, the teens will opt for the equal distribution because each gets higher expected utility from it than from the coin flipEquitable 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 2.53Equitable 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 solutionThe 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 BThe Arrow Impossibility Theorem•Arrow’s impossibility theorem consists of showing that a reasonable social ranking of these three