IntroductionTo include societys value of commodities under alternative resource allocations directly involves welfare economicsStudy of all feasible allocations of resources for a society Establishment of criteria for selecting among these allocationsPublic Choice TheoryAttempts to understand and explain societys actual choice for resource allocationChoice is based on normative economics Involves value judgments Since various agents have conflicting value judgments, it is difficult to establish a socially optimal allocationEven if these differing value judgments prevent a socially optimal allocationTheory of welfare economics provides a method for delineating important conceptual issues facing all societies

IntroductionAim in this chapter is to investigate how economic theory attempts to reconcile individual decentralized resource allocation with overall social values of a societyMay be accomplished with a social-welfare functionRequires a cardinal measure of individual consumer preferencesWe maximize welfare function subject to a utility possibilities frontier based on individual consumers preferencesThen we specify and compare alternative egalitarian social-welfare functionsWe discuss Arrows Impossibility TheoremIndicates that a social-welfare function is impossible given consumers ordinal ranking of utility and based on some reasonable assumptions concerning societys social rankings

IntroductionBecause we cannot determine a social ranking based on individual consumers ordinal preferencesWe evaluate idea of majority voting as a second-best Pareto-optimal allocationWe discuss causes of market failureSuch as monopoly power, externalities, public goods, and asymmetric information As potential constraints on improving social welfareWe demonstrate Theory of the Second Best by showing how any policy designed for improving social welfare that only corrects some constraints may not result in social welfare improvementBecause economists are unable to specify a social-welfare function, an army of applied economists is required to develop and direct mechanism designs for filling in economic gaps resulting from missing marketsObjective of each mechanism is to yield an incremental improvement in social welfareTtonnement process will move a society toward maximum social welfare

Social-Welfare Function Using broad definition of social welfare as a level of happiness for society as a wholeMeasurement for this happiness is needed to determine socially optimal allocation of resourcesSuch a measurement for determining how well off agents are in a society requires a set of welfare criteriaMuch of research on formulation of welfare criteria and their implications for economic policy has relied on Pareto-allocation criterionA Pareto criterion is a value judgment based on unanimity ruleIf one agent could be made better off without reducing welfare of othersSocial welfare could be improved by allocation that makes this one agent better offSince no one agent is made worse off and at least one agent is made better offIt is assumed, given independence of utility functions, that all agents would support Pareto criterion

Social-Welfare Function Pareto-optimal allocation yields an efficient allocation of resources and thus is a necessary condition for a social optimumHowever, many decisions on allocation result in an improvement of one agents utility at expense of other agentsFor example, a redistribution of endowments from taxing rich households and providing subsidized housing for poor households may increase social welfare But cannot be justified by Pareto criterionFundamental inadequacy of Pareto criterion is its inability to yield a complete ranking of all social states within an economyPareto criterion is useless in context of many policy propositions, so additional welfare criteria are necessary to determine if these policies will improve social welfareTo investigate a social-welfare function, a comparison of individual consumers utilities is generally required Assumed that utility functions can be measured on a cardinal scaleUnder this assumption, taking a monotonic transformation of utility function will change preference relationships

Pure-exchange Economy Consider pure-exchange economy developed in Chapter 6Two-consumer (Friday and Robinson), two-commodity (q1 and q2) economy is illustrated in Figure 20.1Only points on contract curve can be considered as possible candidates for a social optimumFor example, points P1, P2, and P3 represent tangencies of Fridays and Robinsons indifference curvesAny point off this contract curve is not Pareto efficientPossible to increase welfare of one consumer without reducing welfare of the otherFrom contract curve in Figure 20.1,we can derive a utility possibilities frontierTheoretically similar in construction to production possibilities frontier

Figure 20.1 Contract curve for a two-consumer, two-commodity pure-exchange economy

Pure-exchange EconomyUtility possibilities frontierMapping of Pareto-efficient utilities for Robinson, R, and Friday, F, corresponding to each point on contract curve For P1, P2, and P3, in Figure 20.1, corresponding utility levels for Robinson and Friday are plotted on horizontal and vertical axes, respectively, in Figure 20.2Points on utility possibilities frontier correspond to tangency of indifference curves along contract curve in Figure 20.1Utility combinations associated with P1, P2, and P3 are same for both figuresEvery point inside this utility possibilities frontier is a feasible allocation Corresponding to points inside Edgeworth box of Figure 20.1Boundary of utility possibilities frontier represents efficiency locus (contract curve) in Figure 20.1

Pure-exchange EconomyFor a given amount of q1 and q2, utility possibilities frontier indicates combination of UR and UF that can be obtainedAn increase in amount of q1 and q2 will result in utility possibilities frontier shifting outwardWith increasing opportunity cost (which yields a concave utility possibilities frontier) Sacrifice in Fridays utility increases for an additional unit increase in Robinsons utilityHowever, although a monotonic transformation of an agents utility function preserves preference orderingIt can result in opportunity cost switching from increasing to decreasingOne basis for assumption of measuring utility on a cardinal scale

Figure 20.2 Utility possibilities frontier

Production and Exchange Economy We can also derive a utility possibilities frontier in a general-equilibrium context by considering productionEfficiency condition is based on a given level of utility for FridayIllustrated in Figure 20.3Changing this level of utility for Friday will result in alternative combinations of q1 and q2 produced and allocated between Robinson and FridayAs illustrated in Figure 20.4, maximizing Robinsons utility given UFas Fridays level of satisfaction results in Pareto-efficient allocation of (qR1, qR2, qF1, qF2) with q*1 and q*2 efficiently producedWith an alternative level of satisfaction for Friday, say UF' maximizing Robins utility will result in an alternative Pareto-efficient allocation, (qR'1, qR'2, qF'1, qF'2) with q*1 and q*2 producedIn general, considering all possible Pareto-efficient allocations (MRSR = MRSF = MRPT)We obtain a collection of Pareto-efficient utility levels for both Robinson and Friday By varying Fridays utility from zero to level where Robinsons utility would be zeroPlotting these Pareto-efficient utility combinations yields utility possibilities frontier in Figure 20.2

Figure 20.3 Efficiency in production and exchange for a two-consumer economy

Figure 20.4 Efficiency in production and exchange for alternative utility levels

Production and Exchange Economy For an economy with production, every utility bundle on this frontier represents a Pareto-efficient allocationWhere MRSR = MRSF and MRSR = MRSF = MRPTA utility bundle in interior of frontier, say point A, is not Pareto optimalIt is possible to increase either Robinsons or Fridays utility without decreasing others utilityIn contrast, on the frontier, say at point P1, Fridays utility cannot be increased without reducing Robinsons utilityAt P1 utility combination and any other utility bundle on frontier are Pareto optimalInitial endowment of resources held by Robinson and Friday will determine agents location on frontierIf Robinson has a proportionally larger share of initial resources, utility bundle P1 may resultA reversal of endowments may yield a higher utility level for Friday, such as bundle P3

Maximizing Social Welfare Even after eliminating all Pareto-inefficient allocations, there remains an infinite number of efficient allocationsRepresented by infinite number of points on utility possibilities frontierFirst Fundamental Theorem of Welfare Economics A perfectly competitive equilibrium will result in a Pareto-efficient allocationDepending on initial distribution of endowments, a perfectly competitive equilibrium can occur at any point on utility possibilities frontierHowever, from a societys point of view, allocation resulting from a perfectly competitive equilibrium may not be equitableSociety may redistribute income (initial endowments) among consumers in an effort to achieve equityMay take form of redistributing income Taxing wealthy and giving tax revenue to poor Providing commodities to poor (for example, Medicare or surplus food from agricultural support programs)Market regulation (for example, rent control or agricultural price supports)

Maximizing Social Welfare Efforts by governments to achieve a more equitable allocation are costly in terms of possibly generating inefficiencies within an economyFor example, government playing Robin Hood dampens incentive to work and investOften directs resources toward tax avoidanceCan use concept of a social-welfare function as method for determining socially optimal allocation among points on a utility possibilities frontierWith a social-welfare function, can determine point that maximizes social welfare in terms of both equity and efficiency criteriaAssuming government is not paternalistic, this function would generally depend on welfare (utility) of agents within an economyGovernment would then maximize social welfare subject to utility possibilities frontier

Maximizing Social Welfare For example, consider following social-welfare function, U, for an economy consisting of two consumers (Robinson, R, and Friday, F)Assuming a diminishing marginal rate of substitution between consumer utilities, we can determine convex social indifference, or isowelfare, curvesAssumption implies that society has inequality aversionWhere (holding social welfare constant) the more satisfaction Robinson has the less society is willing to give up Fridays utility for one more unit of Robinsons utilityAs illustrated in Figure 20.5, tangency between a social indifference curve and utility possibilities frontier results in maximum level of social welfarePoint P2 is only point on utility possibilities frontier where there is no other point preferred to it For example, point P3 is Pareto efficient but there are points that are preferred to P3Even though point A is Pareto inefficient, society prefers it over Pareto-efficient point P3Using maximum level of social welfare, point P2, we determine optimal allocation of commodities in Edgeworth box (Figure 20.1) for a pure-exchange economyOr in production possibilities frontier (Figure 20.3) for a production and exchange economy

Figure 20.5 Maximizing social welfare

Shapes of Isowelfare Curves A social-welfare function represents societys preferences for particular Pareto-efficient points on a utility possibilities frontierVarious social preferences may be represented by social indifference curves taking on various shapesThese shapes (and thus social preferences) are generally based on some equitable allocation among Pareto-efficient allocationsComparison of alternative Pareto-efficient points requires value judgments concerning trade-off among consumer utilitiesCan be no one definition for equitySocial indifference curves will take on a number of forms Depending on which criterion (value judgment) is employed for determining equitable allocationTwo criteriaegalitarian and utilitarian

Egalitarian Egalitarianism can take two formsAllocate each consumer an equal amount of each commodity In terms of our Robinson and Friday two-commodity economy, this egalitarian criterion sets qR1 = qF1 and qR2 = qF2In a pure-exchange economy, Robinson and Friday would split total endowment of each commodity in halfUnless Robinson and Friday have identical utility functions, level of utility achieved by them will not be the sameBut their utility levels are not a factor in this egalitarian equityIn terms of a social-welfare function, social preferences for Robinsons or Fridays utilities are identical Are perfect substitutes as long as commodities are allocated equally between themMaximizing welfare function with additional constraint that it be Pareto-efficient in terms of a utility possibilities frontier will result in maximizing social welfare

Egalitarian Second type of egalitarian criterion is an allocation of commoditiesResulting in equality of utilities across all consumersFor Robinson and Friday, this criterion sets UR = UFA social-welfare function resulting in equality of utilities is Rawlsian criterionMost equitable allocation maximizes utility of least-well-off consumer in societyFor Robinson and Friday, Rawlsian criterion isMaximum level of social welfare given a specific utility possibilities frontier is on Pareto-efficient utility possibilities frontier (Figure 20.6)Unless Robinson and Friday have the same utility functionsEquality of utilities will not result in Robinson and Friday each receiving the same commodity allocation

Figure 20.6 Rawlsian social-welfare function

Utilitarian Maximizes sum of consumers utilityCriterion was formally developed by Bentham and provided initial impetus to utility theoryFor Robinson and Friday, criterion isCalled classical utilitarian, or Benthamite welfare functionMaximized subject to a utility possibilities frontier (Figure 20.7)Under utilitarian criterion, increases or decreases in individual consumers utility results in identical changes in social welfareOnly total utility is relevant, so utilitarian criterion does not consider distribution of utilityAs long as social gain is greater than social loss, it makes no difference that consumer who gains in utility may already be happier than the other consumerUnless utility functions of individual consumers are close to being identicalUtilitarian criteria can result in substantial differences in consumers utilityAlthough ethics teaches that virtue is its own reward, classical utilitarian function teaches that reward is its own virtueOnly total level of utility is important

Figure 20.7 Benthamite (classical utilitarian) social welfare function

Utilitarian By incorporating some virtue into classical utilitarian function, we get a generalization of this function Weighted sum of utilities Weights (R, F) indicate how important each consumers utility is to overall social welfareFor example, utility of an individual such as Mother Teresa will be weighted higher than that of a child sex offenderIn Figure 20.7, utilitarian social welfare optimal allocation is tangency between social indifference curve and utility possibilities curveDepending on weights associated with individual consumers utilityAny Pareto-efficient point on utility possibilities frontier could be a social-welfare maximumThe more egalitarian a society is, the more its social indifference curves will approach right anglesIndicating society is concerned with equity issues of distributionFor a utilitarian society that is indifferent to distribution, curves are more linearShowing society simply maximizes output

Arrows Impossibility Theorem A problem in maximizing social welfare is how to establish this social-welfare functionA welfare function based on individual consumer preferences would be a desirableAssuming social welfare is to reflect some aggregate consumer preferencesHowever, because preference ranking by consumers is generally only ordinalThere is not sufficient information to determine a reasonable social preference ranking of choicesNumerous examples where, due to ordinal preference ranking among individuals, an aggregate ranking is impossibleOne example is Battle of the Sexes game discussed in Chapter 14Couple cannot jointly (socially) rank their preferences for opera or fights

Arrows Impossibility Theorem Arrows Impossibility Theorem Impossible to establish a reasonable social preference ranking based solely on individual ordinal preference rankingsSuppose there are several feasible social statesIt is assumed each individual in society can ordinally rank these states as to their desirabilityTo derive a social-welfare function, there must exist a ranking of these states on a society-wide scale that fairly considers these individual preferencesLets consider just three possible social states (A, B, and C)For example, these states could be sending a human to Mars, building and equipping a new aircraft carrier, or curing cancerArrows Impossibility Theorem says a reasonable social ranking of these three states cannot exist based only on how individual agents ordinally rank these states

Arrows Impossibility Theorem A reasonable social ranking may be stated with the following axioms relating individual consumers preferencesAxiom 1: CompletenessSocial ranking must rank all social statesEither A > B, B > A, or A B for any two statesIdentical to Completeness Axiom for individual preference orderingAxiom 2: TransitivitySocietys social ranking must be transitiveGiven three social states, A, B, and C, if A > B and B > C, then A > CIdentical to Transitivity Axiom for individual preference orderingAxiom 3: ParetoIf every consumer prefers A to B, then A is preferable in a social rankingThis also holds for the other two pairs (A, C) and (B, C)Identical to a Pareto improvementAxiom 4: NondictatorialOne consumers preferences should not determine societys preferencesNo agent paternalismAxiom 5: Pairwise IndependenceSocietys social ranking between A and B should depend only on individual preferences between A and BNot on individual preferences for some other social state, say state CIdentical to Independence Axiom for individual preference ordering of states of nature

Arrows Impossibility Theorem Can now state Arrows Impossibility Theorem more formallyA social preference ranking satisfying these five axioms is impossible, given an ordinal ranking of individual agent preferencesImplies that there is no way to aggregate agents ordinal preferences into a social preference ranking without relaxing at least one of these axiomsAxioms may seem a reasonable set of conditions for democratically choosing among social statesHowever, Arrow demonstrated that it is impossible to socially choose among all possible sets of alternatives without violating at least one of the axiomsThus, social choice must be unreasonable if it is based on agents ordinal preference ranking

Majority Voting To see that Arrows Impossibility Theorem holds, lets consider majority votingImportant social preference mechanism design Set of rules governing procedures for social [collective] choiceMajority voting satisfies both Pareto Axiom and Nondictatorial AxiomSensitive to each individual agents preferencesMajority voting is symmetric among agentsTreats all agents the same and all agents have just one voteIt is also neutral among alternativesBy not making a distinction among alternatives a prioriHowever, majority rule can lead to a pattern of social choices that is not transitive Even though every voter has ordinal and transitive preferencesThus, it violates Axiom 2

Majority Voting Consider ballot in Table 20.1 among three voters, Robinson, Friday, and SimpsonVoters preferences are as followsRobinson and Simpson prefer alternative A to BRobinson and Friday prefer alternative B to CFriday and Simpson prefer alternative C to AMajority (two) prefers A to B and B to C, but majority also prefers C to AThus majority voting results in a cyclical pattern that is intransitiveCalled Condorcet Paradox Presents a major problem for group decision making

Table 20.1 Condorcet Paradox

Majority Voting Next lets consider case in which each voter must vote for just one alternativeAs illustrated in panel (a) of Table 20.2, ordinal preference ranking in Table 20.1 results in a three-way tieAll three alternatives receive equal votesHowever, if one alternative is removed, a clear winner resultsAs illustrated in panel (b), when alternative C is removed, alternative A receives majority voteHere, Axiom 5 is violatedWe see this violation of Axiom 5 often in U.S. presidential electionsWhere a third-party candidate has determined the outcome

Table 20.2 Pairwise Independence

Majority Voting Development of a social-welfare function requires more than just an ordinal ranking of individual consumer preferencesRequires a comparison of utilities across consumers on a cardinal scaleFor example, one reason a third party can influence results of an election is that no weight is given to intensity of voters desiresHowever, intensity of desires is a utility measure that can only be measured on at least a cardinal scaleMagnitude or intensity of an individual voters desires is not known when she votesHowever, allowing voters an ordinal preference ranking (Table 20.1) instead of just one vote (Table 20.2) does elicit additional information on voters preferenceMay result in a social ranking more consistent with a majority of electorateNew voting machines, being put into place after 2000 presidential election, have capability to allow voters to ordinally rank candidatesCalled instantaneous voting, procedure has not yet been widely adopted But offers potential of further revealing voters preferences and mitigating any strategic voting

Strategic Voting A problem with allowing ordinal ranking of candidates (or any other choices) is possibility of strategic votingWhere an agent does not reveal her true preferences but instead votes to enhance outcome in her favorA game-theory strategy Particularly effective when number of voters is relatively small or when a strategic-voting coalition can be formedOne form of strategic voting is for an agent, say Friday, to rank her first choice highestThen rank other alternatives inversely to expected outcomeThus, Friday would rank alternative expected to be in close competition with her first choice last, suppressing competitive threatStrategic voting is illustrated in Table 20.3 for determining social ranking of four alternativesIn panel (a), alternative A, which was not Fridays top choice, comes out on topHowever, as illustrated in panel (b), Friday can change outcome by ranking alternative A low (strategic voting)Now Fridays top choice, alternative B, comes out on top as the social choiceJudges in Olympic games have been accused of practicing this type of strategic voting

Table 20.3 Strategic Voting

Strategic Voting A method for removing this potential of strategic voting is sequential votingLowest-ranking alternative after each vote is dropped and another vote is then taken on remaining alternativesIn panel (b) of Table 20.3, alternative C only received a rating of 5Dropping this alternative from list yields individual preference ranking for the three alternatives listed in panel (a) of Table 20.4Now alternative D receives lowest rankingDropping alternative D and re-voting on alternatives A and B yields outcome in panel (b)From panel (b), alternative A is still selected even given strategic voting by Friday

Table 20.4 Sequential Voting

Strategic Voting Sequential voting is used to elect Speaker of the House in U.S. House of RepresentativesEmploying sequential voting also allows for a social ranking of alternatives based on Pairwise Independence AxiomImplementing such a process for U.S. presidential elections would probably have changed a number of outcomesBy adopting instantaneous voting, where voters rank their choicesLow-ranking alternatives could be automatically dropped until only two alternatives are leftGiven these two remaining alternatives, a president with majority of support would then be elected

Strategic Voting Illustrates that a confederation of individuals forming a society should not be expected to behave with same coherence as would be expected from an individualArrows Theorem implies that institutional detail and procedures of a political process (mechanism design) cannot be neglectedThus, it is not surprising that academic disciplines that complement economics, such as political science and psychologyHave evolved to address process of group choiceAttempt to determine intensities of individual and group desires Formulate policies and rules for group choice and actionsAs demonstrated by Condorcet Paradox and quid pro quo example in Chapter 14An agenda that determines which alternatives are first considered will affect social choice

Market Failure Suppose some process for group decision does exist for determining optimal social choiceA naive solution, based on Second Fundamental Theorem of Welfare EconomicsWould advocate allowing markets freedom to obtain this social optimal given a reallocation of endowmentsUnfortunately, this solution is based on properties of a perfectly competitive equilibriumExtreme theoretical case of resource allocationDoes not generally hold for any societyWhen properties of a perfectly-competitive equilibrium do not holdResulting equilibrium is not efficient, so market failure exists

Market Failure In general, conditions causing market failure are classified into four categoriesMonopoly powerExists when one or a number of agents (suppliers or demanders of a commodity) exert some market power in determining prices ExternalitiesAn interaction among agents that are not adequately reflected in market priceseffects on agents are external to marketAir pollution is classic example of an externality Public goodsOne individuals consumption of a commodity does not decrease ability of another individual to consume itExamples are national defense, income distribution, and street lightsAsymmetric informationWhen perfectly competitive assumption of all agents having complete information about commodities offered in market does not holdIncomplete information can exist when cost of verifying information about a commodity may not be universal across all buyers and sellersFor example, sellers of used automobiles may have information about quality of various automobiles that may be difficult (costly) for potential buyers to acquireWhen there is asymmetry in information buyers may purchase a product in excess of a given quality

Market Failure Existence of monopoly power, externalities, public goods, and asymmetric information are justification for establishment of governments to provide mechanisms to address resulting market failuresGovernments can regulate firms with objectives of mitigating monopoly power and negative externalitiesGovernments can provide for public goods either by direct production or private incentivesGovernments can generate information, aid in its dissemination, and mandate that information be provided in an effort to reduce asymmetric informationThe more a government must intervene in marketplace to correct these failuresThe less dependent will the economy be on freely operating markets

Market Failure In some societies these market failures appear quite large and, thus, freely operating markets are severely limitedTrue in many centrally-planned economiesWhere government determines what and how to produce as well as who should receive commodities producedEven within U.S., which generally relies on free markets to allocate resources and outputs, there is always the question concerning level of government interventionFor example, many environmental regulations directly limit inputs firms can use in their production decisionsFor example, local zoning ordinances may restrict a firms use of inputs that generate noise, smoke, or odors