1. ©2005, Southwestern Slides by Pamela L. Hall Western Washington University Welfare Economics Chapter 20

2. 2 Introduction To include society’s value of commodities under alternative resource allocations directly involves welfare economics  Study of all feasible allocations of resources for a society  Establishment of criteria for selecting among these allocations Public Choice Theory  Attempts to understand and explain society’s actual choice for resource allocation Choice is based on normative economics  Involves value judgments  Since various agents have conflicting value judgments, it is difficult to establish a socially optimal allocation  Even if these differing value judgments prevent a socially optimal allocation  Theory of welfare economics provides a method for delineating important conceptual issues facing all societies

3. 3 Introduction Aim in this chapter is to investigate how economic theory attempts to reconcile individual decentralized resource allocation with overall social values of a society  May be accomplished with a social-welfare function Requires a cardinal measure of individual consumer preferences We maximize welfare function subject to a utility possibilities frontier based on individual consumers’ preferences  Then we specify and compare alternative egalitarian social-welfare functions We discuss Arrow’s Impossibility Theorem  Indicates that a social-welfare function is impossible given consumers’ ordinal ranking of utility and based on some reasonable assumptions concerning society’s social rankings

4. 4 Introduction Because we cannot determine a social ranking based on individual consumers’ ordinal preferences  We evaluate idea of majority voting as a second-best Pareto-optimal allocation We discuss causes of market failure  Such as monopoly power, externalities, public goods, and asymmetric information As potential constraints on improving social welfare We 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 improvement  Because 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 markets Objective of each mechanism is to yield an incremental improvement in social welfare Tâtonnement process will move a society toward maximum social welfare

5. 5 Social-Welfare Function Using broad definition of social welfare as a level of happiness for society as a whole  Measurement for this happiness is needed to determine socially optimal allocation of resources Such a measurement for determining how well off agents are in a society requires a set of welfare criteria Much of research on formulation of welfare criteria and their implications for economic policy has relied on Pareto-allocation criterion  A Pareto criterion is a value judgment based on unanimity rule  If one agent could be made better off without reducing welfare of others Social welfare could be improved by allocation that makes this one agent better off  Since no one agent is made worse off and at least one agent is made better off  It is assumed, given independence of utility functions, that all agents would support Pareto criterion

6. 6 Social-Welfare Function Pareto-optimal allocation yields an efficient allocation of resources and thus is a necessary condition for a social optimum  However, many decisions on allocation result in an improvement of one agent’s utility at expense of other agents For 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 criterion  Fundamental inadequacy of Pareto criterion is its inability to yield a complete ranking of all social states within an economy Pareto criterion is useless in context of many policy propositions, so additional welfare criteria are necessary to determine if these policies will improve social welfare To investigate a social-welfare function, a comparison of individual consumers’ utilities is generally required  Assumed that utility functions can be measured on a cardinal scale Under this assumption, taking a monotonic transformation of utility function will change preference relationships

7. 7 Pure-exchange Economy Consider pure-exchange economy developed in Chapter 6 Two-consumer (Friday and Robinson), two-commodity (q 1 and q 2 ) economy is illustrated in Figure 20.1 Only points on contract curve can be considered as possible candidates for a social optimum  For example, points P 1, P 2, and P 3 represent tangencies of Friday’s and Robinson’s indifference curves Any point off this contract curve is not Pareto efficient  Possible to increase welfare of one consumer without reducing welfare of the other From contract curve in Figure 20.1,we can derive a utility possibilities frontier  Theoretically similar in construction to production possibilities frontier

8. 8 Figure 20.1 Contract curve for a two- consumer, two-commodity pure-exchange economy

9. 9 Pure-exchange Economy Utility possibilities frontier  Mapping of Pareto-efficient utilities for Robinson, R, and Friday, F, corresponding to each point on contract curve  For P 1, P 2, and P 3, in Figure 20.1, corresponding utility levels for Robinson and Friday are plotted on horizontal and vertical axes, respectively, in Figure 20.2  Points on utility possibilities frontier correspond to tangency of indifference curves along contract curve in Figure 20.1 Utility combinations associated with P 1, P 2, and P 3 are same for both figures  Every point inside this utility possibilities frontier is a feasible allocation  Corresponding to points inside Edgeworth box of Figure 20.1  Boundary of utility possibilities frontier represents efficiency locus (contract curve) in Figure 20.1

10. 10 Pure-exchange Economy For a given amount of q 1 and q 2, utility possibilities frontier indicates combination of U R and U F that can be obtained  An increase in amount of q 1 and q 2 will result in utility possibilities frontier shifting outward With increasing opportunity cost (which yields a concave utility possibilities frontier)  Sacrifice in Friday’s utility increases for an additional unit increase in Robinson’s utility However, although a monotonic transformation of an agent’s utility function preserves preference ordering  It can result in opportunity cost switching from increasing to decreasing One basis for assumption of measuring utility on a cardinal scale

11. 11 Figure 20.2 Utility possibilities frontier

12. 12 Production and Exchange Economy We can also derive a utility possibilities frontier in a general-equilibrium context by considering production Efficiency condition is based on a given level of utility for Friday  Illustrated in Figure 20.3 Changing this level of utility for Friday will result in alternative combinations of q 1 and q 2 produced and allocated between Robinson and Friday As illustrated in Figure 20.4, maximizing Robinson’s utility given U F  as Friday’s level of satisfaction results in Pareto-efficient allocation of (q R 1, q R 2, q F 1, q F 2 ) with q* 1 and q* 2 efficiently produced  With an alternative level of satisfaction for Friday, say U F ' maximizing Robin’s utility will result in an alternative Pareto-efficient allocation, (q R' 1, q R' 2, q F' 1, q F' 2 ) with q* 1 and q* 2 produced In general, considering all possible Pareto-efficient allocations (MRS R = MRS F = MRPT)  We obtain a collection of Pareto-efficient utility levels for both Robinson and Friday By varying Friday’s utility from zero to level where Robinson’s utility would be zero Plotting these Pareto-efficient utility combinations yields utility possibilities frontier in Figure 20.2

13. 13 Figure 20.3 Efficiency in production and exchange for a two-consumer economy

14. 14 Figure 20.4 Efficiency in production and exchange for alternative utility levels

15. 15 Production and Exchange Economy For an economy with production, every utility bundle on this frontier represents a Pareto-efficient allocation  Where MRS R = MRS F and MRS R = MRS F = MRPT A utility bundle in interior of frontier, say point A, is not Pareto optimal  It is possible to increase either Robinson’s or Friday’s utility without decreasing other’s utility In contrast, on the frontier, say at point P 1, Friday’s utility cannot be increased without reducing Robinson’s utility  At P 1 utility combination and any other utility bundle on frontier are Pareto optimal Initial endowment of resources held by Robinson and Friday will determine agent’s location on frontier  If Robinson has a proportionally larger share of initial resources, utility bundle P 1 may result  A reversal of endowments may yield a higher utility level for Friday, such as bundle P 3

16. 16 Maximizing Social Welfare Even after eliminating all Pareto-inefficient allocations, there remains an infinite number of efficient allocations  Represented by infinite number of points on utility possibilities frontier First Fundamental Theorem of Welfare Economics  A perfectly competitive equilibrium will result in a Pareto-efficient allocation  Depending on initial distribution of endowments, a perfectly competitive equilibrium can occur at any point on utility possibilities frontier  However, from a society’s point of view, allocation resulting from a perfectly competitive equilibrium may not be equitable Society may redistribute income (initial endowments) among consumers in an effort to achieve equity  May 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)

17. 17 Maximizing Social Welfare Efforts by governments to achieve a more equitable allocation are costly in terms of possibly generating inefficiencies within an economy  For example, government playing Robin Hood dampens incentive to work and invest Often directs resources toward tax avoidance Can use concept of a social-welfare function as method for determining socially optimal allocation among points on a utility possibilities frontier  With a social-welfare function, can determine point that maximizes social welfare in terms of both equity and efficiency criteria  Assuming government is not paternalistic, this function would generally depend on welfare (utility) of agents within an economy Government would then maximize social welfare subject to utility possibilities frontier

18. 18 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, curves  Assumption implies that society has inequality aversion Where (holding social welfare constant) the more satisfaction Robinson has the less society is willing to give up Friday’s utility for one more unit of Robinson’s utility  As illustrated in Figure 20.5, tangency between a social indifference curve and utility possibilities frontier results in maximum level of social welfare Point P 2 is only point on utility possibilities frontier where there is no other point preferred to it  For example, point P 3 is Pareto efficient but there are points that are preferred to P 3  Even though point A is Pareto inefficient, society prefers it over Pareto-efficient point P 3  Using maximum level of social welfare, point P 2, we determine optimal allocation of commodities in Edgeworth box (Figure 20.1) for a pure-exchange economy Or in production possibilities frontier (Figure 20.3) for a production and exchange economy

19. 19 Figure 20.5 Maximizing social welfare

20. 20 Shapes of Isowelfare Curves A social-welfare function represents society’s preferences for particular Pareto-efficient points on a utility possibilities frontier  Various social preferences may be represented by social indifference curves taking on various shapes These shapes (and thus social preferences) are generally based on some equitable allocation among Pareto-efficient allocations Comparison of alternative Pareto-efficient points requires value judgments concerning trade-off among consumer utilities  Can be no one definition for equity Social indifference curves will take on a number of forms  Depending on which criterion (value judgment) is employed for determining equitable allocation Two criteria—egalitarian and utilitarian

21. 21 Egalitarian Egalitarianism can take two forms  Allocate each consumer an equal amount of each commodity In terms of our Robinson and Friday two-commodity economy, this egalitarian criterion sets q R 1 = q F 1 and q R 2 = q F 2 In a pure-exchange economy, Robinson and Friday would split total endowment of each commodity in half  Unless Robinson and Friday have identical utility functions, level of utility achieved by them will not be the same But their utility levels are not a factor in this egalitarian equity In terms of a social-welfare function, social preferences for Robinson’s or Friday’s utilities are identical  Are perfect substitutes as long as commodities are allocated equally between them Maximizing welfare function with additional constraint that it be Pareto-efficient in terms of a utility possibilities frontier will result in maximizing social welfare

22. 22 Egalitarian Second type of egalitarian criterion is an allocation of commodities  Resulting in equality of utilities across all consumers For Robinson and Friday, this criterion sets U R = U F A social-welfare function resulting in equality of utilities is Rawlsian criterion  Most equitable allocation maximizes utility of least-well-off consumer in society  For Robinson and Friday, Rawlsian criterion is Maximum 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 functions Equality of utilities will not result in Robinson and Friday each receiving the same commodity allocation

23. 23 Figure 20.6 Rawlsian social- welfare function

24. 24 Utilitarian Maximizes sum of consumers’ utility Criterion was formally developed by Bentham and provided initial impetus to utility theory For Robinson and Friday, criterion is  Called classical utilitarian, or Benthamite welfare function  Maximized 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 welfare  Only total utility is relevant, so utilitarian criterion does not consider distribution of utility As 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 consumer Unless utility functions of individual consumers are close to being identical  Utilitarian criteria can result in substantial differences in consumers’ utility Although ethics teaches that virtue is its own reward, classical utilitarian function teaches that reward is its own virtue  Only total level of utility is important

25. 25 Figure 20.7 Benthamite (classical utilitarian) social welfare function

26. 26 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 consumer’s utility is to overall social welfare  For example, utility of an individual such as Mother Teresa will be weighted higher than that of a child sex offender In Figure 20.7, utilitarian social welfare optimal allocation is tangency between social indifference curve and utility possibilities curve  Depending on weights associated with individual consumers’ utility Any Pareto-efficient point on utility possibilities frontier could be a social-welfare maximum The more egalitarian a society is, the more its social indifference curves will approach right angles  Indicating society is concerned with equity issues of distribution For a utilitarian society that is indifferent to distribution, curves are more linear  Showing society simply maximizes output

27. 27 Arrow’s Impossibility Theorem A problem in maximizing social welfare is how to establish this social- welfare function  A welfare function based on individual consumer preferences would be a desirable Assuming social welfare is to reflect some aggregate consumer preferences  However, because preference ranking by consumers is generally only ordinal There is not sufficient information to determine a reasonable social preference ranking of choices Numerous examples where, due to ordinal preference ranking among individuals, an aggregate ranking is impossible  One example is Battle of the Sexes game discussed in Chapter 14 Couple cannot jointly (socially) rank their preferences for opera or fights

28. 28 Arrow’s Impossibility Theorem  Impossible to establish a reasonable social preference ranking based solely on individual ordinal preference rankings Suppose there are several feasible social states  It is assumed each individual in society can ordinally rank these states as to their desirability  To derive a social-welfare function, there must exist a ranking of these states on a society-wide scale that fairly considers these individual preferences Let’s 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 cancer  Arrow’s Impossibility Theorem says a reasonable social ranking of these three states cannot exist based only on how individual agents ordinally rank these states

29. 29 Arrow’s Impossibility Theorem A reasonable social ranking may be stated with the following axioms relating individual consumers’ preferences  Axiom 1: Completeness—Social ranking must rank all social states Either A > B, B > A, or A  B for any two states  Identical to Completeness Axiom for individual preference ordering  Axiom 2: Transitivity—Society’s social ranking must be transitive Given three social states, A, B, and C, if A > B and B > C, then A > C  Identical to Transitivity Axiom for individual preference ordering  Axiom 3: Pareto—If every consumer prefers A to B, then A is preferable in a social ranking This also holds for the other two pairs (A, C) and (B, C)  Identical to a Pareto improvement  Axiom 4: Nondictatorial—One consumer’s preferences should not determine society’s preferences No agent paternalism  Axiom 5: Pairwise Independence—Society’s social ranking between A and B should depend only on individual preferences between A and B Not on individual preferences for some other social state, say state C  Identical to Independence Axiom for individual preference ordering of states of nature

30. 30 Arrow’s Impossibility Theorem Can now state Arrow’s Impossibility Theorem more formally  A social preference ranking satisfying these five axioms is impossible, given an ordinal ranking of individual agent preferences Implies that there is no way to aggregate agents’ ordinal preferences into a social preference ranking without relaxing at least one of these axioms Axioms may seem a reasonable set of conditions for democratically choosing among social states  However, Arrow demonstrated that it is impossible to socially choose among all possible sets of alternatives without violating at least one of the axioms Thus, social choice must be unreasonable if it is based on agents’ ordinal preference ranking

31. 31 Majority Voting To see that Arrow’s Impossibility Theorem holds, let’s consider majority voting  Important social preference mechanism design Set of rules governing procedures for social [collective] choice Majority voting satisfies both Pareto Axiom and Nondictatorial Axiom  Sensitive to each individual agent’s preferences Majority voting is symmetric among agents  Treats all agents the same and all agents have just one vote It is also neutral among alternatives  By not making a distinction among alternatives a priori However, majority rule can lead to a pattern of social choices that is not transitive  Even though every voter has ordinal and transitive preferences Thus, it violates Axiom 2

32. 32 Majority Voting Consider ballot in Table 20.1 among three voters, Robinson, Friday, and Simpson  Voters’ preferences are as follows Robinson and Simpson prefer alternative A to B Robinson and Friday prefer alternative B to C Friday and Simpson prefer alternative C to A  Majority (two) prefers A to B and B to C, but majority also prefers C to A  Thus majority voting results in a cyclical pattern that is intransitive  Called Condorcet Paradox  Presents a major problem for group decision making

33. 33 Table 20.1 Condorcet Paradox

34. 34 Majority Voting Next let’s consider case in which each voter must vote for just one alternative  As illustrated in panel (a) of Table 20.2, ordinal preference ranking in Table 20.1 results in a three-way tie All three alternatives receive equal votes  However, if one alternative is removed, a clear winner results As illustrated in panel (b), when alternative C is removed, alternative A receives majority vote  Here, Axiom 5 is violated  We see this violation of Axiom 5 often in U.S. presidential elections  Where a third-party candidate has determined the outcome

35. 35 Table 20.2 Pairwise Independence

36. 36 Majority Voting Development of a social-welfare function requires more than just an ordinal ranking of individual consumer preferences  Requires a comparison of utilities across consumers on a cardinal scale For example, one reason a third party can influence results of an election is that no weight is given to intensity of voters’ desires  However, intensity of desires is a utility measure that can only be measured on at least a cardinal scale  Magnitude or intensity of an individual voter’s desires is not known when she votes However, allowing voters an ordinal preference ranking (Table 20.1) instead of just one vote (Table 20.2) does elicit additional information on voter’s preference  May result in a social ranking more consistent with a majority of electorate New voting machines, being put into place after 2000 presidential election, have capability to allow voters to ordinally rank candidates  Called instantaneous voting, procedure has not yet been widely adopted  But offers potential of further revealing voters’ preferences and mitigating any strategic voting

37. 37 Strategic Voting A problem with allowing ordinal ranking of candidates (or any other choices) is possibility of strategic voting  Where an agent does not reveal her true preferences but instead votes to enhance outcome in her favor A game-theory strategy  Particularly effective when number of voters is relatively small or when a strategic- voting coalition can be formed One form of strategic voting is for an agent, say Friday, to rank her first choice highest  Then rank other alternatives inversely to expected outcome Thus, Friday would rank alternative expected to be in close competition with her first choice last, suppressing competitive threat Strategic voting is illustrated in Table 20.3 for determining social ranking of four alternatives  In panel (a), alternative A, which was not Friday’s top choice, comes out on top However, as illustrated in panel (b), Friday can change outcome by ranking alternative A low (strategic voting)  Now Friday’s top choice, alternative B, comes out on top as the social choice  Judges in Olympic games have been accused of practicing this type of strategic voting

38. 38 Table 20.3 Strategic Voting

39. 39 Strategic Voting A method for removing this potential of strategic voting is sequential voting  Lowest-ranking alternative after each vote is dropped and another vote is then taken on remaining alternatives In panel (b) of Table 20.3, alternative C only received a rating of 5  Dropping this alternative from list yields individual preference ranking for the three alternatives listed in panel (a) of Table 20.4 Now alternative D receives lowest ranking Dropping 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

40. 40 Table 20.4 Sequential Voting

41. 41 Strategic Voting Sequential voting is used to elect Speaker of the House in U.S. House of Representatives Employing sequential voting also allows for a social ranking of alternatives based on Pairwise Independence Axiom Implementing such a process for U.S. presidential elections would probably have changed a number of outcomes  By adopting instantaneous voting, where voters rank their choices Low-ranking alternatives could be automatically dropped until only two alternatives are left  Given these two remaining alternatives, a president with majority of support would then be elected

42. 42 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 individual  Arrow’s Theorem implies that institutional detail and procedures of a political process (mechanism design) cannot be neglected Thus, it is not surprising that academic disciplines that complement economics, such as political science and psychology  Have evolved to address process of group choice  Attempt to determine intensities of individual and group desires  Formulate policies and rules for group choice and actions As demonstrated by Condorcet Paradox and quid pro quo example in Chapter 14  An agenda that determines which alternatives are first considered will affect social choice

43. 43 Market Failure Suppose some process for group decision does exist for determining optimal social choice  A naive solution, based on Second Fundamental Theorem of Welfare Economics Would advocate allowing markets freedom to obtain this social optimal given a reallocation of endowments  Unfortunately, this solution is based on properties of a perfectly competitive equilibrium Extreme theoretical case of resource allocation  Does not generally hold for any society When properties of a perfectly-competitive equilibrium do not hold  Resulting equilibrium is not efficient, so market failure exists

44. 44 Market Failure In general, conditions causing market failure are classified into four categories  Monopoly power Exists when one or a number of agents (suppliers or demanders of a commodity) exert some market power in determining prices  Externalities An interaction among agents that are not adequately reflected in market prices—effects on agents are external to market  Air pollution is classic example of an externality  Public goods One individual’s consumption of a commodity does not decrease ability of another individual to consume it  Examples are national defense, income distribution, and street lights  Asymmetric information When perfectly competitive assumption of all agents having complete information about commodities offered in market does not hold  Incomplete information can exist when cost of verifying information about a commodity may not be universal across all buyers and sellers  For example, sellers of used automobiles may have information about quality of various automobiles that may be difficult (costly) for potential buyers to acquire When there is asymmetry in information buyers may purchase a product in excess of a given quality

45. 45 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 failures  Governments can regulate firms with objectives of mitigating monopoly power and negative externalities  Governments can provide for public goods either by direct production or private incentives  Governments can generate information, aid in its dissemination, and mandate that information be provided in an effort to reduce asymmetric information The more a government must intervene in marketplace to correct these failures  The less dependent will the economy be on freely operating markets

46. 46 Market Failure In some societies these market failures appear quite large and, thus, freely operating markets are severely limited  True in many centrally-planned economies Where government determines what and how to produce as well as who should receive commodities produced  Even within U.S., which generally relies on free markets to allocate resources and outputs, there is always the question concerning level of government intervention For example, many environmental regulations directly limit inputs firms can use in their production decisions  For example, local zoning ordinances may restrict a firm’s use of inputs that generate noise, smoke, or odors