Chapter 20: Welfare Economics Welfare Economics

SocialWelfare Function

Utility Possbilities Frontier

Maximizing Social Welfare

Market Failure

Compensation Principle

Theory of the Second Best

Kaldor Compensation

Arrow’s Impossibility Theorem

Monopoly Power

Externalities

Public Goods

Asymmetric Information

Majority Voting

Outline and Conceptual Inquiries Deriving a Social-Welfare Function Is such a function only an economic illusion? Revising the Pure-Exchange Economy Consider Production and Exchange How to Maximize Social Welfare Shapes of Isowelfare Curves What type of society do you live in? Application: Egalitarian Households Arrow's Impossibility Theorem How are society’s preferences for commodities ranked? What is wrong with Majority Voting? Does majority voting result in a preference ordering of society’s alternatives? Strategic Voting Can your optimal revealed preferences deviate from your true preferences? Application: Nonpartisan Blanket Primaries Market Failure Why have a government? Appendix to Chapter 20 Understanding the Compensation Principle If you are compensated for your loss, can social welfare then improve? Application: Counting Losses in Natural Resource Damages Theory of the Second Best Are free-market zealots correct? Application: Following Directions © Michael E. Wetzstein, 2012

Summary 1. A measure of social welfare based on a Pareto criterion implies unanimity rule. Given a Pareto criterion, an allocation where agents must be made no worse off and at least one agent made better is required for improving social welfare. 2. The utility possibilities frontier is a mapping of the Pareto-efficient utilities for agents corresponding to each point on a contract curve. 3. A social-welfare function represents society’s preferences for particular Pareto-efficient points on a utility possibilities frontier. 4. An egalitarian social-welfare function can be where either the total endowment of commodities is allocated equally among all the agents or the allocation of commodities makes all agents’ utilities equal. In contrast, the utilitarian criterion maximizes some weighted sum of all agents’ utilities. 5. Arrow’s Impossibility Theorem states that it is impossible to establish a reasonable social preference ranking based solely on individual ordinal preference rankings. 6. Majority voting, a mechanism design for determining social choice, can result in a social preference ranking that is not transitive. 7. By not revealing his or her true preferences, an agent can employ strategic voting to potentially alter a social choice toward improving his or her satisfaction. Sequential voting is a method that counters some forms of strategic voting. 8. Conditions resulting in market failure are classified into four categories: monopoly power, externalities, public goods, and asymmetric information. 9. (Appendix) The compensation principle is a revealed preference approach that does not rely on specifying a welfare function to measure changes in social welfare. 10. (Appendix) The Theory of the Second Best states that social welfare can be improved even if market impediments exist in some markets by fostering perfectly competitive markets in other markets. This second-best solution does not generally hold when markets are interconnected.

© Michael E. Wetzstein, 2012

Key Concepts Arrow’s Impossibility Theorem compensation principle first-best solution isowelfare curve Kaldor compensation market failure mechanism design second-best Pareto-optimal allocation single-peaked preferences

Key Equations

The Rawlsian criterion for social welfare.

The Benthamite welfare function.

© Michael E. Wetzstein, 2012

social indifference curve social-welfare function strong compensation test Theory of the Second Best utility bundle utility possibilities frontier weak compensation test welfare economics

TEST YOURSELF Multiple Choice 1. A function that orders commodity bundles for society is a(n) a. Welfare function b. Efficiency function c. Pareto-optimal function d. Social-welfare function. 2. The points on a utility possibilities frontier a. Indicate it is impossible to increase the utility of one individual without reducing the utility of another b. Maximize social welfare when the utility levels are equal c. Are points on the contract curve d. All of the above are correct. 3. A social indifference curve will be convex if a. The utility each consumer receives is equal b. There is a diminishing MRS between consumers c. Increasing the utility of one consumer lowers the utility of another d. Social utility is increased only if all consumers’ utility levels increased. 4. Suppose the criterion for determining the socially optimal allocation of commodities requires each consumer receive an equal amount of each commodity. This type of criterion is known as a. Utilitarian b. Rawlsian c. Benthamite d. Egalitarian. 5. A Rawlsian social-welfare function has indifference curves that are a. Strictly convex b. Strictly concave c. Right angles d. Negatively sloped and linear. 6. The utilitarian criterion a. Maximizes the sum of consumers’ utility b. Requires each consumer receives an equal level of utility c. Results in an equal allocation of commodities across all consumers d. Maximizes each consumer’s level of utility separately.

© Michael E. Wetzstein, 2012

7. A utilitarian social-welfare function has indifference curves that are a. Strictly convex b. Strictly concave c. At right angles d. Negatively sloped and linear. 8. According to Arrow’s Impossibility Theorem, a. There is sufficient information concerning individual preferences to develop a socialwelfare function. b. It is allowable for one consumer’s preferences to determine society’s preferences c. A reasonable social preference ranking based solely on individual preferences does not exist d. Individuals are unable to rank commodity bundles consistently. 9. Which is not an axiom that must be satisfied before a reasonable social ranking of consumer preferences is found? a. Completeness b. Pairwise independence c. Dictatorial d. Pareto. 10. The following table lists preferences for three alternatives by three voters: Voters Marjean Hazel Bernie Total

A 5 3 4 12

B 4 5 2 11

C 3 1 2 6

Which of the following would be an example of successful strategic voting? a. Marjean ranks alternative B with a 6 b. Bernie ranks alternative A with a 2 c. Hazel ranks alternative C with a 2 d. Hazel ranks alternative A with a 1.

© Michael E. Wetzstein, 2012

Short Answer 1. Explain how an attempt to improve social welfare may conflict with the Pareto criterion for efficiency. 2. Illustrate graphically how social welfare can be maximized. Assume there is diminishing marginal rate of substitution between consumers’ utilities. 3. Describe the two forms of egalitarianism. 4. Illustrate graphically the Rawlsian criteria for maximizing social welfare. 5. Compare the indifference curves for the Rawlsian criteria with those from utilitarianism. Explain their shapes. 6. List the five axioms that must be met for a reasonable social ranking of consumer preferences to exist. 7. Majority voting is a popular mechanism. Explain how majority voting satisfies some of the axioms necessary for developing a reasonable social ranking of preferences. Which axioms does it violate? Explain. 8. What is the Condorcet Paradox? Demonstrate it with an example. 9. What is strategic voting? Describe how the voting system can be altered to reduce or eliminate the use of strategic voting.

© Michael E. Wetzstein, 2012

Problems 1. Suppose there are only two commodities Bernice, B). Their utility functions are

and

and two consumers (Hazel, H, and and

With 12 units each of

derive the utility possibilities frontier equation. 2. Refer to Problem 1. Suppose the social-welfare function is Determine the socially optimal levels of utility for both Hazel and Bernice. How much of each commodity should each consume? 3. Suppose the utility possibilities frontier for two consumers (Douglas and Sandra) is

a. Consider a Rawlsian criterion,

b. Consider a utilitarian criterion,

What is the optimal level of

What is the optimal level of

and

and

4. Erick, E, and Gale, G, are snowed in. They have 8 cans of beans B to share between them. Their utility functions are and a. If the cans are shared equally between them, what are their levels of utility? b. How should the cans be allocated between them to ensure that they each receive an equal level of utility? c. Suppose Erick and Gale determine their joint welfare function is will the cans be allocated to maximize social welfare?

© Michael E. Wetzstein, 2012

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