Download Chapter 20: Welfare Economics

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
How