财政学第十二章答案

Chapter 12 – Income Redistribution: Conceptual Issues

Brief Outline

1.Distribution of Income

a.Interpreting the Distributional Data

2.Rationales for Income Redistribution

a.Simple Utilitarianism

b.The Maximin Criterion

c.Pareto Efficient Income Redistribution

d.Nonindividualistic Views

e.Other Considerations

3.Expenditure Incidence

a.Relative Price Effects

b.Public Goods

c.Valuing In-Kind Transfers

d.Reasons for In-Kind Transfers

4.Conclusion

Suggested Answers to End-of-Chapter Questions

1.Utilitarianism suggests that social welfare is a function of individuals’ utilities. Whether

the rich are vulgar is irrelevant, so this part of the statement is inconsistent with

utilitarianism. On the other hand, Stein’s assertion that inequality per se is unimportant is consistent with utilitarianism.

2.

a.To maximize W, set marginal utilities equal; the constraint is I s + I c = 100. So,

400 - 2I s = 400 - 6I c, substituting I c = 100 - I s gives us 2I s = 6 (100 – Is).

Therefore, I s = 75, I c = 25.

b.If only Charity matters, then give money to Charity until MU c = 0 (unless all the

money in the economy is exhausted first). So,400-6 I c = 0; hence, I c = 66.67.

Giving any more money to Charity causes her marginal utility to become negative,

which is not optimal. Note that we do n’t care if the remaining mone y ($33.33) is

given to Simon or not.

If only Simon matters, then, proceeding as above, MU s. 0 if I s = 100; hence, giving

all the money to Simon is optimal. (In fact, we would like to give him up to $200.)

c.MU s = MU c for all levels of income. Hence, society is indifferent among all

distributions of income.

3.Suppose the government is initially providing an in-kind benefit of 10 units of free public

transportation, worth $2 each, so the cost of the subsidy is $20. Without the subsidy,

income is $40. With no subsidy, the consumer maximizes utility at point A, and with an in-kind benefit of 10 units of free public transportation, the consumer maximizes utility at point B. A cash subsidy equal to $20 would allow the consumer to reach point B as well, so the government could convert an in-kind subsidy valued at $20 to a cash subsidy of

$20 and leave people equally well off.

Another possibility is that the utility-maximizing point for a cash subsidy differs from the utility-maximizing point for an in-kind subsidy, as illustrated in the next graph.

In this case, an in-kind subsidy, costing $20, would allow the consumer to move from

point A’ to point C’, while a cash subsidy of $20 would make the consumer better off at point B’. I n order to make the consumer equally well off, the cash subsidy should be a little less than $20.

4. If the poverty measure was fixed at the level of the supplemental poverty measure and if

the actual level of consumption of food, clothing, shelter, and utilities doubled because prices doubled, the new poverty measure will drastically understate the level of poverty in America. The families in poverty as determined by the new measure before the

Other goods Public Transportation

10 20 30 A’

B’

C’

Other goods Public Transportation

10 20 30 A

B