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罗森 财政学 public finance 第10版 课后习题答案 英文版 第122章 docx - 图文

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Chapter 11 - Social Security

Brief Outline

1. Why Have Social Security?

a. Consumption Smoothing and the Annuity Market b. Adverse Selection and the Annuity Market c. Other Justifications

2. Structure of Social Security

a. Basic Components b. Distributional Issues c. The Trust Fund

3. Effect of Social Security on Economic Behavior

a. Saving Behavior

b. Retirement Decisions c. Implications

4. Long-term Stresses on Social Security 5. Social Security Reform

a. Maintain the Current System b. Privatize the System

6. Conclusions Answers

1. With adverse selection, insurance contracts with more comprehensive coverage are chosen by people with higher unobserved accident probabilities. To make up for the fact that a ben efit is more likely to be paid to such individuals, the insurer charges a higher premium per unit of in sura nee coverage. 2. Individuals who do not save eno ugh for their retirement years may believe that the governmentwill feel obliged to come to their aid if they are in a sufficiently desperate

situation. With this belief, younger individuals may purposely neglect to save adequately. One justification for the compulsory nature of Social Security is to address the inefficiently low saving caused by moral hazard. 3. Use the basic formula for balance in a pay-as-you-go social security system: t =(Nb/Nw)*(B/w). Call 1990 year 1 and 2050 year 2. Then ti = .267*(B/w)i

t2

= .458*(B/W)2

It follows that to keep (B/W)I=(B/W)2 we require t2/ti=.458/.267=1.71. That is, tax rates would have to increase by 71 percent. Similarly, to keep the initial tax rate constant, we would require (B/W)2/(B/W)I=.267/.458=0.58. Benefits would have to fall almost by half.

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Copyright ? 2014 McGraw-Hill Education. All rights reserved? No reproduction or distribution without the prior written consent of McGraw-Hill Educati on.

Part 3 一 Public Expenditure: Social Insurance and Income Maintenanee

4. The sharp increase in the number of elderly men who marry young women affects the

solvency of the Brazilian system because, after the earner dies, the non-earning spouse can continue to receive pension benefits. The young women collect for many more years than an older non-earning spouses, resulting in higher-than-expected payouts. 5. Austen's quote seems like it could relate adverse selection, but perhaps more likely, to moral

hazard. The quote “If you observe, people always live forever when there is any arinuity to be paid them” in a sense sounds like they act differently (e.g., better diet, more exercise, etc.) when an annuity is to be paid 一 the idea of moral hazard. In contrast, adverse

selection suggests that people who expect to live a long time to be the ones who purchase annuities. A recent paper by Finkelstein and Poterba (NBER working paper, December 2000) found that “mortality patter ns are consistent with models of asymmetric information” and that annuity “insurance markets may be characterized by adverse selection/1 6. Equation (11.1) relates taxes paid into the Social Security system to the dependency ratio

and the replacement ratio, that is, t=(Nb/ Nw)*(B/w). If the goal of public policy is to maintain a constant level of benefits, B, rather than a constant replacement ratio, (B/w), then taxes may not need to be raised. If there is wage growth (through productivity), then it is possible to maintain B at a constant level, even if the dependency ratio is growing.

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By rearranging the equation, we can see that B=t*w*(Nb/ Nw) . That is, in creases in wage rates (the sec ond term) offset in creases in the depe ndency ratio (the third term). Thus, constant benefits do not necessarily imply higher tax rates.

7. The state me nt about how the differe nt rates of retur n in the stock market and gover nment

bond market affect the solvency of the trust fund is false. If the trust fund buys stocks, someone else has to buy the government bonds that it was holding. So, there is no new saving and no new capacity to take care of future retirees. 8.

a. The problem does not provide in formation about the utility function, so the optimal point is where the indifferenee curve is drawn tangent to the budget line, which can occur at different values depending on how the curve is drawn. In the diagram below, the optimal point involves saving $8,000 and future con sumption consists of period 2 income ($5,000) plus savings with interest ($8,800).

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Copyright ? 2014 McGraw-Hill Education. All rights reserved? No reproduction or distribution without the prior written consent of McGraw-Hill Educati on.

Chapter 11 - Social Security

b. If Social Security takes $3,000 from the individual in the first period and pays him this

amount with interest in the second period, then private savings falls from $8,000 to $5,000. There would be no change in optimal consumption values.

8. If the implicit rate of return from Social Security is lower than the private return, the

endowment point shifts from A to B as present consumption falls from $20,000 to $17,000 when $3,000 is taken for social security. The arrow connecting the old endowment point A to the new endowment B is flatter than the budget line, reflecting the lower rate of return on Social Security compared to private saving. For savings beyond the $3,000 taken for Social Security, the private rate of return is available, so the new budget line is parallel to the

original line? This would cause the optimal point to change and put the individual on a lower

indifferenee curve. In the graph below, the effect is to in crease private saving slightly ?

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Copyright ? 2014 McGraw-Hill Education. All rights reserved? No reproduction or distribution without the prior written consent of McGraw-Hill Educati on.

Part 3 一 Public Expenditure: Social Insurance and Income Maintenanee

Consumptio n

9. Moving the financing of Social Security from a pay-roll tax financing to income-tax financing makes sense from the perspective of the fact that the system is pay-as-you-go. The payroll-tax system implies that workers are \not accurate. This financing would also broaden the base for the tax to be paid on. The change may be politically difficult, because benefits are calculated based on earned income, while income taxes can be based on more than earned income. 10. If the expected present value of the benefit reduction just equals the decrease in taxes, then the solvency of the system is unaffected. The pay-as-you-go formula shows that the system is solve nt if taxes collected equal ben efits paid, or twNw = BNb. Dividing both sides by the number of covered workers yields tw = B(Nb/Nw). If a worker diverts $1,000 from payroll taxes to a private account, then the left-hand side of this expression falls by $1,000. To maintain solvency, the right-hand side must also fall by $1,000, so benefits must fall by 1,000 times the ratio Nw/Nb. If, for example, there are three covered workers for every retired worker, so that Nw/Nb is equal to 3, then the necessary reduction in the expected value of benefits is $3,000. If a worker invests $1,000 for 40 years at about 3 percent per year, that worker will have eno ugh in his private acco unt to compensate for the lost ben efits. If the offset rate is lower tha n the rate of return workers can earn on private accounts, workers will gain, and vice versa.

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Chapter 12 一 Income Redistribution: Conceptual Issues Brief Outline

1 ? Distribution of Income

a. Interpret!ng the Distributional Data

Copyright ? 2014 McGraw-Hill Education. All rights reserved? No reproduction or distribution without the prior written consent of McGraw-Hill Educati on.

Chapter 11 - Social Security

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 Incidenee

a. Relative Price Effects b. Public Goods

c. Valuing In-Kind Transfers

d. Reasons for ln?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, SteirTs assertion that inequality perse is unimportant is consistent with utilitarianism. 2.

a. To maximize W, set marginal utilities equal; the constraint is Is + lc= 100. So, 400 - 2ls = 400 ? 6lc, substituting lc= 100 ? Is gives us 2ls = 6 (100 - Is). Therefore, Is = 75, lc= 25. b? If only Charity matters, then give money to Charity until MUc= 0 (unless all the money in the economy is exhausted first). So,400-6 lc= 0; hence, lc= 66.67. Giving any more money to Charity causes her marginal utility to become negative, which is not optimal. Note that we don't care if the remaining money ($33.33) is given to Simon o「not. If only Simon matters, then, proceeding as above, MUs. 0 if Is = 100; hence, giving all the money to Simon is optimal. (In fact, we would like to give him up to $200.) c. MUs= MUc 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, in come is $40. With no subsidy, the con sumer 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,

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Copyright ? 2014 McGraw-Hill Education. All rights reserved? No reproduction or distribution without the prior written consent of McGraw-Hill Educati on.

罗森 财政学 public finance 第10版 课后习题答案 英文版 第122章 docx - 图文

Chapter11-SocialSecurityBriefOutline1.WhyHaveSocialSecurity?a.ConsumptionSmoothingandtheAnnuityMarketb.AdverseSelectionandtheAnnuityMarketc.O
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