Chapter 11 - Social Security 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 benefit is more likely to be paid to such individuals, the insurer charges a higher premium per unit of insurance coverage.
Individuals who do not save enough for their retirement years may believe that the government will 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.
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=l .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))=.26刀.458=0?5& Benefits would have to fall almost by half.
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Social Security redistributes incomes from younger generations to older generations, from men to women, from high- to low-income individuals, and from two-eamer to one- earner married couples.
Social Security benefits older generations because it is largely financed on a pay?as-you? go basis. The most extreme example is Ida Fuller, the first Social Security beneficiary, who paid only $24.85 and received benefits of $20,897 over her lifetime.
Wome n have gained because they have lived Ion ger. The text cites Liebmanns calculations, which show that among people who retired in the 1990s, on average men came out behind by about $43,000 while women came out ahead by $37,000.
For recent and future retirees, generally the higher the earnings, the smaller the gain from Social Security. For example, a high-earner single male who retires in the year 2015 is expected to lose $196,350 to Social Security, whereas a low-earner single male retiring at the same time is expected to lose only $8,605. The difference occurs because the payroll tax used to finance Social Security is proportional, up to $94,200 in 2006, so most workers are paying the same percentage of earnings to Social Security. Benefits are related to contributions, but not proportionately, so the low-income individuals come out better.
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One-earner maiTied couples benefit because a non-working spouse is entitled to 50 percent of a working spoused benefit. For a two-earner married couple, the individual with lower earnings may gain little or nothing in benefits from working, since he or she would have been entitled to benefits based on the other spoused earnings.
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AusterTs 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 annuity to be paid theirT in a sense sounds like they act differently (e.gM 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 \\
6? Equation (9.1) 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. By rearranging the equation, we can see that B=t*w*(Nb/ Nw)' . That is, increases in wage rates (the second term) offset increases in the dependency ratio (the third term). Thus, constant benefits do not necessarily imply higher tax rates- 7.
The statement about how the different rates of return in the stock market and government 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-
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a. The problem does not provide information about the utility function, so the optimal point
is where the indifference 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 consumption consists of period 2 income ($5,000) plus savings with interest ($8,800).
Consumption
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.
财政学课本习题答案(第8版)chapter_11.doc
