中级宏观经济学试题-Chapter13

Solutions to the Problems in the Textbook

Conceptual Problems

1.a. According to the life-cycle theory of consumption, people try to maintain fairly stable consumption

paths over their lifetimes. Individuals save during their working years so they can keep up the same consumption stream after they retire. This implies that wealth increases steadily until retirement. But since consumption remains stable, we should expect the ratio of consumption to accumulated saving (wealth) to decrease over time up to retirement.

1.b.The life-cycle hypothesis asserts that wealth is used up after retirement to finance consumption during

the remaining years. This implies that the ratio of consumption to accumulated saving (wealth) increases after retirement, eventually approaching 1.

2.a. Suppose that you and your neighbor both work the same number of years until retirement and you

both have the same annual income. If your neighbor is in bad health and does not expect to live as long as you, she will expect to have fewer retirement years in which to use accumulated wealth. Your neighbor's goal for retirement saving will not be as high as yours, and compared to you, she will have

a higher level of consumption over her working years.

Since planned annual consumption (C) is determined by the number of working years (WL), the number of years to live (NL), and income from labor (YL), we get the equation:

C = [(WL)/(NL)](YL).

WL and YL are the same for you and your neighbor, but NL is smaller for your neighbor. Therefore you will have a lower level of consumption (C).

(Note: Students may come up with a variety of different answers. For one, your neighbor who is in bad health currently has much larger medical bills than you do. Therefore she may not be able to save as much for retirement, even if she might expect to live as long as you. On the other hand, she may not have large medical bills now, but expects them later, as she gets older. This may induce her to save more now. While such arguments are valid, instructors should point out that the answer should be related to the life-cycle theory and the equation used above.)

2.b. If we assume for simplicity that the rate of return on Social Security is the same as the rate of return

on private saving, then the introduction of a Social Security system based on a trust fund should not have any effect on your level of consumption. Social Security may be considered a form of "forced saving," since you are forced to pay Social Security taxes during your working years and will, in return, receive benefits during your retirement years. However, most likely you would have voluntarily saved just as much as the government is now “forcing” you to save by levying the Social Security tax. Therefore your consumption behavior will not change. Still, the levying of a Social Security tax reduces disposable income during your working years, increasing the ratio of consumption to disposable income (the average propensity to consume).

As we have just discussed, if private saving were simply replaced with government saving, national saving would not be affected. However, the Social Security system is actually not strictly financed through a trust fund, but largely on a pay-as-you-go basis. This means that most of the Social Security taxes are not "saved" but immediately used by the government to finance the benefits of current retirees. For this reason, many economists claim that the Social Security system has led to a decrease in the national savings rate and a decrease in the rate of capital accumulation. The magnitude of this

decrease, however, has not been clearly established.

The size of the Social Security trust fund was fairly insignificant until the system was amended in 1983. But now the trust fund is increasing and, in effect, largely contributed to the decreases in the federal budget deficits in the 1990s. However, because of our aging population, predictions are that the Social Security system will experience severe financial difficulties within the next 30 years unless it is reformed. If the credibility of the system becomes an issue, people may intensify their saving efforts, since they no longer feel they can rely on the public system to provide for them during retirement.

3.a. If you expect to get a Christmas bonus every year from now on, you immediately treat it as part of

your permanent income and spend accordingly, that is, ?C = c(?Y). In other words, your current consumption will change significantly.

3.b. If you get a Christmas bonus for only this year but not for any future years, then you will consider it

as transitory income. There is very little effect on your permanent income, so you will consume only

a small fraction of the bonus and save the rest. In other words, your current consumption will not be

significantly affected.

4.Gamblers (or thieves) seldom have a very stable income. However, their consumption is determined

by their permanent income, that is, their expected average lifetime income. Since their permanent income is not significantly affected by any temporary change in income, their consumption pattern remains relatively stable, whether they do well or not in any given period.

5.Both the life-cycle theory and the permanent-income theory try to explain why the short-run mpc is

smaller than the long-run mpc. The life-cycle theory attributes the difference to the fact that people prefer a smooth consumption stream over their lifetime. Therefore the average expected lifetime income is the true determinant of current consumption. The permanent-income theory suggests that the difference is due to measurement errors. Measured income has two components—permanent and transitory income. But only permanent income is a true determinant of current consumption.

6.a. One possible explanation for the low U.S. savings rate in the 1980s could be that the “baby boomers”

were still in their dissaving phase. Since the households of the baby boom generation were still in their late twenties, they probably still had large expenses related to childcare and the purchase of houses. Therefore, they may not have been able to save for retirement.

6.b.If the above explanation is correct, one can expect an increase in saving as these “baby boomers” age,

become more financially solvent, and begin to prepare for retirement.

7.The ranking from highest to lowest value should most likely be (a), (c), (d), and then (b). Clearly,

(c) should be lower than (a), but it is not certain whether it should rank before or after (d); its exact

ranking depends largely on how severe the liquidity constraint is.

8. A series follows a random walk when future changes cannot be predicted from past behavior. In

other words, it does not have a clear mean or long-run value and any major change results from a random shock. Hall asserted that changes in current consumption largely come from unanticipated changes in income. According to the life-cycle theory and permanent-income theory, people try to smoothen out their consumption stream in such a way that its expected value is always the same in each period. Therefore, we can express future consumption as the expected value plus some error

term, that is, some random value that is unpredictable. This error term is a shock to future income that is spread over the remaining lifetime. Hall supported the permanent-income hypothesis by showing that lagged consumption is the most significant determinant of future consumption.

9. The problem of excess sensitivity means that consumption responds more strongly to predictable

changes in current income than the life-cycle theory and permanent-income theories predict. The problem of excess smoothness means that consumption does not respond as strongly to unpredictable changes in current income as these theories predict. However, the existence of these problems does not invalidate the theories. It simply means that the theories can explain consumption behavior only to a certain degree.

10.Precautionary (or buffer-stock) saving can be explained by uncertainty. It could be uncertainty in

regard to one’s life expectancy or one’s time of retirement (affecting the accumulated saving needed to finance retirement), or uncertainty about future spending needs (which may be caused by a change in family composition or health). Clearly, if we account for such uncertainties, we bring the model closer to reality. For example, many elderly continue to save after retirement in anticipation of later high medical costs.

11.a.It is unclear whether an increase in the interest rate leads to an increase or a decrease in saving. On

the one hand, as the interest rate increases, the return on saving increases and people may therefore increase their savings effort (due to the substitution effect). On the other hand, a higher return on saving implies that a given future savings goal can now be reached with a smaller savings effort in each year (due to the income effect).

11.b.The income effect and the substitution effect generally tend to go in different directions; the overall

outcome depends on the relative magnitude of these two effects. Until now, empirical evidence has not established a significant sensitivity of saving to changes in the interest rate. This would imply that the income and substitution effects have about the same magnitude.

12.a. According to the Barro-Ricardo proposition, it does not matter whether an increase in government

spending is financed by taxation or by issuing debt.

12.b. The Barro-Ricardo proposition states that people realize that when the government finances its debt

by issuing bonds, it simply postpones taxation. In other words, people know that the government will have to raise taxes in the future to pay back what they have borrowed now, and people want to be prepared to pay future taxes. Therefore, expansionary fiscal policy that results in an increase in the budget deficit will not stimulate the economy since it will lead to an increase in saving rather than consumption.

12.c.There are two main objections to the Barro-Ricardo hypothesis. One is based on liquidity constraints,

that is, people cannot consume out of their permanent income, since they can’t borrow. Therefore, a tax cut eases their liquidity constraints and they consume more rather than save the tax cut. The other argument is that those people who benefit from a tax cut or an increase in government spending are not the same as those who will have to pay the higher taxes to pay off the debt. This argument assumes that people are not concerned about the welfare of their descendants.

Technical Problems

1.a. If income remains constant over time, permanent income equals current income. Your permanent

income this year is YP0 = (1/5)(5*20,000) = 20,000.

1.b.Your permanent income next year is YP1 = (1/5)(30,000 + 4*20,000) = 22,000.

1.c.Since C = 0.9YP, your consumption this year is C0 = 0.9*20,000 = 18,000.

Your consumption next year is C1 = 0.9*22,000 = 19,800.

1.d.In the short run, the mpc = (0.9)(1/5) = 0.18; but in the long run, the mpc = 0.9.

1.e. In 1.a. and 1.b., we have already calculated this and next year's permanent income. For each of the

coming years you add $30,000 and subtract $20,000. Therefore your permanent income (which is your average over a five year period) will increase by $2,000 each year until it reaches $30,000 after

5 years.

YP o=(1/5)(5*20,000) =20,000

YP1 = (1/5)(1*30,000 + 4*20,000) = 22,000

YP2 = (1/5)(2*30,000 + 3*20,000) = 24,000

YP3 = (1/5)(3*30,000 + 2*20,000) = 26,000

YP4 = (1/5)(4*30,000 + 1*20,000) = 28,000

YP5=(1/5)(5*30,000) =30,000

2.a.The person lives for NL = 4 periods and earns a lifetime income of

YL = 30 + 60 + 90 + 0 = 180.

Therefore consumption in each period will be

C i = (1/4)180 = 45, i = 1, 2, 3, 4.

This implies that saving in each period is:

S1 = 30 - 45 = - 15; S2 = 60 - 45 = + 15; S3 = 90 - 45 = + 45; S4 = 0 - 45 = - 45. 2.b. If there are liquidity constraints and the person cannot borrow in the first period, then she will

consume all of her income, that is, Y1 = C1 = 30.

For the remaining three periods the person wants a stable consumption stream. Thus she will consume C(i) = (1/3)(60 + 90 + 0) = 50 in each of the remaining three periods i = 2, 3, 4.

2.c. An increase in wealth of only $13 is not enough to offset the difference in consumption patterns

between period 1 and the other periods. Therefore all of the increase in wealth will be consumed in period 1, such that C1 = 43. In the remaining three periods, consumption will be the same as in 2.b.

An increase in wealth of $23 will be enough to offset the difference in consumption patterns.

Lifetime consumption in each period will now be C i = (1/4)(180 + 23) = 50.75. This means that 20.75 (or almost all of the additional wealth) will be used up in the first period; the remaining 2.25 will be distributed over the next three years.

3.a.According to the life-cycle theory and permanent-income hypothesis (LC-PIH), the change in

consumption equals the surprise element, that is, ?C LC-PIH = ?. According to the traditional theory, the change in consumption equals ?C tr = c(?YD). Therefore if a fraction λ of the population behaves according to the traditional theory and the other fraction behaves according to LC-PIH, the total change in consumption is

?C = λ(?C tr) + (1 - λ)(?C LC-PIH) = λc(?YD) + (1 - λ)? = (0.7)(0.8)10 + (0.3) = 5.6 + (0.3)?.

3.b.?C = (0.3)(0.8)10 + (0.7)ε = 2.4 + (0.7)?

3.c.?C = (0)(0.8)10 + 1? = ?

4.a. If the real interest rate increases, the opportunity cost of consuming should increase.

Therefore, the average propensity to save, that is, the fraction of total income that is saved, should increase.

4.b. If you only save for retirement and your savings goal is fixed, then you actually will save

less. With a higher interest rate it will take less saving each year to achieve your goal.

4.c. The first case (4.a.) describes the substitution effect, whereas the second case (4.b.)

describes the income effect. Unless the magnitude of each of these effects is known, we cannot predict the overall effect of the interest rate increase on saving.

5. One way to increase national saving would be to either privatize or eliminate the Social

Security system, so people would have to save for retirement on their own. (Eliminating Social Security is not a very popular measure, although the privatization of Social Security is often discussed.) This would do away with the negative effect on saving that comes from the pay-as-you-go nature of financing Social Security. Another way might be to make it more difficult to borrow. The U.S. tax system encourages people (and firms) to borrow rather than save. Finally, since national saving is equal to private saving plus government saving, lowering the budget deficit would increase national savings. However, to accomplish this, the government would have to either cut spending or raise taxes.