ECO209 MACROECONOMIC THEORY. Chapter 14

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1 Prof. Gustavo Indart Department of Economics University of Toronto ECO209 MACROECONOMIC THEORY Chapter 14 CONSUMPTION AND SAVING Discussion Questions: 1. The MPC of Keynesian analysis implies that there is a short run multiplier. If these countries return to fiscal deficits, this implies a short run stimulus to their economies. Therefore in the short run there will be some temporary increase in income through the consumption multiplier. Notice, however, that this ignores any long run effects of budget deficits. 2.a. According to the life-cycle theory of consumption, people try to maintain a fairly stable consumption path over their lifetime. 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 while consumption remains stable. We should therefore expect the ratio of consumption to accumulated saving (wealth) to decrease over time up to retirement. 2.b. After retirement, wealth is used up to finance consumption during the remaining years. Therefore the ratio of consumption to accumulated saving (wealth) increases again after retirement, eventually approaching 1. 3.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 do, she will expect to have fewer retirement years in which to use accumulated wealth to finance a steady consumption stream. 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 labour (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).

2 2 (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.) 3.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 could thus be considered a form of "forced saving," since you are forced to pay social security taxes during your working years; in return you will receive benefits during your retirement years. The levying of social security taxes reduces your disposable income during your working years, increasing the ratio of consumption to disposable income (the average propensity to consume). Since private saving is simply replaced with "government saving," national saving is not affected. In reality, however, the Old Age Pension and Canada Pension Plan social security system is not strictly financed through a trust fund, but largely on a pay-as-you-go basis and, in fact, until recently, the size of the social security trust fund was fairly insignificant. Your social security contributions were not "saved" but immediately used by the government to finance the benefits of the current retirees. This is why most 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. Because of changing demographics (an increasing segment of elderly in the population), predictions are that the social security system will be experiencing severe financial difficulties within the next 30 years. But if the credibility of the system becomes an issue, then people may intensify their saving efforts, since they no longer feel they can rely on the public system to provide for them during retirement. 4.a. If you get a yearly Christmas bonus, you immediately treat it as part of your permanent income and spend it accordingly, that is, C = c( Y). In other words, your current consumption will change significantly. 4.b. If you get a Christmas bonus for only this year, you will consider it as transitory income. Since your permanent income is hardly affected, you will consume only a small fraction of it and save the rest. In other words, your current consumption will not be significantly affected. 5. 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. Whether they have a large or small income during any given period, their consumption pattern remains relatively stable, since their permanent income is not significantly affected by temporary changes in earnings. 6. Both theories, in their own way, 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, that is, permanent and transitory income. But only permanent income is a true determinant of current consumption.

3 3 7.a. One possible explanation could be that the baby boomers were still in their dissaving phase. In other words, if households of the baby boom generation still had to buy houses or pay for expenses related to childcare in their late twenties, they may not have been able to save for retirement yet. 7.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. 8. The ranking from highest to lowest value should be first (a), then (d), and then (b). Clearly, (c) should be lower than (a), but where exactly it ranks after that depends largely on the severity of the liquidity constraint. 9. A series follows a random walk when future changes cannot be predicted from past behaviour. In other words, it does not have a mean or clear long-run value. Any major change comes about because of random shocks. Hall asserted that changes in current consumption largely come from unanticipated changes in income. According to the life-cycle theory or permanent-income theory, people try to smooth 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. 10. 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 behaviour only to a certain degree. 11. 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 much closer to reality. For example, many elderly still continue to save after retirement in anticipation of predicted high medical costs not covered by Medicare. 12.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). 12.b. The income effect and the substitution effect generally tend to go in different directions, and 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

4 4 interest rate. This would imply that the income and the substitution effects have about the same magnitude. Application Questions: 2. This question can be answered by altering Figure 14-6 from the text so that the new equilibrium would involve reduced consumption in either period t or period t+1. In either period that consumption is reduced, the consumption would be a non normal good. 3.a. If income remains constant over time, permanent income equals current income. Your permanent income this year is YP 0 = (1/5)(5*20,000) = 20, b. Your permanent income next year is YP 1 = (1/5)(15, *20,000) = 19, c. Since C = 0.9YP, your consumption this year is C 0 = 0.9*20,000 = 18,000. Your consumption next year is C 1 = 0.9*19,000 = 17, d. In the short run, the mpc = (0.9)(1/5) = 0.18; but in the long run, the mpc = e. We have already calculated this and next year's permanent income. In each of the coming years you add $30,000 and subtract $20,000, and 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 YP 1 = (1/5)(1*30, *20,000) = 22,000 YP 2 = (1/5)(2*30, *20,000) = 24,000 YP 3 = (1/5)(3*30, *20,000) = 26,000 YP 4 = (1/5)(4*30, *20,000) = 28,000 YP 5 = (1/5)(5*30,000) = 30,000 Y 30,000 28,000 26,000 24,000 22,000 20, time 4.a. The person lives for NL = 4 periods and earns a lifetime income of YL = = 180. Therefore consumption in each period will be C i = (1/4)180 = 45, i = 1, 2, 3, 4.

5 This implies that saving in each period is: S 1 = = - 15; S 2 = = + 15; S 3 = = + 45; S 4 = 0-45 = b. If liquidity constraints exist and the person cannot borrow in the first period, then she will consume all of her income, that is, Y 1 = C 1 = 30. For the remaining three periods the person wants a stable consumption stream. Thus she will consume C(i) = (1/3)( ) = 50 in each of the remaining three periods i = 2, 3, 4. 4.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 C 1 = 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)( ) = This means that (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. 5.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 = ε. 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, then the total change in consumption is C = λ( C tr ) + (1 - λ)( C LC-PIH ) = λc( YD)+ (1 - λ)cε = (.7)(.8)10 + (.3)ε = (.3)ε 5.b. 5.c. C = (.3)(.8)10 + (.7)ε = (.7)ε C = (0)(.8)10 + 1ε = ε 6.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. 6.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. 6.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 this interest rate increase on saving.