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史蒂芬 威廉森 宏观经济学 第四版 课后题答案 最新Solution_CH10

史蒂芬 威廉森 宏观经济学 第四版 课后题答案 最新Solution_CH10
史蒂芬 威廉森 宏观经济学 第四版 课后题答案 最新Solution_CH10

Chapter 10

A Real Intertemporal Model with Investment

Textbook Question Solutions

Questions for Review

1. An increase in the real interest rate makes future leisure less expensive than current leisure. Therefore,

current labor supply increases when the real interest rate increases. An increase in the real interest rate also makes future consumption less expensive than current consumption. Therefore, current consumption falls when the real interest rate increases. Alternatively, an increase in the real interest rate raises the rate of return on savings. The consumer can save more both by working more and

consuming less in the current period.

2. The primary determinants of current labor supply are the current real wage, the real interest rate, and

lifetime wealth.

3. Current labor demand is exclusively governed by the current-period marginal product of labor

schedule. Therefore, labor demand depends on total factor productivity and the current-period

capital stock.

4. The representative firm maximizes the present value of its profits.

5. The representative firm should invest until the point at which the net marginal product of capital

equals the real rate of interest.

6. The current capital stock does not affect the optimal amount of capital that the firm wants in place

next period. However, if the firm has more capital in the current period, a lower amount of

investment is needed to achieve the desired amount of capital.

7. An increase in future total factor productivity raises the net marginal product of capital, and therefore

investment increases.

8. The government must equate the present value of government spending with the present value of

taxes. The government may run a deficit in the current period, but if it does so it must run a surplus in the future period.

9. Changes in the lifetime wealth of consumers, changes in current-period total factor productivity, and

changes in the current capital stock all shift the output supply curve.

10. Changes in current and future government spending and the present value of taxes shift the output

demand curve. Changes in expected future income, future total factor productivity, and the current capital stock also shift the output demand curve.

90 Williamson ? Macroeconomics, Fourth Edition

11. In a competitive equilibrium, output supply is equal to output demand and labor supply is

simultaneously equal to labor demand. The point of intersection of the output supply curve and the output demand curve allows us to find the competitive equilibrium levels of aggregate output and the real rate of interest.

12. A temporary increase in government purchases increases the real interest rate, increases aggregate

output, increases employment, decreases the real wage, decreases consumption, and decreases

investment.

13. A permanent increase in government purchases does not modify the real interest rate, increases

aggregate output, increases employment, decreases the real wage, and does not change investment and consumption.

14. A decrease in the current capital stock increases the real interest rate, decreases the real wage,

decreases consumption, and increases investment. However, the effects on output and employment are ambiguous. The decrease in the capital stock lowers the marginal product of labor and shifts labor demand to the left. The decrease in lifetime wealth shifts labor supply to the right. According to which of these effects is strongest, employment may either decrease or increase. If employment falls, then we have fewer workers and less capital, so output must decline. However, if there is a sufficiently large increase in employment, the increase in employment more than makes up for the lost capital, and output may rise. In terms of output supply and demand, less capital shifts output demand to the right due to the increase in investment, while the reduction in capital also shifts output supply to the left. The effect on output depends on which of these competing forces is strongest. 15. A temporary increase in total factor productivity decreases the real interest rate, increases aggregate

output, increases employment, increases the real wage, increases consumption, and increases

investment. These results are consistent with the facts that employment, real wages, investment, and consumption are all procyclical.

16. An increase in future total factor productivity increases the real interest rate, increases aggregate

output, increases employment, decreases the real wage, decreases consumption, and increases

investment. There are two principle differences between changes in current and future total factor productivity. First, an increase in future total factor productivity does not help with current

production. Therefore, if the productivity effect is in the future, the increase in current output requires an increase in current employment and employment may only increase if the current real wage

decreases. Second, an increase in future total factor productivity affects current investment demand, while an increase in current total factor productivity does not. This accounts for the fact that the

current increase in z lowers the real interest rate, while the future increase in z increases the real

interest rate. This rise in the real interest rate also accounts for the fact that consumption rises when current z rises and falls when future z rises.

17. As seen in Chapter 9, credit market uncertainty translates into larger interest rate spreads. This mean

that the marginal product of capital needs to be higher, and investment demand drops.

Chapter 10 A Real Intertemporal Model with Investment 91 Problems

1. There are two effects of an increase in the depreciation rate. First, there is the direct effect, which

implies that, given the marginal product of capital in period two, ,K

MP ′the net marginal product of capital, ,K

MP d ′? will decrease when the depreciation rate increases. For any given real interest rate, this effect lowers investment demand, and so the investment demand schedule shifts to the left. This direct effect is the result of the fact that a higher depreciation rate implies that the scrap value of the capital the firm invests in will be lower at the end of period two.

In addition to this direct effect, there is also an indirect effect of the depreciation rate on investment.

Since (1),K'd K I =?+ given the initial capital stock, K , the quantity of capital in period two will be smaller, for any I , if the depreciation rate is higher. Therefore, when d increases, the investment

schedule shifts to the right. The direct and indirect effects work in opposite directions, and so, given the real rate of interest, investment may either rise or fall with an increase in the depreciation rate.

2. The problem supplies the following production function, where future output only depends on the

level of second-period capital, in this case the number of trees.

Future Trees Future Output 15 155.0

16 162.0

17 168.0

18 173.0

19 177.0

20 180.0

21 182.0

22 183.8

23 184.8

24 185.2 25 185.4

(a) The production function is depicted below.

92 Williamson ? Macroeconomics, Fourth Edition (b) The marginal product of capital schedule is computed from the previous table. In table form:

Future Trees Future Output ′K MP 15 155.0 —

16 162.0 7.0

17 168.0 6.0

18 173.0 5.0

19 177.0 4.0

20 180.0 3.0

21 182.0 2.0

22 183.8 1.8

23 184.8 1.0

24 185.2 0.4

25 185.4 0.2

These data are plotted in the figure below.

(c) Tom’s first-year profits are equal to .Y I π=? The present value of second-year profits is equal to (1)(1).(1)2

Y'd K'Y'd K 'r π′????==+ These calculations are given in the column V , below.

Chapter 10 A Real Intertemporal Model with Investment 93 (d) The net marginal product of capital is equal to 0.1.K

K MP d MP ′′?=? These calculations are also included in the table below.

Future Trees Future Output Required I V ′K

MP d ? 15 155.0 ?3 267.25 — 16 162.0 ?2

270.20 6.9 17 168.0 ?1 279.65 5.9

18 173.0 0 274.60 4.9

19 177.0 1 276.05 3.9

20 180.0 2 277.00 2.9

21 182.0 3 277.45 1.9

22 183.8 4 277.80 1.7

23 184.8 5 277.75 0.9

24 185.2 6 277.50 0.3

25 185.4 7 276.95 0.1

(e) Tom’s optimal level of V is equal to 277.80. To earn this amount of profit, Tom needs to plant 4

new trees. Note that at 4, 1.7 1.0.K I MP d r ′=?=>= Planting the 4th tree is therefore profitable.

However, at 4, 0.9

1.0.K I MP d r ′=?=<= Planting the 5th tree is not profitable. The maximum V is therefore attained at the last tree for which .K

MP d r ′?> 3. The costs of the output subsidy and the investment subsidy would each require an increase in other

(lump-sum) taxes to satisfy the government budget constraint with unchanged government purchases. This increase in taxes reduces consumer wealth and so labor supply shifts to the right and output supply also shifts to the right. This effect tends to increase output and decrease the real interest rate. In the case of the output subsidy, the decrease in the real interest rate increases both consumption spending and investment spending to match the increase in output. In the case of the subsidy to

investment, there is also a shift to the right in the output demand curve. This effect provides an

additional increase in output. Also the increase in the real interest rate (or the smaller-sized decrease in the real interest rate) reduces consumption spending so that more of the increase in output goes to investment spending and less goes to consumption spending. Therefore, the investment subsidy is likely to be more effective in increasing investment.

4. The new second-period profits of the firm are now (1).K Y w N d p K π′′′′′=?+?

(a) The new marginal benefit from investment is now

()(1(1))/(1)K

K MB I MP d p r ′′=+?+ As the marginal cost from investment remains at one, the new investment rule is then

(1)(1)K K MP r d p ′′=+??

94 Williamson ? Macroeconomics, Fourth Edition

p′ the marginal product of future capital needs to be reduced, thus more

(b) With an increase in ,

K

future capital is needed and investment rises. Indeed, as the liquidation value of capital goes up,

you want to invest more in capital. Thus investment is positively correlated with stock prices.

5. Slope of the output demand curve.

(a) A reduction in the real interest rate increases consumption and investment spending. This is the

primary reason for the downward slope of the output demand curve. However, as output rises,

there is a further increase in consumption spending according to the size of the marginal

propensity to consume. The larger the marginal propensity to consume, the flatter is the

aggregate demand curve.

(b) The intertemporal substitution effect on consumption is one of the primary reasons why demand

rises at lower interest rates. The larger the sensitivity of consumption spending to the real rate of

interest, the flatter is the output demand curve.

(c) The responsiveness of investment demand to the real rate of interest is one of the primary reasons

why demand rises at lower interest rates. The larger the responsiveness of investment demand to

the real rate of interest, the flatter is the output demand curve.

6. (a) As government expenses are unchanged, future taxes need to increase to satisfy the intertemporal

budget constraint of the government. We are therefore in the context of the Ricardian equivalence.

Thus, neither of the real interest rate, aggregate output, employment or the real wage is affected.

Chapter 10 A Real Intertemporal Model with Investment 95 (b) We are now violating the conditions of the Ricardian equivalence. There is potentially an impact.

Indeed, the endowment point is moving towards the right, and some borrowers now become lenders, and thus face a lower interest rate. This leads to a positive income effect (and thus an increase in current consumption demand and a decrease in labor supply) and a substitution effect that increases demand for current goods. In then end, consumption demand increases and labor supply decreases.

The implications are that the interest rate increases, thus leading to a second shift in the labor supply, an increase that has to be larger than the initial decrease, as equilibrium out is up. In the end, aggregate output, consumption, labor and the real interest rate are all up, while the real wage is down.

96 Williamson ? Macroeconomics, Fourth Edition

7. Slope of the output supply curve.

(a) The figure below depicts the effect of an increase in labor supply, due to an increase in the real

interest rate, on the equilibrium level of employment. The diagram shows two alternate labor

demand curves with differing slopes. Note that the equilibrium level of employment increases

more when the marginal product of labor declines at a slower rate with increases in the level of

employment. Therefore, when the marginal product of labor declines at a faster rate as the

quantity of labor used in production increases, there is a smaller increase in employment and

therefore a smaller increase in output supply. The output supply curve is steeper in this case.

(b) When the substitution effect of an increase in the real rate of interest decreases, there is a smaller

effect on equilibrium employment of an increase in the real interest rate. Therefore there is a

smaller increase in output supply. The output supply curve is steeper in this case.

8. Labor supply shifts to the right, so output supply also shifts to the right. Consumption demand also

increases, so the output demand curve must also shift to the right. Output must increase although the real rate of interest may rise or fall. In light of the increase in output, equilibrium employment must increase. A higher level of employment, in the absence of a shift in the labor demand curve, assures us that the real wage rate must also fall. Investment rises if the real rate of interest declines, and investment falls if the real rate of interest increases. Because output has increased, consumption will rise as long as investment remains the same or declines. Consumption falls only in the case of a decline in the rate of interest of sufficient size to increase investment by more than the increase in output.

(a) To summarize: ,,,?,?,?, but most likely increases.

↑↑↓

Y N w r I C

(b) As one possibility, at low levels of nutrition, it may be infeasible for the consumer to work very

much (a very high MRS l, C). In this case, an increase in nutrition would make the consumer more willing (and able) to work more and consume more. One could also imagine some change in the technology of using leisure that is more goods intensive. In this case the value of leisure is low

without a lot of consumption goods.

9. A temporary increase in z increases output and employment, raises the real wage, and lowers the

real rate of interest. Consumption and investment both increase. An increase in future total factor productivity, z′, shifts the current-period output demand curve to the right. Current output and

employment increase, and the real interest rate increases. Since the current-period labor demand curve does not shift, the shift in labor supply due to the lower real interest rate causes the real

wage rate to decline.

Chapter 10 A Real Intertemporal Model with Investment 97

A permanent increase in total factor productivity simply combines the effects of the temporary and

permanent changes in z. Current output and employment unambiguously increase. The real wage rate may either rise or fall. The real interest rate may either rise or fall. As long as the direct effect of the MP′ outweighs any indirect effect due to a possible increase in the real interest rate, then increase in

K

investment will increase. As long as the direct effects of the increases in current and future income dominate any indirect effect of a possible rise in the real interest rate, then consumption will also

increase.

10. The increase in z′ shifts the output demand curve to the right, but has no effect on the output supply

curve. The increase in K shifts the output demand curve to the left, and shifts the output supply curve to the right. The combined effects shift the output supply curve to the right. The shift in the output demand curve is uncertain. An increase in the current capital stock lowers investment spending. An increase in future total factor productivity increases investment spending. As one possibility, suppose that the effect of the prospective increase in total factor productivity is that investment increases. In this case, both the output supply curve and the output demand curve shift to the right. Output rises unambiguously, but the effect on the real interest rate is uncertain.

If a lack of capital were the only reason for low output in poor countries, then we would expect that the real interest rates in poor countries would be higher than the real interest rates in rich countries.

This is not the case. Alternatively, if poor countries are poor both because they have less capital and because they have worse prospects for future investment, then this explanation of the difference

between poor and rich countries need not be in conflict with observed differences in real interest rates.

11. A temporary increase in the price of energy is best modeled as a reduction in current-period total

factor productivity. Such a disturbance shifts output supply to the left. Therefore, output falls and the real interest rate increases. In question 3, above, we showed that a larger value for the marginal

propensity to consume implied a flatter output demand curve. In the figure below, we show the shift in output supply with two alternative output demand curves. When the marginal propensity to

consume is high, the output demand curve is flat and the reduction in z results in a large reduction in output and a small increase in the real interest rate. When the marginal propensity to consume is

smaller, there is a smaller reduction in output, and a larger increase in the real interest rate.

98 Williamson ? Macroeconomics, Fourth Edition

12. A hurricane destroys a significant amount of capital. This disturbance may be analyzed as an

exogenous decrease in the stock of capital. The production function shifts downward. Labor demand shifts to the left. These effects result in a leftward shift in the goods supply curve. The loss in capital also increases the expected marginal product of capital, and so the goods demand curve shifts to the right. The figures below depict the case in which equilibrium output decreases.

(a) The analysis of the effects of the hurricane suggests that it is reasonable to expect a decrease in

national income. However, because the model is based upon maximizing principles, it is likely

that the reduction in national income represents an optimal response to the reduction in the

capital stock. There is therefore no presumption that policy will improve the situation.

Chapter 10 A Real Intertemporal Model with Investment 99 (b) An appropriate-sized increase in government spending can restore the economy to the original

level of output, *

1.

Y A temporary increase in government spending generates a negative wealth effect shifting the labor supply curve to the right. The temporary increase in government

spending also shifts the output demand curve to the right. The figure below depicts a case in

which the increase in government spending exactly returns the economy to the original level of

output.

Output is unchanged. The real interest rate increases. Employment must increase. In order to

produce the same amount of output an increase in employment is needed to substitute for the lost capital.

(c) A more sensible rationale for an increase in government spending would be based upon needs to

replace government-provided capital. That is, the government might want to increase spending to replace roads, sewer systems, and other infrastructure.

13. A short war is best modeled as a temporary increase in government spending. Such a disturbance

shifts the output demand curve to the right because the increase in current-period government

spending will be larger than the reduction in consumption demand due to the decline in consumers’ lifetime wealth. The output supply curve also shifts to the right because of the reduction in

consumers’ lifetime wealth. Output and employment unambiguously increase. Because the increase in government spending is only temporary, the effect on lifetime wealth is likely to be small, so the demand curve shifts farther than the supply curve. Therefore, the interest rate most likely increases.

100 Williamson ? Macroeconomics, Fourth Edition

In order to more clearly see how the size of the intertemporal substitution effect on consumption comes into play, let us assume that the lifetime wealth effect is small enough to be ignored. In this case we need only be concerned with the shift in output demand and not the shift in output supply.

The flatter output demand curves correspond to the case in which the interest rate effect on

consumption is stronger. As the figure below depicts, the increase in output in this case is smaller.

The intuition is as follows. When consumption is very sensitive to changes in the interest rate, it takes

a smaller increase in the interest rate to crowd out demand to fit the increased G. With a smaller

increase in the real interest rate, there is a smaller shift in labor supply, and so there is a smaller

increase in employment and output.

14. The increase in aggregate credit uncertainty leads to an increase in interest spreads. This reduces

consumption demand and increases the labor supply, as current goods (consumption and leisure) are less used. The impact on consumption can be counteracted by increasing government expenses. But let us not forget that this means that taxes will need to increase this period or next, leading to a

negative income shock for households. This depresses consumption demand further, but not as much as the push in G, and increases further the labor supply. So the government needs to increase G even more. How much depends how much the output supply increased as a consequence of the increase in the labor supply. As now the interest rate has dropped and we have the same output as before, there needs to be a shift back of the labor supply to its original level.

Chapter 10 A Real Intertemporal Model with Investment 101 Is this good policy? In the end, households end up in the same situation as before for the current period. However, they still face a higher tax burden and their second period consumption and leisure will suffer.

宏观经济学习题及答案

第9章 一、选择题 1.政府预算赤字增加()。 A.提高了真实利率并挤出了投资 B.降低了真实利率并挤出了投资 C.对真实利率没有影响,也不会挤出投资,因为外国人购买有赤字国家的资产 D.以上各项都不是 2.在其他条件不变的情况下,一国较高的真实利率()。 A.增加了该国的资本净流出,因为本国居民和外国人都喜欢在该国投资 B.减少了该国的资本净流出,因为本国居民和外国人都喜欢在该国投资 C.减少了该国的资本净流出,因为本国居民和外国人都喜欢在国外投资 D.以上各项都不是 3.欧洲人对美国生产的福特汽车的偏好提高,引起美元()。 A.贬值,且美国净出口增加 B.贬值,且美国净出口减少 C.升值,且美国净出口增加 D.升值,且美国净出口减少 E.升值,但美国净出口总额保持不变 4.“孪生赤字”这个词是指()。 A.一国的贸易赤字和它的政府预算赤字 B.一国的贸易赤字和它的资本净流出赤字 C.一国的储蓄赤字和它的投资赤字的相等 D.如果一国有贸易赤字,其贸易伙伴必定也有贸易赤字 5.以下哪一项关于外汇市场的表述是正确的?()。 A.一国净出口增加增加了本币供给,本币贬值 B.一国净出口增加减少了本币供给,本币贬值 C.一国净出口增加减少了本币需求,本币升值 D.一国净出口增加增加了本币需求,本币升值 6.以下哪一项关于外汇市场的表述是正确的?()。 A.一国资本净流出增加增加了本币供给,本币升值 B.一国资本净流出增加增加了本币供给,本币贬值 C.一国资本净流出增加增加了本币需求,本币升值 D.一国资本净流出增加增加了本币需求,本币贬值 7.如果美国对中国生产的服装的进口实行配额,以下哪一项关于美国外汇市场的表述是正确的?()。 A.美元供给增加,且美元贬值 B.美元供给减少,且美元升值 C.美元需求增加,且美元升值 D.美元需求减少,且美元贬值 8.如果美国对中国生产的服装的进口实行配额,以下哪一项关于美国净出口的表述是正确的?()。 A.净出口将增加 B.净出口将减少 C.净出口将保持不变 D.以上各项都不是 二、判断题 1.资本净流出是外国人购买的本国资产减国内居民购买的外国资产。 2.一国的资本净流出(NCO)总等于其净出口(NX)。

宏观经济学试题及答案99694

宏观经济学B卷答案 一、名词解释(10分每小题2分) 1GNP:国民生产总值。某国身份家的公民在一定时期内运用生产要素所能生产的全部最终产品的市场价值。 2、税收乘数:税收增加一个单位所引起的均衡国民收入增加的倍数。 3、货币流动偏好:由于货币具有使用上的灵活性人们宁肯牺牲利息收入来保持财富的心理倾向。 4、LM曲线:货币市场均衡时L m =,此时反映利率r和国民收入y之间对应关系的曲线。 5、扩张性的货币政策:货币当局通过改变货币供给m或利率r等金融杠杆进而使国民收入增加的政策。 二、单项选择(20分每小题2分) 1——5 DDADB 6——10 BBABC 三、简答题(20分每小题5分) 1、在其他条件不变的前提下,如果国家增加政府转移支付,IS曲线将如何移动, 请画图分析并说明理由。 答:在三部门经济中,IS曲线为 1 e g t tr r y d d αβββ ++-+- =-,当其他条 件不变,政府转移支付tr增加时,纵截距 e g t tr d αββ ++-+ 增大,斜率不变, 所以IS曲线向右上方平移。 2、什么是汇率?汇率有几种标价法?并举例说明。 答:汇率是一国货币交换另一国货币的比率。有直接标价法和间接标价法。直接标价法如:1美元=6.19人民币;间接标价法如:1人民币=1/6.19美元。 3、宏观经济政策目标是什么?为达到这些目标可采用的政策工具有哪些? 宏观经济政策目标包括充分就业、物价稳定、经济增长和国际收支平衡。工具有财政政策和货币政策。财政政策又包括扩张性的财政政策和紧缩性的财政政策。货币政策又包括扩张性的货币政策和紧缩性的货币政策。

最新宏观经济学题库及答案

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6.实际GDP等于(B)。 A.价格水平/名义GDP; B.名义GDP/价格水平×100; C.名义GDP乘以价格水平; D.价格水平乘以潜在GDP。 7.下列各项中属于流量的是(A)。 A.国内生产总值; B.国民债务; C.现有住房数量; D.失业人数。 8.存量是(A)。 A.某个时点现存的经济量值; B.某个时点上的流动价值; C.流量的固体等价物; D.某个时期内发生的经济量值。 9. 下列各项中哪一个属于存量?(C)。 A. 国内生产总值; B. 投资; C. 失业人数; D. 人均收入。 10.古典宏观经济理论认为,利息率的灵活性使得(B)。 A.储蓄大于投资; B.储蓄等于投资; C.储蓄小于投资; D.上述情况均可能存在。

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2008/2009学年第一学期 A 二、单项选择题(每小题 1 分,共10 分) 1. 下列哪一项不列入国内生产总值的核算?() A. 出口到外国的一批货物; B. 政府给贫困家庭发放的一笔救济金; C. 经济人为一笔旧房买卖收取佣金; D. 保险公司收到一笔家庭财产保险 1. B; 2. 在两部门经济中,均衡发生于()之时。 A. 实际储蓄等于实际投资; B. 计划储蓄等于计划投资; C. 实际的消费加实际的投资等于产出值; D. 总支出等于企业部门的收入 2. B; 3. 假定其他条件不变,税收增加将引起国民收入()。 A. 增加,但消费水平下降; B. 增加,同时消费提高; C. 减少,同时消费水平下降; D. 减少,但消费水平上升 3. C; 4. 利率和收入的组合点出现在IS 曲线右上方,LM 曲线的左上方的区域中,则表示( )。 A.is ,L>M ; C.i>s ,LM 4. A; 5. 在IS- LM 模型中,若经济处于中间区域,货币供给增加将导致( ) 。A.收入增加,利率上升; B .收入减少,利率上升; C.收入增加,利率降低; D .收入减少,利率降低 5. C; 6. 在其它因素不变情况下,自发性投资增加10 亿美元,IS 曲线将( )。A.右移10 亿美元;B.左移10 亿美元; C.右移支出乘数乘以10 亿美元;D.左移支出乘数乘以10 亿美元 6. C; 7. 中央银行提高再贴率会导致货币供给量()。 A.增加和利率提高;B.减少和利率提高; C.增加和利率降低;D.减少和利率降低 7. B;

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宏观经济学参考题目及答案

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