《宏观经济学》课程教学资源（英文版）Lecture 2 Answers to Textbook Questions and Problems_Mankiw

Answers to Textbook questions and Problems traded in markets and, thus, does not show up in measured gDP, but is neverthe less a good that people value. f. Real GDP rises because the high-school students go from an activity in which they are not producing market goods and services to one in which they are. Economic well-being, however, may decrease. In ideal national accounts, attending school would show up as investment because it presumably increases the future produc tivity of the worker. Actual national accounts do not measure this type of invest- ment. Note also that future GDP may be lower than it would be if the students stayed in school, since the future work force will be less educated. g. Measured real GDP falls because fathers spend less time producing market good and services. The actual production of goods and services need not have fallen, however Measured production(what the fathers are paid to do)falls, but unmea- sured production of child-rearing services rises 9. As Senator Robert Kennedy pointed out, GDP is an imperfect measure of economic per formance or well-being. In addition to the left-out items that Kennedy cited, gDP alse ignores the imputed rent on durable goods such as cars, refrigerators, and lawnmowers many services an nd products produced as part of household activity, such as cooking and cleaning; and the value of goods produced and sold in illegal activities, such as the drug trade. These imperfections in the measurement of gdp do not necessarily reduce its usefulness. As long as these measurement problems stay constant over time, then GDP useful in comparing economic activity from year to year. Moreover a large GDP allows us to afford better medical care for our children newer books for their education and more toys for their play

traded in markets and, thus, does not show up in measured GDP, but is neverthe￾less a good that people value. f. Real GDP rises because the high-school students go from an activity in which they are not producing market goods and services to one in which they are. Economic well-being, however, may decrease. In ideal national accounts, attending school would show up as investment because it presumably increases the future produc￾tivity of the worker. Actual national accounts do not measure this type of invest￾ment. Note also that future GDP may be lower than it would be if the students stayed in school, since the future work force will be less educated. g. Measured real GDP falls because fathers spend less time producing market goods and services. The actual production of goods and services need not have fallen, however. Measured production (what the fathers are paid to do) falls, but unmea￾sured production of child-rearing services rises. 9. As Senator Robert Kennedy pointed out, GDP is an imperfect measure of economic per￾formance or well-being. In addition to the left-out items that Kennedy cited, GDP also ignores the imputed rent on durable goods such as cars, refrigerators, and lawnmowers; many services and products produced as part of household activity, such as cooking and cleaning; and the value of goods produced and sold in illegal activities, such as the drug trade. These imperfections in the measurement of GDP do not necessarily reduce its usefulness. As long as these measurement problems stay constant over time, then GDP is useful in comparing economic activity from year to year. Moreover, a large GDP allows us to afford better medical care for our children, newer books for their education, and more toys for their play. 10 Answers to Textbook Questions and Problems

chaPteR 3 National Income Where it comes from and where|tG。es questions for Review 1. Factors of production and the production technology determine the amount of output an economy can produce. Factors of production are the inputs used to produce goods and services: the most important factors are capital and labor. The production technology determines how much output can be produced from any given amounts of these inputs An increase in one of the factors of production or an improvement in technology leads to 2. When a firm decides how much of a factor of production to hire, it considers how this decision affects profits. For example hiring an extra unit of labor increases output and therefore increases revenue; the firm compares this additional revenue to the addition al cost from the higher wage bill. The additional revenue the firm receives depends on the marginal product of labor (MPL) and the price of the good produced(P). An addi tional unit of labor produces MPL units of additional output, which sells for P dollars Therefore, the additional revenue to the firm is P x MPL. The cost of hiring the addi- tional unit of labor is the wage w. Thus, this hiring decision has the following effect on △ Profit=△ Revenue-△Cost =(P×MPL)-W If the additional revenue, Px MPL, exceeds the cost (w) of hiring the additional unit of labor, then profit increases. The firm will hire labor until it is no longer profitable to do so-that is, until the MPL falls to the point where the change in profit is zero In the equation above, the firm hires labor until Aprofit=0, which is when(Px MPL)= w This condition can be rewritten as MPL= W/P Therefore, a competitive profit-maximizing firm hires labor until the marginal product of labor equals the real wage. The same logic applies to the firms decision to hire capi- tal: the firm will hire capital until the marginal product of capital equals the real capi- a production function has constant returns if an equal percentage increase in all factors of production causes an increase in t of the same percentage. For exam- ple, if a firm increases its use of capital and by 50 percent, and output increases by 50 percent, then the production function has constant returns to scale If the production function has constant returns to scale, then total income(or equivalently, total output) in an economy of competitive profit-maximizing firms is divided between the return to labor, MPL XL, and the return to capital, MPK K. That is, under constant returns to scale, economic profit is zero 4. Consumption depends positively on disposable income-the amount of income after all taxes have been paid. The higher disposable income is, the greater consumption is The quantity of investment goods demanded depends negatively on the real inter est rate. For an investment to be profitable, its return must be greater than its cost Because the real interest rate measures the cost of funds gher real interest rate makes it more costly to invest, so the demand for investment goods fall 5. Government purchases are those goods and services purchased directly by the govern ment. For example, the government buys missiles and tanks, builds roads, and provides

Questions for Review 1. Factors of production and the production technology determine the amount of output an economy can produce. Factors of production are the inputs used to produce goods and services: the most important factors are capital and labor. The production technology determines how much output can be produced from any given amounts of these inputs. An increase in one of the factors of production or an improvement in technology leads to an increase in the economy’s output. 2. When a firm decides how much of a factor of production to hire, it considers how this decision affects profits. For example, hiring an extra unit of labor increases output and therefore increases revenue; the firm compares this additional revenue to the addition￾al cost from the higher wage bill. The additional revenue the firm receives depends on the marginal product of labor (MPL) and the price of the good produced (P). An addi￾tional unit of labor produces MPL units of additional output, which sells for P dollars. Therefore, the additional revenue to the firm is P × MPL. The cost of hiring the addi￾tional unit of labor is the wage W. Thus, this hiring decision has the following effect on profits: ∆Profit = ∆Revenue – ∆Cost = (P × MPL) – W. If the additional revenue, P × MPL, exceeds the cost (W) of hiring the additional unit of labor, then profit increases. The firm will hire labor until it is no longer profitable to do so—that is, until the MPL falls to the point where the change in profit is zero. In the equation above, the firm hires labor until ∆profit = 0, which is when (P × MPL) = W. This condition can be rewritten as: MPL = W/P. Therefore, a competitive profit-maximizing firm hires labor until the marginal product of labor equals the real wage. The same logic applies to the firm’s decision to hire capi￾tal: the firm will hire capital until the marginal product of capital equals the real rental price. 3. A production function has constant returns to scale if an equal percentage increase in all factors of production causes an increase in output of the same percentage. For exam￾ple, if a firm increases its use of capital and labor by 50 percent, and output increases by 50 percent, then the production function has constant returns to scale. If the production function has constant returns to scale, then total income (or equivalently, total output) in an economy of competitive profit-maximizing firms is divided between the return to labor, MPL × L, and the return to capital, MPK × K. That is, under constant returns to scale, economic profit is zero. 4. Consumption depends positively on disposable income—the amount of income after all taxes have been paid. The higher disposable income is, the greater consumption is. The quantity of investment goods demanded depends negatively on the real inter￾est rate. For an investment to be profitable, its return must be greater than its cost. Because the real interest rate measures the cost of funds, a higher real interest rate makes it more costly to invest, so the demand for investment goods falls. 5. Government purchases are those goods and services purchased directly by the govern￾ment. For example, the government buys missiles and tanks, builds roads, and provides 11 CHAPTER 3 National Income: Where It Comes From and Where It Goes

Answers to Textbook questions and Problems services such as air traffic control. All of these activities are part of GDP. Transfer pay ments are government payments to individuals that are not in exchange for goods or services. They are the opposite of taxes: taxes reduce household disposable income hereas transfer payments increase it. Examples of transfer payments include Social Security payments to the elderly, unemployment insurance, and veterans'benefits 6. Consumption, investment, and government purchases determine demand for the econo- my's output, whereas the factors of production and the production function determine the supply of output. The real interest rate adjusts to ensure that the demand for the economy's goods equals the supply. At the equilibrium interest rate, the demand goods and services equals the supply 7. When the government increases taxes, disposable income falls, and therefore consump tion falls as well. The decrease in consumption equals the amount that taxes increase multiplied by the marginal propensity to consume(MPC). The higher the MPC is, the fixed by the fact gative effect of the tax increase on consumption. Because output chases have not changed, the decrease in consumption must be offset by an increase in investment. For investment to rise. the real interest rate must fall. Therefore. a tax increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest rate Problems and applications 1. a. According to the neoclassical theory of distribution, the real wage equals the mar- ginal product of labor. Because of diminishing returns to labor, an increase in the labor force causes the marginal product of labor to fall. Hence, the real wage falls. b. The real rental price equals the marginal product of capital. If an earthquake destroys some of the capital stock(yet miraculously does not kill anyone and lower the labor force), the marginal product of capital rises and, hence, the real rental price rises. c. If a technological advance improves the production function, this is likely to increase the marginal products of both capital and labor. Hence the real wage and the real rental price both increase 2. A production function has decreasing returns to scale if an equal percentage increase in all factors of production leads to a smaller percentage increase in output. For example if we double the amounts of capital and labor, and output less than doubles, then the production function has decreasing returns to capital and labor. This may happen if there is a fixed factor such as land in the production function, and this fixed factor becomes scarce as the economy grows larger a production function has increasing returns to scale if an equal percentage increase in all factors of production leads to a larger percentage increase in output. For example, if doubling inputs of capital and labor more than doubles output, then the pro- luction function has increasing returns to scale. This may happen if specialization labor becomes greater as population grows. For example, if one worker builds a car, then it takes him a long time because he has to learn many different skills, and he must constantly change tasks and tools; all of this is fairly slow. But if many workers build a car, then each one can specialize in a particular task and become very fast at it 3. a. According to the neoclassical theory, technical progress that increases the margin al product of farmers causes their real wage to rise. b. The real wage in(a)is measured in terms of farm goods. That is, if the nominal wage is in dollars, then the real wage is W/PF, where PF is the dollar price of

services such as air traffic control. All of these activities are part of GDP. Transfer pay￾ments are government payments to individuals that are not in exchange for goods or services. They are the opposite of taxes: taxes reduce household disposable income, whereas transfer payments increase it. Examples of transfer payments include Social Security payments to the elderly, unemployment insurance, and veterans’ benefits. 6. Consumption, investment, and government purchases determine demand for the econo￾my’s output, whereas the factors of production and the production function determine the supply of output. The real interest rate adjusts to ensure that the demand for the economy’s goods equals the supply. At the equilibrium interest rate, the demand for goods and services equals the supply. 7. When the government increases taxes, disposable income falls, and therefore consump￾tion falls as well. The decrease in consumption equals the amount that taxes increase multiplied by the marginal propensity to consume (MPC). The higher the MPC is, the greater is the negative effect of the tax increase on consumption. Because output is fixed by the factors of production and the production technology, and government pur￾chases have not changed, the decrease in consumption must be offset by an increase in investment. For investment to rise, the real interest rate must fall. Therefore, a tax increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest rate. Problems and Applications 1. a. According to the neoclassical theory of distribution, the real wage equals the mar￾ginal product of labor. Because of diminishing returns to labor, an increase in the labor force causes the marginal product of labor to fall. Hence, the real wage falls. b. The real rental price equals the marginal product of capital. If an earthquake destroys some of the capital stock (yet miraculously does not kill anyone and lower the labor force), the marginal product of capital rises and, hence, the real rental price rises. c. If a technological advance improves the production function, this is likely to increase the marginal products of both capital and labor. Hence, the real wage and the real rental price both increase. 2. A production function has decreasing returns to scale if an equal percentage increase in all factors of production leads to a smaller percentage increase in output. For example, if we double the amounts of capital and labor, and output less than doubles, then the production function has decreasing returns to capital and labor. This may happen if there is a fixed factor such as land in the production function, and this fixed factor becomes scarce as the economy grows larger. A production function has increasing returns to scale if an equal percentage increase in all factors of production leads to a larger percentage increase in output. For example, if doubling inputs of capital and labor more than doubles output, then the pro￾duction function has increasing returns to scale. This may happen if specialization of labor becomes greater as population grows. For example, if one worker builds a car, then it takes him a long time because he has to learn many different skills, and he must constantly change tasks and tools; all of this is fairly slow. But if many workers build a car, then each one can specialize in a particular task and become very fast at it. 3. a. According to the neoclassical theory, technical progress that increases the margin￾al product of farmers causes their real wage to rise. b. The real wage in (a) is measured in terms of farm goods. That is, if the nominal wage is in dollars, then the real wage is W/PF, where PF is the dollar price of farm goods. 12 Answers to Textbook Questions and Problems

Chapter 3 National Income: Where It Comes From and Where It Goes c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged d. The real wage in(c)is measured in terms of haircuts. That is, if the nominal wage is in dollars, then the real wage is W/PH, where PH is the dollar price of a hair cut e. If workers can move freely between being farmers and being barbers then they must be paid the same wage w in each sector. f. If the nominal wage w is the same in both sectors but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods g. Both groups benefit from technological progress in farming 4. The effect of a government tax increase of $100 billion on(a) public saving, (b)private saving, and(c)national saving can be analyzed by using the following relationship National Saving =[Private Saving]+[Public Saving] TY-T-c(Y-T)+IT-GI Y-C(Y-T)-G a. Public Saving-The tax increase causes a l-for-l increase in public saving. T increases by $100 billion and, therefore, public saving increases by $100 billion b. Private Saving-The increase in taxes decreases disposable income, Y-T, by $100 billion. Since the marginal propensity to consume(MPC)is 0.6, consumption falls by 0.6 x $100 billion, or $60 billion. Hence APrivate Saving=-$1006-06(-$1006)=-$406 Private saving falls $40 billion c. National Saving-Because national saving is the sum of private and public sav ing, we can conclude that the $100 billion tax increase leads to a $60 billion increase in national savin Another way to see this is by using the third equation for national saving expressed above, that national saving equals Y-C(Y -T)-G. The $100 billion tax increase reduces disposable income and causes consumption to fall by $60 bil lion. Since neither G nor Y changes, national saving thus rises by $60 billion d. Investment--to determine the effect of the tax increase on investment, recall the national accounts identity Y=c(Y-T)+I(r)+G Rearranging, we find Y-C(Y-⑦)-G=I(r). The left-hand side of this equation is national saving, so the equation just says the national saving equals investment. Since national saving increases by $60 billion investment must also increase by $60 billion

c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. d. The real wage in (c) is measured in terms of haircuts. That is, if the nominal wage is in dollars, then the real wage is W/PH, where PH is the dollar price of a hair￾cut. e. If workers can move freely between being farmers and being barbers, then they must be paid the same wage W in each sector. f. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods. g. Both groups benefit from technological progress in farming. 4. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c) national saving can be analyzed by using the following relationships: National Saving = [Private Saving] + [Public Saving] = [Y – T – C(Y – T)] + [T – G] = Y – C(Y – T) – G. a. Public Saving—The tax increase causes a 1-for-1 increase in public saving. T increases by $100 billion and, therefore, public saving increases by $100 billion. b. Private Saving—The increase in taxes decreases disposable income, Y – T, by $100 billion. Since the marginal propensity to consume (MPC) is 0.6, consumption falls by 0.6 × $100 billion, or $60 billion. Hence, ∆Private Saving = – $100b – 0.6 ( – $100b) = – $40b. Private saving falls $40 billion. c. National Saving—Because national saving is the sum of private and public sav￾ing, we can conclude that the $100 billion tax increase leads to a $60 billion increase in national saving. Another way to see this is by using the third equation for national saving expressed above, that national saving equals Y – C(Y – T) – G. The $100 billion tax increase reduces disposable income and causes consumption to fall by $60 bil￾lion. Since neither G nor Y changes, national saving thus rises by $60 billion. d. Investment—To determine the effect of the tax increase on investment, recall the national accounts identity: Y = C(Y – T) + I(r) + G. Rearranging, we find Y – C(Y – T) – G = I(r). The left-hand side of this equation is national saving, so the equation just says the national saving equals investment. Since national saving increases by $60 billion, investment must also increase by $60 billion. Chapter 3 National Income: Where It Comes From and Where It Goes 13

Answers to Textbook questions and Problems How does this increase in investment take place? We know that investment depends on the real interest rate. For investment to rise, the real interest rate must fall. Figure 3-1 graphs saving and investment as a function of the real inter- S S (r) 5. i able The tax increase causes national saving to rise, so the supply curve for loan- ole funds shifts to the right. The equilibrium real interest rate falls, and invest- ment rises 5. If consumers increase the amount that they consume today, then private saving and therefore, national saving will fall We know this from the definition of national saving National Saving =[Private Saving]+[Public Saving =ⅣY-T-CY-T+[-G] An increase in consumption decreases private saving, so national saving falls. Figure 3-2 graphs saving and investment as a function of the real interest rate. If national saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest rate and reducing investment S Figure 3-2 L. S

How does this increase in investment take place? We know that investment depends on the real interest rate. For investment to rise, the real interest rate must fall. Figure 3–1 graphs saving and investment as a function of the real inter￾est rate. The tax increase causes national saving to rise, so the supply curve for loan￾able funds shifts to the right. The equilibrium real interest rate falls, and invest￾ment rises. 5. If consumers increase the amount that they consume today, then private saving and, therefore, national saving will fall. We know this from the definition of national saving: National Saving = [Private Saving] + [Public Saving] = [Y – T – C(Y – T)] + [T – G]. An increase in consumption decreases private saving, so national saving falls. Figure 3–2 graphs saving and investment as a function of the real interest rate. If national saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest rate and reducing investment. 14 Answers to Textbook Questions and Problems S1 S2 I (r) I, S Investment, Saving r1 r2 r Real interest rate Figure 3–1 Figure 3–1 S2 S1 I (r) I, S Investment, Saving r1 r2 r Real interest rate Figure 3–2 Figure 3–2