1、Chapter 3National Income: Where It Comes From and Where It Goes 9Answers to Textbook Questions and ProblemsCHAPTER 3 National Income: Where It Comes From and Where It GoesQuestions for Review1. The factors of production and the production technology determine the amount of output an economy can prod
2、uce. The 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 impro
3、vement in technology leads to an increase in the economys output.2. When a firm decides how much of a factor of production to hire or demand, it considers how this decision affects profits. For example, hiring an extra unit of labor increases output and therefore increases revenue; the firm compares
4、 this additional revenue to the additional 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 additional unit of labor produces MPL units of additional output, which sells for P dollars pe
5、r unit. Therefore, the additional revenue to the firm is P MPL. The cost of hiring the additional 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 addition
6、al unit of labor, then profit increases. The firm will hire labor until it is no longer profitable to do sothat 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 rewr
7、itten 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 regarding how much capital to hire: the firm will hire capital until the marginal product of capital equals the real r
8、ental 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 example, if a firm increases its use of capital and labor by 50 percent, and output increases by 50 percent, then t
9、he 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
10、is, under constant returns to scale, economic profit is zero.4. A CobbDouglas production function has the form F(K,L) = AKL1. The text showed that the parameter gives capitals share of income. So if capital earns one-fourth of total income, then = 0.25. Hence, F(K,L) = AK0.25L0.75.5. Consumption dep
11、ends positively on disposable incomei.e. the amount of income after all taxes have been paid. Higher disposable income means higher consumption. The quantity of investment goods demanded depends negatively on the real interest rate. For an investment to be profitable, its return must be greater than
12、 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.Chapter 3National Income: Where It Comes From and Where It Goes 106. Government purchases are a measure of the value of goods and
13、 services purchased directly by the government. For example, the government buys missiles and tanks, builds roads, and provides services such as air traffic control. All of these activities are part of GDP. Transfer payments are government payments to individuals that are not in exchange for goods o
14、r 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.7. Consumption, investment, and government purchas
15、es determine demand for the economys 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 economys goods equals the supply. At the equilibrium interest rate, the demand for goods and ser
16、vices equals the supply.8. When the government increases taxes, disposable income falls, and therefore consumption 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 negati
17、ve effect of the tax increase on consumption. Because output is fixed by the factors of production and the production technology, and government purchases have not changed, the decrease in consumption must be offset by an increase in investment. For investment to rise, the real interest rate must fa
18、ll. Therefore, a tax increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest rate.Problems and Applications1. a. According to the neoclassical theory of distribution, the real wage equals the marginal product of labor. Because of diminishing returns to
19、 labor, an increase in the labor force causes the marginal product of labor to fall. Hence, the real wage falls.Given a CobbDouglas production function, the increase in the labor force will increase the marginal product of capital and will increase the real rental price of capital. With more workers
20、, the capital will be used more intensively and will be more productive.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, h
21、ence, the real rental price rises.Given a CobbDouglas production function, the decrease in the capital stock will decrease the marginal product of labor and will decrease the real wage. With less capital, each worker becomes less productive.c. If a technological advance improves the production funct
22、ion, this is likely to increase the marginal products of both capital and labor. Hence, the real wage and the real rental price both increase.d. High inflation that doubles the nominal wage and the price level will have no impact on the real wage. Similarly, high inflation that doubles the nominal r
23、ental price of capital and the price level will have no impact on the real rental price of capital.2. a. To find the amount of output produced, substitute the given values for labor and land into the production function:Y = 1000.51000.5 = 100.b. According to the text, the formulas for the marginal p
24、roduct of labor and the marginal product of capital (land) are:MPL = (1 )AKL.MPK = AK1L1.Chapter 3National Income: Where It Comes From and Where It Goes 11In this problem, is 0.5 and A is 1. Substitute in the given values for labor and land to find the marginal product of labor is 0.5 and marginal p
25、roduct of capital (land) is 0.5. We know that the real wage equals the marginal product of labor and the real rental price of land equals the marginal product of capital (land).c. Labors share of the output is given by the marginal product of labor times the quantity of labor, or 50.d. The new level
26、 of output is 70.71.e. The new wage is 0.71. The new rental price of land is 0.35.f. Labor now receives 35.36.3. 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 dou
27、ble the amounts of capital and labor output increases by less than double, then the production function has decreasing returns to scale. 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 f
28、unction 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 the amount of capital and labor increases the output by more than double, then the production function has increasing returns
29、 to scale. This may happen if specialization of labor becomes greater as the population grows. For example, if only 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. But if many workers build a car, th
30、en each one can specialize in a particular task and become more productive.4. a. A CobbDouglas production function has the form Y = AKL1. The text showed that the marginal products for the CobbDouglas production function are:MPL = (1 )Y/L.MPK = Y/K.Competitive profit-maximizing firms hire labor unti
31、l its marginal product equals the real wage, and hire capital until its marginal product equals the real rental rate. Using these facts and the above marginal products for the CobbDouglas production function, we find:W/P = MPL = (1 )Y/L.R/P = MPK = Y/K.Rewriting this:(W/P)L = MPL L = (1 )Y.(R/P)K =
32、MPK K = Y.Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively. Given that the value of = 0.3, then the above formulas indicate that labor receives 70 percent of total output (or income) and capital receives 30 percent of total output (or income).b. To de
33、termine what happens to total output when the labor force increases by 10 percent, consider the formula for the CobbDouglas production function:Y = AKL1.Chapter 3National Income: Where It Comes From and Where It Goes 12Let Y1 equal the initial value of output and Y2 equal final output. We know that
34、= 0.3. We also know that labor L increases by 10 percent:Y1 = AK0.3L0.7.Y2 = AK0.3(1.1L)0.7.Note that we multiplied L by 1.1 to reflect the 10-percent increase in the labor force.To calculate the percentage change in output, divide Y2 by Y1: Y21AK0.31.L0.70.3.7.10.7.069.That is, output increases by
35、6.9 percent.To determine how the increase in the labor force affects the rental price of capital, consider the formula for the real rental price of capital R/P:R/P = MPK = AK1L1.We know that = 0.3. We also know that labor (L) increases by 10 percent. Let (R/P)1 equal the initial value of the rental
36、price of capital, and let (R/P)2 equal the final rental price of capital after the labor force increases by 10 percent. To find (R/P)2, multiply L by 1.1 to reflect the 10-percent increase in the labor force:(R/P)1 = 0.3AK0.7L0.7.(R/P)2 = 0.3AK0.7(1.1L)0.7.The rental price increases by the ratio R/P
37、2/10.3AK0.71.L0.7.0.7.10.7.069So the rental price increases by 6.9 percent. To determine how the increase in the labor force affects the real wage, consider the formula for the real wage W/P:W/P = MPL = (1 )AKL.We know that = 0.3. We also know that labor (L) increases by 10 percent. Let (W/P)1 equal
38、 the initial value of the real wage, and let (W/P)2 equal the final value of the real wage. To find (W/P)2, multiply L by 1.1 to reflect the 10-percent increase in the labor force:(W/P)1 = (1 0.3)AK0.3L0.3.(W/P)2 = (1 0.3)AK0.3(1.1L)0.3.To calculate the percentage change in the real wage, divide (W/
39、P)2 by (W/P)1:Chapter 3National Income: Where It Comes From and Where It Goes 13W/P2/10.3AK0.31.L0.31.0.30.3.0.30.972That is, the real wage falls by 2.8 percent.c. We can use the same logic as in part (b) to setY1 = AK0.3L0.7.Y2 = A(1.1K)0.3L0.7.Therefore, we have: Y21A1.K0.3L0.70.3.7.10.3.029This e
40、quation shows that output increases by about 3 percent. Notice that 0.5 means that proportional increases to capital will increase output by less than the same proportional increase to labor.Again using the same logic as in part (b) for the change in the real rental price of capital: R/P2/10.3A1.K0.
41、7L0.7.0.7.10.70.935The real rental price of capital falls by 6.5 percent because there are diminishing returns to capital; that is, when capital increases, its marginal product falls.Finally, the change in the real wage is: W/P2/10.7A1.K0.3L0.3.0.30.3.10.3.029Hence, real wages increase by 2.9 percen
42、t because the added capital increases the marginal productivity of the existing workers. (Notice that the wage and output have both increased by the same amount, leaving the labor share unchangeda feature of CobbDouglas technologies.)d. Using the same formula, we find that the change in output is: Y
43、21.1AK0.3L.70.3.7.Chapter 3National Income: Where It Comes From and Where It Goes 14This equation shows that output increases by 10 percent. Similarly, the rental price of capital and the real wage also increase by 10 percent: R/P2/10.31.AK0.7L.0.7. W/P2/10.71.AK0.3L0.3.0.30.3.5. Labor income is def
44、ined as WPLPLabors share of income is defined as WLP/YWLPFor example, if this ratio is about constant at a value of 0.7, then the value of W/P = 0.7*Y/L. This means that the real wage is roughly proportional to labor productivity. Hence, any trend in labor productivity must be matched by an equal tr
45、end in real wages. Otherwise, labors share would deviate from 0.7. Thus, the first fact (a constant labor share) implies the second fact (the trend in real wages closely tracks the trend in labor productivity).6. a. Nominal wages are measured as dollars per hour worked. Prices are measured as dollar
46、s per unit produced (either a haircut or a unit of farm output). Marginal productivity is measured as units of output produced per hour worked.b. According to the neoclassical theory, technical progress that increases the marginal product of farmers causes their real wage to rise. The real wage for
47、farmers is measured as units of farm output per hour worked. The real wage is W/PF, and this is equal to ($/hour worked)/($/unit of farm output).c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The real wage for barbers is measured as haircuts per hour work
48、ed. The real wage is W/PB, and this is equal to ($/hour worked)/($/haircut).d. If workers can move freely between being farmers and being barbers, then they must be paid the same wage W in each sector.e. 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. We know that W/P = MPL so that W = P MPL. This means that PFMPLF = PHMPLB, given that the nominal wages are the sa
