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Gregory Mankiw, Macroeconomics (10th)
Chapter 3 - Problems and Applications #1,3,7

PROBLEMS AND APPLICATIONS 1. Use the neoclassical theory of distribution to predict the impact on the real wage and the real rental price of capital of each of the following events: a. A wave of immigration increases the labor force b. An earthquake destroys some of the capital c. A technological advance improves the d. High inflation doubles the prices of all factors stock production function. and outputs in the economy.
3. If a 10 percent increase in both capital and labor causes output to increase by less than 10 percent, the production function is said to exhibit decreasing returns to scale. If it causes output to increase by more than 10 percent, the production function is said to exhibit increasing returns to scale. Why might a production
function exhibit decreasing or increasing returns to scale
7. (This problem requires the use of calculus.) Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is a. Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? b. Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital? c. What is the income share paid to labor What is the income share paid to human capital? In the national income accounts of this economy, what share of total income do you think workers would appear to receive? (Hint Consider where the return to human capital shows up.)
d. An unskilled worker earns the marginal product of labor, whereas a skilled worker earns the marginal product of labor plus the marginal product of human capital. Using your answers to parts (a) and (b), find the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain. e. Some people advocate government funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate?
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Answer #1

ANSWER-1)

a. Solution: Real wage decreases.

Explanation: As per the neoclassical theory of distribution, the real wage equals the marginal product of labor. Due to the diminishing returns to labor, a rise in the labor force causes the marginal product of labor to decline. Therefore, the real wage decreases. As now the capital is relatively scarcer, it becomes more productive thus demand for capital by firms increases. Graph-1

b. Solution: Real rental price increases.

Explanation: As per the neoclassical theory of distribution, real rental price equals the marginal product of capital. When an earthquake destroys some of the capital stock (however miraculously does not kill anyone and reduces the labor force), the marginal product of capital increases and, therefore, the real rental price increases. As now the labor is relatively more scarce, it becomes less productive thus the demand for labor by firms increases. Graph-2

c. Solution: Real wage and real rental price both increases.

Explanation: Due to the technological advancement there will be an improved production function, thus will increase the marginal products of both capital and labor. Therefore the real wage as well as the real rental price increases due to increases in demand for both factors. Graph-3

d. Solution: They remain unchanged

Explanation: High inflation doubles the prices of all factors as well as outputs in the economy as a result there will be no change


GRAPH-1 D 13 13 GRAPH-:2 ID GRAPH-3 1) 1)

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