find solutions;

Problem 3.1: 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 stock.

C. A technological advance improves the production function.

Problem 3.2: 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 increasing or decreasing

returns to scale?

Problem 3.3: Suppose that an economy's production function is Cobb-Douglas with

parameter alpha=0.3. One way to solve B.-D., assume numerical values, e.g.: Assume A=1,

K=1, L0=1 and L1=1.1.

3.3A. What fractions of income do capital and labor receive?

3.3B. Suppose that immigration raises the labor force by 10 percent. What happens to total

output (in percent)? The rental price of capital? The real wage?

One way to solve B., assume A=1, K=1, L0=1 and L1=1.1.

3.3C. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What

happens to total output (in percent)? The rental price of capital? The real wage?

3.3D. Suppose that a technological advance raises the value of the parameter A by 10 percent.

What happens to total output (in percent)? The rental price of capital? The real wage?

Problem 3.4.: Empirically the trend in the real wage closely tracks the trend in labor

productivity. Explain why?

Problem 3.5. A. Over the past century, the productivity of farmers has risen substantially

because of technological progress. According to the neoclassical theory, what should have

happened to their real wage? B. In what units is the real wage in part (a) measured? C. Over

the same period, the productivity of barbers has remained constant. What should have

happened to their real wage? D. In what units is the real wage in part (c) measured? E.

Suppose workers can move freely between farmers and being barbers. What does this

mobility imply for the wages of farmers and barbers? F.

imply for the price of haircuts relative to the price of food? G. Who benefits from

technological progress in farming - farmers or barbers?

Problem 3.6.: (Harder) 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:

1/ 3 1/ 3 1/3 Y K L H =

Problem 3.6A. 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?

Problem 3.6B. 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?

Problem 3.7C. 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.)

Problem 3.7D. An unskilled workers 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 (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.

Problem 3.7E. 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. Summit answers to the preceding questions shed light on this debate?