劳动经济学练习1

劳动经济学练习1

1.Suppose that an economy has the Phillips curve: 10.5u0.06

(1) What is the natural rate of unemployment?

(2) Graph the short-run and long-run relationships between inflation and unemployment.

(3) How much cyclical unemployment is necessary to reduce inflation by 5 percentage points? Using Okun’s law, compute the sacrifice ratio. The sacrifice ratio is the accumulated loss in output that results when the central bank lowers its target for inflation by 1 percentage point.

(4) Inflation is running at 10 percent. The Fed wants to reduce it to 5 percent. Give two scenarios that will achieve that goal.

2. Consider a Cobb–Douglas production function with three inputs. Kis capital (the number of machines), Lis labor (the number of workers), andHis human capital (the number of college degrees among the workers). The

131313production function isYKLH.

(1) 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?

(2) 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?

(3) 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?

(4) 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 (1) and (2), 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.

(5) 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?

3. Two countries, Richland and Poorland, are described by the Solow growth

ALFK,LKmodel. They have the same Cobb–Douglas production function,

1,

but with different quantities of capital and labor. Richland saves 32 percent of its income, while Poorland saves 10 percent. Richland has population growth of 1 percent per year, while Poorland has population growth of 3 percent. (The numbers in this problem are chosen to be approximately realistic descriptions of

rich and poor nations.) Both nations have technological progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year.

(1) What is the per-worker production functionfk?

(2) Solve for the ratio of Richland’s steady-state income per worker to Poorland’s. (Hint: The parameterwill play a role in your answer.)

(3) If the Cobb–Douglas parametertakes the conventional value of about 1/3, how much higher should income per worker be in Richland compared to Poorland?

(4) Income per worker in Richland is actually 16 times income per worker in Poorland. Can you explain this fact by changing the value of the parameter? What must it be? Can you think of any way of justifying such a value for this parameter? How else might you explain the large difference in income between Richland and Poorland?