1) Explain why the profit-maximizing level of employment for a firm occurs when the marginal revenue product of labor equals the nominal wage. How can the profit-maximizing condition be expressed in real terms?

2) Define full-employment output. How is full-employment output affected by an increase in labor supply? By a beneficial supply shock?

3) Why is the classical model of the labor market discussed in this chapter not very useful for studying unemployment?

4) Define the following: Labor force, unemployment rate, participation rate, and  employment ratio.

5) The following data gives real GDP, Y, Capital, K, and Labor, N, for the U.S. economy in various years.

Units and sources are the same as in Table 3.1. Assume that the production function is

Y = AK^0.3 N^0.7.

a.    By what percentage did U.S. total factor productivity grow between 1960 and 1970? Between 1970 and 1980? Between 1980 and 2000?

b.    What happened to the marginal product of labor between 1960 and 2000? Calculate the marginal product numerically as the extra output gained by adding 1 million workers in each of the two years. (The data for employment, N, are measured in millions of workers, so an increase of 1 million workers is an increase of 1.0)

6) Acme Widget, Inc., has the following production function.

a.    Find the MPN for each level of employment.

b.    Acme can get &5 for each widget it produces. How many workers will it hire if the nominal wage is $38? If it is $27? If it is $22?

c.    Graph the relationship between Acme’s labor demand and the nominal wage. How does this graph differ from a labor demand curve? Graph Acme’s labor demand curve.

d.    With the nominal wage fixed at $38, the price of widgets doubles from $5 each to $10 each. What happens to Acme’s labor demand and production?

e.    With the nominal wage fixed at $38 and the price of widgets fixed at $5, the introduction of a new automatic widget maker doubles the number of widgets that the same number of workers can produce. What happens to labor demanded and production?

f.     What is the relationship between your answers to part (d) and part (e)? Explain.

7) Consider an economy in which the marginal product of labor MPN is MPN = 309 - 2N, where N is the amount of labor used. The amount of labor supplied, NS, is given by NS = 22 + 12w + 2T, where w is the real wage and T is a lump-sum tax levied on individuals.

a.    Use the concepts of income effect and substitution effect to explain why an increase in lump-sum taxes will increase the amount of labor supplied.

b.    Suppose that T = 35. What are the equilibrium values of employment and the real wage?

c.    With T remaining equal to 35, the government passes minimum-wage legislation that requires firms to pay a real wage greater than or equal to 7. What are the resulting values of employment and the real wage?

8) Suppose that the production function is Y = 9K0.5N0.5. With this production function, the marginal product of labor is MPN = 4.5K0.5N-0.5. The capital stock is K= 25. The labor supply curve is NS = 100[(1 - t)w]2, where w is the real wage rate, t is the tax rate on labor income, and hence (1 - t)w is the after-tax real wage rate.

a.    Assume that the tax rate on labor income, t, equals zero.,  Find the equation of the labor demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after--tax wage income of workers.

b.    Repeat part (a) under the assumption that the tax rate on labor income, t, equals 0.6.

c.    Suppose that a minimum wage of w = 2 is imposed. If the tax rate on labor income, t, equals zero, what are the resulting values of employment and the real wage? Does the introduction of the minimum wage increase the total income of workers, taken as a group?

9) How would each of the following affect Helena Handbasket’s supply of labor?

a.    The value of Helena’s home triples in an unexpectedly hot real estate market.

b.    Originally an unkilled worker, Helena acquires skills that give her access to a higher-paying job. Assume that her preferences about leisure are not affected by the change in jobs.

c.    A temporary income tax surcharge raises the percentage of her income that she must pay in taxes, for the current year only. (Taxes are proportional to income in Helena’s country.)