5. Consider an economy with the following Cobb–

Douglas production function:

Y = K1/3L2/3.

The economy has 1,000 units of capital and a labor force of 1,000 workers.

a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review the appendix to Chapter 3.)

b. If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employment, output, and the total amount earned by workers?

c. Now suppose that Congress, concerned about the welfare of the working class, passes a law requiring firms to pay workers a real wage of 1 unit of output. How does this wage compare to the equilibrium wage?

d. Congress cannot dictate how many workers firms hire at the mandated wage. Given this fact, what are the effects of this law? Specifi- 6. Suppose that a country experiences a reduction in productivity—that is, an adverse shock to the production function.

a. What happens to the labor demand curve?

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b. How would this change in productivity affect the labor market—that is, employment, unemployment, and real wages—if the labor market were always in equilibrium?

c. How would this change in productivity affect the labor market if unions prevented real wages from falling?