Consider an economy with the following Cobb–Douglas production function: = 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.

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 one 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? Specifically, what happens to employment, output,

and the total amount earned by workers?

e. Will Congress succeed in its goal of helping the working class? Explain.

f. Do you think that this analysis provides a good way of thinking about a minimum wage

law? Why or why not?​