Consider an economy with the following Cobb–Douglas production function:
Y = K1/3L2/3.
The economy has 1,000 units of capital and a labour force of 1,000 workers.
a. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock.
b. If the real wage can adjust to equilibrate labour supply and labour demand, what is the real wage? In this equilibrium, what are employment, output, and the total amount earned by workers?
c. Now suppose that the government, concerned about the welfare of the working class, passes a law requiring firms to pay workers a real wage of 1 unit of out-put. How does this wage compare to the equilibrium wage?
d. The government 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 the government 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?