Question

Consider an economy with the following Cobb–Douglas production function: Y=5K^1/3L^2/3.

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

b. The economy has 27,000 units of capital and a labor force of 1,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage, total output, and the total amount earned by workers.

c. Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 10 percent above the equilibrium wage you derived in part (b). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the effects of this law? Specifically, calculate what happens to the real wage, employment, output, and the total amount earned by workers.

d. Does Congress succeed in its goal of helping the working class? Explain.

e. Do you think that this analysis provides a good way of thinking about a minimumwage law? Why or why not?

Answer 1

d) The policy redistributes output from the 249 workers who became involuntarily unemployed to the 751 workers who get paid more than before.

Total benefits to the workers also falls from 10000 to 8264.4 so congress has failed in its goal of helping the working class.

e) This problem focus on the analysis of minimum wage laws which have the following effects- they raise the wage for some workers while downward sloping demand reduce total number of jobs.

If the labor demand was less elastic than the one in this problem,then the loss of employment may be smaller and the change in worker income might be positive.