Suppose that there are 100 identical firms, each with the following technology: f = K^1/4 L^1/2. Suppose also that in the short run K =1,with r = 1, and P = 4. For the short run:

(a) If we assume that each firm is a profit maximizer, what is the problem that each firm solves?

(b) Calculate the MPL and each firm's demand for labor.

(c) Calculate each firm’s profits.

(d) Calculate the market demand of labor. Suppose that after considering basic activities required for life, there are 200 hours in a month which an individual can distribute between leisure and hours worked, that is 200 =h+l where his leisure and l is labor. Suppose there are 1000 identical individuals, each with the same preferences:U(h,x) = x^1/2 +h^1/2 over leisure and consumption x. Normalize the prize of consumption x to 1.

(e) State the individual budget restriction.

(f) State the individual’s problem and the first order conditions.

(g) If w=1, find the optimum of leisure h and consumption x.

(h) Find the individual supply of l (do not assume w =1).

(i) Find the market supply of labor. Assume that the amount of labor(hours worked) is traded in a competitive market.

(j) What will be the equilibrium wage rate w?

(k) What will be the equilibrium level of labor?