Suppose that there are 100 identical firms, each with the following technology: f D K1=4L1=2 . Suppose also that in the short run K D 1, with r D 1,and P D 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 D hCl where h is leisure and l is labor. Suppose there are 1000 identical individuals, each with the same preferences: U.h; x/ D x 1=2 C 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 D 1, find the optimum of leisure h and consumption x.
(h) Find the individual supply of l (do not assume w D 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?