Problem 2 (30 pts) (Explain your answers!) Firm A has the production function f(l, k) = 21+2k where I is units of labor, with price w = 2 and k is capital, with price r = 1. The output price is p. (a) Find the marginal product of labor. Is it diminishing? l (b) What is the maximum output which firm A can produce from 1 = 1 and k = 4? Find the slope of A's isoquant at 1 and k = 4. l = (c) Show that firm A's production function has decreasing returns to scale. (d) Suppose that, in the short run, capital is fixed at k = 16. Find the firm's input demand function for labor and its maximum short-run profit for any p > 0. (e) Write down and solve the firm's long run profit maximization problem for any p > 0. (f) Use your results in (d) and (e) to prove that the firm's long run profits are never smaller than its short run profits. Explain why.