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 A firm has production function 0 if 1 1 where p > 0 is a parameter

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 A firm has production function 0 if 1 1 where p > 0 is a parameter. The price of labor is w > 0) and the price of capital is v > 0. The price of the firm's output is p > 0. (e) Calculate the firm's marginal cost function MC(w,v,9) and its average cost func- tion AC(w,v,9) (for q> 0). (f) Suppose p= 1/2. Make a diagram where you draw both MC(w,v,9) and AC(w, v,q) (in the same diagram) as functions of q. (8) Discuss how the specific nature of the production function f(1,k) above explains the shape of the AC(W, 0, 9) curve that you drew in the (f) part. (h) Suppose p= 1/2. Obtain the firm's supply function q(p, w, v). Hint: Use the cost functions you calculated above and consider the problem max 20 pq - C(w, v,9). (i) Suppose p=1. Obtain the firm's supply function (p, w, v). Hint: Use the cost functions you calculated above and consider the problem max. 20 P9 - C(w, v,q).