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Question 14] A competitive producer has a production function given by q =ftk. I) = 319/312\". where k denotes the quantity of capital, and I denotes labor hours. The factor prices are v, and w. [a] Write down the producer's cost minimization problem and nd the contingent factor demands and cost function. (h) From now on assume that the factor prices are fixed at w = $15, and v = $0.20. Suppose that, in the short run, the capital stock is xed at k = 125. Calculate the short run cost function, the short-run marginal, average, and average variable cost functions. (c) Plot the short-run marginal, average, and average variable cost functions. (d) Suppose now that, in the short run, the capital stock is xed at E. Calculate the short run cost function as a function of q and I}. (e) On one diagram, plot the short run cost functions for I? = 27, 64-, 125, 216 and the long run cost function [for w = 15 and v = 0.2). Show that the long run cost function envelopes the short run cost functions