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A competitive producer has a production function given by 9 = f (k, l) = 8/3/4/1/4 where & denotes the quantity of capital, and / denotes labor hours. The factor prices are v, and w. 3 (a) Write down the producer's cost minimization problem and find the con- tingent factor demands and cost function. (b) From now on assume that the factor prices are fixed at w = $16, and v = $0.25. Suppose that, in the short run, the capital stock is fixed at k = 81. 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 func- tions