(1) A rm has a production function f (9:) = [931562933]? (a) Does f have increasing returns to scale? Does f have decreasing returns to scale? (b) Find the long run cost function LC (111,102, w3,q) and the conditional input demand function x(w,q) for any output q 2 0. Assume that an = 1, W2 = 2, 1113 = 4, and let LC(q) = LC(1, 2, 4,q). What are the correSponding LMC(q) and LAC(q) functions? (c) Now assume that in the short run, the rm cannot adjust input 1 because it has signed a long term contract that commits it to purchase x1 = 100 at a price wl = 1. Find the short run cost function SC(w2, mg, q). Again, assume that 11.12 = 2 and 103 = 4, and let SC(q) = 80(2, 4, q). What are the corresponding short run xed cost, variable cost, marginal cost and average cost functions? Find the quantity q for which SAC (q) is minimized