4) Derive the profit function for a perfectly competitive firm if its production function is given by f(L,K) = LK2. a) Does the chosen combination of L and K profit maximizing? Verify using the second order conditions. b) Does your answer differ from that in 1 above, why or why not? 5) Let's say the production function is f(K,L) = f(k, () = 1.1. Also, to simplify your expressions you may assume w = 4 and r = 1. Let's assume that in the short run the capital is fixed at k = 4. a) Derive the short run and the long run cost function for this firm. b What are the short run MC, VC and TC functions. C) What is the firm's short run supply curve? (hint: it will be the portion of MC above minimum AVC). d) What is the efficient scale of production in the short run? (hint: this is minimum point of ATC) e) What are the long run conditional demand for & and /. What is long run ATC function? Find the minimum point of LR ATC. (hint: what is the returns to scale for this function?)