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Suppose that the production function is q = F (L, K) = (KL)1'3. The output and input prices are (p, w, r) = (1, 1, 1). ** Part a (5 marks) Derive the long-run cost function C(q). ** Part b (7 marks) Solve the longrun profit maximization problem directly: max1*F(L,K)1*L1*K K,L and find the profitmaximizing output. [Hintz there are two first-order conditions, and you need to solve them jointly] ** Part c (8 marks) As an alternative to Part b, solve for the profit-maximizing output using the long-run cost function you derived in Part a