78 pts. 1. Consider a monopolist who produces one good and is a price-taker in the factor markets for unskilled labor L>0 and capital K>0, paying the minimum wage w>0 per hour of unskilled la- bor and renting capital at the rate v>0 per hour. Total revenue is a C(2) function R() of capital and labor, with value R(K,L). The owner of the firm is asserted to be a profit maximizer and thus faces the following short-run profit maximization problem: def (K,v,w) max (L; K,v,w) def R(L,K)wL vK {r(L; / WL-VK}. Assume that at (K,v,w)=(K,v,w), L = L is a solution of the first-order necessary condition and that the second-order sufficient holds at the aforesaid point. 6 pts. (a) At (K,v,w)=(K,v,w), does L = L solve the maximization problem? Explain why or why not. What additional assumption would you make, if any, in order to conclude that L= L is a locally unique solution? 6 pts. (b) Derive the FONC and provide an economic interpretation of it. Is the marginal revenue product of unskilled labor positive at the profit-maximizing solution? Explain.