Problem 7.1: Search Model. (35 points) Consider the static DMP model we saw in class. Suppose that instead of finding the wage via Nash Bargaining, the government imposes a wage by law, say w. Otherwise, the setup is identical. Workers receive b if they do not match with a firm, firms pay a cost k to post a vacancy. If a firm and a worker match, they produce output worth y. The matching function is given by m(u, j) = uj' (a) If there are j vacancies, what is the probability that a worker gets matched? What is the probability that a firm finds a worker? (b) Calculate the expected profits of a firm, that is, the probability it will find a worker times the profits when it matched with a worker. (c) Use the free entry condition to find the number of vacancies in the economy. (d) Set up the social planners problem and find the efficient number of vacancies. (e) Suppose the social planner can choose w. What wage would they choose