Suppose that the matching function is em(Q, A) = eQ/?A/2, where the matching efficiency e = .7, the supply curve is P(Q) = 1+Q, the productivity z = 20, the cost of posting a vacancy k = 3, and the worker's bargaining power is a = 2/3. (a) (15 points) Suppose that the UI benefit is b = 2. Find the equilibrium values for the wage w, labor market tightness j, labor force Q, unemployment rate u, vacancy rate v, number of firms A, total number of matches M, and total output Y. (b) (10 points) Suppose the UI benefit increases from b = 2 to b = 8. Find the new values for w, j, Q, u, v, A, M, and Y. Discuss your results. (c) (10 points) Are consumers who choose to join the labor force better or worse off as a result of the increase in the unemployment benefit? Explain your answer intuitively.