finding rate. (a) [2 points] Solve for the steady-state unemployment rate. Explain what happens to the steady state unemployment rate and the duration of unemployment if the job separation rate s increase Suppose that the matching function is such that the job finding rate is given by f(0, ) = 10,/2, where Of = Ut/u, is the labor market tightness and U, is the vacancy rate at time t. Coefficient A captures the efficiency of the matching process. (b) [2 points] Using the steady-state unemployment rate and the functional form for f(0), derive the Beveridge curve (i.e., express U, in terms of ut) and explain how U, and u, are related. (c) [2 points] Suppose that there is free entry, i.e., firms post vacancies until the expected value o posting a vacancy is equal to its cost: q(0, ) J = c. Here, J is the value of a filled job and c is the cost of posting a vacancy. Solve for the equilibrium labor market tightness 0" and the steady-stat unemployment and vacancy rates. Note: Given the functional form for f(0) above, you should be able to find the functional form for q(0). Now suppose that J is explicitly determined by firm profits (rather than taken as given as before). Assume that the revenue generated by a worker-firm match is one and wage paid to the worker i inversely proportional to the unemployment rate and is given by w(u) = 1/(1 + u). Thus, we ca express firm value as J(u) = 1 - w(u) = 1 - 1/(1 + u). (d) [2 points] Use the free-entry condition and the Beveridge curve to find the equilibrium unemployment rate in terms of model parameters for this new case where J(u) depends on u. (e) [2 points] How does the equilibrium unemployment rate depend on the matching efficiency parameter A? How does wage depend on the matching efficiency parameter A? Provide intuition for your answers