question archive Suppose that the law of motion for unemployment is given by u+1 – uy = s(1 – u) - fut, where u, denotes the unemployment rate at time t, s is the job separation rate and f is the job finding rate
Suppose that the law of motion for unemployment is given by u+1 – uy = s(1 – u) - fut, where u, denotes the unemployment rate at time t, s is the job separation rate and f is the job finding rate
Subject:BusinessPrice: Bought3
Suppose that the law of motion for unemployment is given by u+1 – uy = s(1 – u) - fut, where u, denotes the unemployment rate at time t, s is the job separation rate and f is the job 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 increases. Suppose that the matching function is such that the job finding rate is given by f(0) = AO!!?, where 0, = vlu, is the labor market tightness and v; 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 V, in terms of up) and explain how y, and u, are related. (c) [2 points] Suppose that there is free entry, i.e., firms post vacancies until the expected value of posting a vacancy is equal to its cost: g(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-state unemployment and vacancy rates. Note: Given the functional form for f(e) above, you should be able to find the functional form for qe). Now suppose that I 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 is inversely proportional to the unemployment rate and is given by w(u) = 1/(1 + u). Thus, we can 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.
