Labour Market Flows Consider the labour market model studied in class. Recall that the law of motion for unemployment is given by +1 us(1) fur, = where ut denotes the unemployment rate in period t, s is the job separation rate and f is the job finding rate. Assume that the labour force is normalized to one and hence the unemployment rate is equal to the number of unemployed workers. The job separation rate equals s = 0.03 per period. Suppose that the number of new worker-firm matches per period is given by the following function m(u, v) = 0.5uv A. (2 points) Derive formulas for the job finding rate f for workers and the vacancy filling rate q for firms in terms of labour market tightness 0=v/u. Is the firm vacancy filling rate q increasing or decreasing in market tightness? Provide economic intuition for your answer. B. (3 points) Suppose that the value of a filled job is J = 4 and the cost of posting a vacancy is c=2. What is the equilibrium labour market tightness 0? Given this value for market tightness, calculate the job finding rate f and the steady-state unemployment rate u. C. (3 points) Suppose the economy enters a recession and the job separation rate increases to = 0.05. Calculate the new equilibrium values of unemployment and vacancies. Provide = 8 economic intuition for your answers. D. (2 points) Evaluate the claim that "recessions are caused by high job separation rates" considering your answers to part (C). [Hint: Think about the movements in market tightness, unemployment, and vacancies and their cross-correlation when the job separation increases. Are the implications consistent with the empirical Beveridge curve we saw in class?]