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3. Assume that there are a number of unemployed workers (U) looking for jobs, and a number of firms posting vacancies (V). Hires are formed according to the matching function H(U, V) = 0.6U1/2V1/2 Each period, an employed worker (E) loses their job with 2% probability. For the purposes of this question, you can allow firms to hire a fraction of a worker (so if you get decimals for unemployment it's ok round to the nearest tenth). (a) Assume there are currently 100,000 employed workers, 10,000 unemployed workers, and 6400 vacancies posted. Given these numbers, how many matches would we expect to be created each period? What is the probability that any given worker finds a job this period? What is the probability that any given vacancy will be filled this period? (b) Assume that vacancies adjust each period to keep the job finding rate you found in the previous question constant. What will be the level of employment and unemployment in period 2? Period 3? What happens to the unemployment rate in each period? (c) Calculate the equilibrium steady state unemployment rate given the constant match proba bility. (d) Now assume that labor market tightness is determined endogenously, but the wage is taken as given. Assume a worker can produce 10 units of output each period and the wage is 9. The cost of posting a vacancy is 30. If tightness is equal to its value in part a (so the match probability is equal to the probability you calculated in part a), would it be profitable for a firm to create a new vacancy? (e) Assuming free entry, how many vacancies will be created in the first period (i.e. when there are still 10,000 unemployed workers). What are the new match probabilities at the equilibrium labor market tightness? (f) At the new match probabilities, what will happen to unemployment (and the unemployment rate) in periods 2 and 3? What is the new steady state unemployment rate? (g) Now assume that the wage is endogenous as well and that bargaining power is equal for workers and firms (/8 = 0.5). Also assume that the worker can get an outside option of b=6 units of benefit from remaining unemployed (To summarize, we are given A = 0.6, oz 2 0.5, A = 0.02, y = 10, n = 30, = 0.5, b = 6). Find the equilibrium wage, labor market tightness, and unemployment rate (note: there are multiple equilibria - choose the one where the wage is less than the worker's production. You do not need to solve by hand - feel free to use Wolfram Alpha or equivalent especially in solving for 0) (h) Show graphically what would happen to wages, labor market tightness, and the unemploy- ment rate given the following shocks (you do not need to solve for the exact numbers - they don't come out nicely). You should also show the transition of the unemployment rate over time. The graphs do not need to be perfectly to scale. i. An increase in the bargaining power of workers 3 ii. An increase in matching efficiency A iii. An increase in the job separation rate A