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) 0.6U1/21/2 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?