Hello I need answers in details please

4. (20) Consider a version of the continuous time Mortensen-Pissarides labor market model with match- specific productivity. Labor force is normalized to 1, and there is a large measure of firms that can enter the market and search for workers. A firm can enter the labor market with exactly one vacancy, and the total measure of vacancies v will be determined endogenously by free entry. A matching function, m = m(u, v), brings together unemployed workers and vacant firms; m is increasing in both arguments and exhibits CRS. As is standard, let 6 = v/u denote the market tightness. Unlike the baseline model, here not all meetings result in a match. When a firm and an unemployed worker first meet, they draw a match-specific productivity a from a cdf F(2), with support in the set (0, 1). The random draws of a are rid across matches and time. Upon observing the specific realization of z, the firm and worker decide whether they will form a productive match, which can produce a units of the numeraire good per unit of time. Alternatively (if the realization of r is too low), they may decide that it is not worth forming a match. In this case, the worker stays unemployed, and the firm stays in the large pool of firms that can potentially search for workers. If a match is indeed formed, the two parties negotiate over the wage, which will be contingent on the match-specific productivity, z. In the negotiation process, let # E (0, 1) denote the worker's bargaining power. Crucially, a productive match keeps its idiosyncratic productivity a for as long as it is active/alive. Existing productive matches are terminated at an exogenous Poisson rate, A > 0. To close the model, we will make a few more standard assumptions. While a firm is searching for a worker it has to pay a recruiting cost, c > 0, per unit of time. All agents discount future at the rate r > 0, and all unemployed workers enjoy a benefit > > 0 per unit of time. We further impose that z 0,= (0) = 1, lim =(M/P) =0. The function f (ky) has standard properties. The money supply in this economy is growing at the constant rate a > 0 and capital depreciates at the constant rate of 6