3. (25) Search frictions and the gender gap. Consider the following version of the search model of the labor market by Burdett and Mortensen (1998). There are two labor markets, one for men (m) and one for women (f). On one side of the m labor market, there is a continuum of male workers with measure 1. Each worker has preferences described by the lifetime utility 3 ;- 5c;, where 3 denotes the worker's discount factor and ; denotes the worker's consumption in period , which is equal to b it the worker is unemploved and w if the worker 1s employed. On the other side of the m labor market, there is a continuum of firms. Each firm maximizes the present value of profits discounted at the factor 3. Assume 5 = 1. Workers and firms come together through a decentralized process of search. In particular, a worker finds a firm with probability Al when unemployed and A" when employved. Assume A = A" = A,,. When a worker meets a firm, it chserves the wage of the firm and decicdles whether to join the firm or not. It he does, he produces y units of output per period until he either finds a better job or he is forced into unemployment (an event which happens with probability per period). The labor market f is the same as the labor market m, except that A7 = Af = Ay with Ap