Consider a modification of MaCall's (1970) search model. As in the original model, an unemployed worker receives a wage offer, w, drawn from an i.i.d. distribution F(w) with support [0,B]. (Assume that the c.d.f, F(w), and its associated density function, dF(w) are continuous.) If it rejects the offer it receives c in the current period in the form of unemployment insurance. In contrast to the original model, the worker can be fired from his job. Specifically, at the end of each period an employed worker faces probability 0< <1 of being fired. The probability of being fired is independent of how long a worker has worked. It can also quit his job, which means it earns the unemployment compensation, c, in the period. a. Write down Bellman's Functional Equation for a currently unemployed worker who has offer, w, in hand (or a worker who did not lose his job at the end of last period). (Assume utility is linear in period income, which is w if working and c if not working. The discount rate is < 1)