We usually assume that firms were price-takers in the labor market.

Problem 3: We usually assume that firms were price-takers in the labor market. Here, we relax this assumption and instead allow firms to take into account the fact that they have monopsony power (i.e., they are single buyers of labor in this market; think about a mining town where there is only one employer). A flexible-price firm which maximizes profits is thus maximizing the following problem: max P. (i)Y. (i) - W.(D)N.(i) subject to the following constraints: Ye(i) = AtNt(i) Pt(i) E Ye(i) = Yt Pt We(i) = P-NY (i)Yge-ItNote that the difference between this problem and our standard assumptions is that the firm is not taking the nominal wage as given here, but rather takes the labor supply condition directly into account in its maximization problem. a) Show that the optimal price for a flexible price firm is given by 1 E Pt (i) = Pt (1 + ( )ypt -(1+9) -gt 1+EQ b) Assume all firms have flexible prices and firms. Show that the natural level of GDP is now given by 1 1+4egt + (p. Explain intuitively why, as long as o > 0, the natural level of GDP is lower than in the case in which firms are price-takers in the labor market