3 Problem Consider the labor market model that was described in class. A worker is characterized by their type 0, which is uniformly distributed on the interval [0, 1]. A worker with type 0 produces an output worth 0 for the firm that employs them. A worker with ability 0 can produce and earn r(0) at their outside option. There is a competitive labor market in which a certain wage is paid, and all potential employers (firms) are risk neutral. Suppose that the outside option of workers is r(0) = r 1/2 for all 0. Show that this labor market does not have an equilibrium in which firms pay workers a wage w 2 T