In a competitive labor market there are three types of workers present in equal proportions, whose productivities and reservation utilities are (a1, 1) = (1, 1/2), (a2, U2) = (2, 1) and (, U) = (3, 22/10) respectively. A worker's productivity is his private information. Before entering the market each worker chooses his level of education, which is observed by the firms. The cost of acquiring a level of education y for a worker of type i is equal to Ci (y) = y/a;. The (expected) revenue for a firm is equal to the productivity of its labor force, i.e. X L1, L2, L3) = a1L1 + a212 + a3L3, where Li is the number of workers of type i employed by the firm (Hint: What does this tell us about the payments of workers in this competitive labor market?) i. Determine whether there is a fully separating equilibrium, i.e. an equilibrium in which each type chooses a different level of education, and if so identify among these equlibria the most favorable to the workers. (Hint: start by arguing that y1 = 0, and find the levels of education 0 < 2 < that will form an equilibrium. Make explicit the beliefs of the firm.) ii. Find, if possible, a semi-separating equilibrium in which y1 = Y2 = 0, and y > 0, i.e. in which the firm treats differently only the type 3 workers. Compute the most favorable such equilibrium for the workers of type 3. Write explicitly the beliefs of the company. Compare the workers' utilities with those of part (i)