5. (15 pts.) There are two types of workers, high-ability and low-ability workers. There are 6 share of high-ability workers, and 1 6 of low-ability workers. The firms are competitive and pay their workers according to the worker's marginal productivities. The high-ability workers can attend college and graduate at the cost of c, and their marginal revenue product is wh, while low-ability workers cannot graduate college and their marginal revenue product is w. The firms cannot differentiate the workers' types. a) Find the conditions that allow separating equilibria to exist. (3 pts.) b) Find the conditions that allow pooling equilibria to exist, and list what each worker does and the wage he receives in each equilibrium. (3 pts.) c) Find the conditions that allow hybrid equilibria to exist (where some workers pool across types, and some workers separate), and list what each worker does and wage he receives. (3 pts.) d) What is the maximum tuition colieges can charge such that there are enrolling students? (3 pts.) e) What is the tuition price that maximizes the colleges' revenue and what is the economic intuition behind it? (3 pts.)