5. Suppose some workers are capable and others are extraordinary. Firms are willing to pay capable workers a salary of $12,000 and extraordinary workers a salary of $15,000. Workers know if they are capable or extraordinary but firms do not—that is, ability is private information. It would cost capable persons $6,000 to earn a college degree, but it would cost extraordinary persons just $2,000 to earn a college degree since they can finish their education much faster. Show that in equilibrium in this labor market (i) extraordinary people go to college but capable people do not, and (ii) firms pay college graduates $15,000 and high school graduates $12,000.