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 a capable person $6,000 to earn a college degree but it would cost an extraordinary person 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 .

If an extraordinary person goes to college her salary would be $15,000, she would pay $2,000 for her education, and so she would be left with $15,000 – $2,000 = $13,000 . Since her salary would be just $12,000 if she did not go to college she is better off if she completes her education. If a capable person goes to college his salary would also be $15,000 but he would pay $6,000 for his education, and so he would be left with $15,000 – $6,000 = $9,000 . Since his salary would be $12,000 if he did not go to college, he would be worse off if he completes his education. Therefore, given these wages, only extraordinary people go to college. Firms know college graduates are extraordinary and high school graduates are capable and are willing to pay college graduates a salary of $15,000 .
You should see the similarities between this problem and Problem 4 . Some workers and some cars are peaches and some are lemons. A college degree in this problem plays the same role as the certificate in the used car market problem.