This question pertains to signaling in the labour market. Suppose students come in two types: highly competent and less competent. Both types of students can get university degree, but for the less competent type getting a university degree takes extra time and effort:

Highly competent students have to spend N years to graduate from university.

Less competent students take three times as long.

Students with university degrees can earn 81 (thousand dollars) each year working, whereas without a degree they can earn only 36 (thousand dollars) each year. Most companies would not hire them.

Each type of student gets a payoff equal to , where S is the salary measured in thousands of dollars and N is the number of years spent getting a university degree.

(a) What is the range of values for N for which a highly competent student will choose to get a university degree?

(b) What is the range of values for N for which a less competent student will choose to get a university degree?

(c) What is the range of values of N for which a highly competent student will choose to get a university degree to signal their competence, but a less competent student will not?