A barber shop offers haircuts to both students and faculty.Student demand for haircuts is given by pS(QS) = 24− 1QS. Facultydemand for haircuts is given by pF(QF) = 24− 1QF.

Students have more hair than professors (even the youngprofessors), and longer hair costs more to cut. Reflecting thisfact, the barber shop’s total costs are

C(QS,QF)=16QS +10QF
Suppose first that the barber shop can engage in perfect pricediscrimination.

1. (3 pts.) How many students get haircuts (Q∗S )? How many facultyget haircuts (Q∗F )? How much profit will the barber shop make?

2. (3 pts.) Under perfect price discrimination, is each of thesestatements true or false? Briefly explain your reasoning.

   i. Every faculty member with positive willingness to pay ends upgetting a haircut. ii. Among the people who get haircuts, studentspay more than faculty on average.

   iii. The cheapest haircut sold is sold to a faculty member

Now suppose that the barbershop cannot engage in personalizedpricing. However, it is able to offer one price for students and adifferent price for faculty.

c. (3 pts.) Find the monopoly’s profit-maximizing prices p∗S andp∗F under group price discrimination. Which group is charged abigger price markup?

Upset about discriminatory prices, student groups organizeprotests against the barber shop, using the catchy slogan “It’sunfair / to tax our hair!” The protests go viral, and the barbershop reluctantly agrees to charge everybody the same price,regardless of cost.

d. (3 pts.) Compute the market demand curve Q(p), then write thebarber shop’s profits as a function of p. (Be careful with thecosts!) What price will the barber shop charge?