Question

In: Economics

A barber shop offers haircuts to both students and faculty. Student demand for haircuts is given...

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

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

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

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

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

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

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

Now suppose that the barbershop cannot engage in personalized pricing. However, it is able to offer one price for students and a different price for faculty.

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

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

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

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