Question

1. Suppose that consumers see haircuts as an undifferentiated good and that there are hundreds of barbershops in the market. The current market equilibrium price of a haircut is $15. Bob’s Barbershop has a daily short-run total cost given by TC = 0.5Q2. The associated marginal cost curve is MC = Q. [up to 2 points] a. How many haircuts should Bob give each day if he wants to maximize profit? b. If Bob maximizes profit, how much profit will he earn each day?

Answer 1

a) We know the price = $15 and hence, the TR = 15Q. We're given that TC = 0.5Q².

From these, we can find MR and MC bu differentiating the TR and TC equations with respect to Q.

MR= 15

MC= Q

The profit-maximizing rule is, MR = MC

Hence, we get Q = 15. So, Bob should give 15 haircuts a day to maximize profit.

b) The profit function is Profit = TR - TC, i.e. profit = 15Q - 0.5Q² .

Substituting for Q=15 in the equation we get,

Profit = 15*15 - 0.5* 15² = 225 - 112.5 = 112.5

Therefore, profit earned in a day = $112.5