Question

Assume that consumers view haircuts as the same among sellers and there are hundreds of barbers in a given market. The current market equilibrium price for a haircut is $15. Bob’s Barbershop has a daily, short-run total cost given by TC=0.5Q 2 with marginal cost MC=Q. How many haircuts should Bob prepare each day to maximize profits? How much will he earn in profit each day

Answer 1

Answer

In order to maximize profit a perfect competitive firm produces that quantity at which P(=MR) = MC. Note here there are hundreds of barbers and hence this market is like a perfect competitive market

Here P = Price = 15

MR = dTR/dQ and TR = Total Revenue = PQ = 15Q => MR = Marginal Revenue = dTR/dQ = 15

Hence, here P = MR(like a perfect competitive market)

MC = dTC/dQ = 2*0.5Q = Q

P(= MR) = MC

=> 15 = Q

Hence In order to maximize profit It should produce 15 units

Profit = TR - TC = PQ - 0.5Q²

= 15*15 - 0.5*15²

= 112.5.

Hence, he will earn a profit of $112.5 each day.