The answer to calculating optimal output and profit
Calvin’s Barbershop is a popularly-priced hair cutter on the
south side of Chicago. Given the large number of competitors, the fact that
barbers routinely tailor services to meet customer needs, and the lack of entry
barriers, it is reasonable to assume that the market is perfectly competitive
and that the average $15 price equals marginal revenue, P = MR = $15.
Furthermore, assume that the barbershop’s monthly operating expenses are
typical of the 50 barbershops in the local market and can be expressed by the
following total and marginal cost functions:
TC = $7,812.50 + $2.5Q + $0.005Q2
MC =dTC/dQ = $2.5 + $0.01Q
where TC is total cost per month including capital costs, MC
is marginal cost, and Q is the number of hair cuts provided. Total costs
include a normal profit.
A. Calculate Calvin’s profit-maximizing output level.
B. Calculate the Calvin’s economic profits at this activity
level. Is this activity level sustainable in the long run?
