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?

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