Competitive Strategy. Bob Ice owns and operates Bob\'s Music Center, Ltd., a sma

Question

Competitive Strategy. Bob Ice owns and operates Bob's Music Center, Ltd., a small firm that offers music lessons in Huntsville, Alabama. Given the large number of competitors and the lack of entry barriers, it is reasonable to assume that the market for music lessons is perfectly competitive and that the average $60 per hour price equals marginal revenue, P = MR = $60. Assume that Bob's annual operating expenses are typical of several such firms and individuals operating in the local market, and can be expressed by the following total and marginal cost functions:

TC = $100,000 + $10Q + $0.005Q2

MC = $10 + $0.01Q

where TC is total cost per year, MC is marginal cost, and Q is the number lessons given. Total costs include a normal profit and allow for Bob's employment opportunity costs.

A. Calculate Bob's profit-maximizing output level.
B. Calculate Bob's economic profits at this activity level. Is this activity level sustainable in the long run?

Explanation / Answer

Profit maximization is where MC=MR so 10 +.01Q= 60 Q= 50/.01= 5,000 Profits are 60*5,000 -100,000 -10*5,000- .005 *5000^2= 25,000 Not sustainable in long run because new firms entering the market will drive economic profits to zero in a perfectly competitive market.

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