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Profit maximization where MR = MC

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10. Cleaners R Us. offers professional motel room cleaning to motel owners in Danville, Illinois. The company estimates that each additional room it cleans costs the firm $10. The owner's daughter did a study and estimated the firm's demand could be described by the following equation, where P stands for price, and Q for Quantity demanded. She also estimated the marginal revenue equation for the company could be described by the equation below the demand equation. Lastly, since each additional room costs $10 to clean, she also derived a marginal cost equation.

demand P = $20 - $0.01Q (or Q = 2,000 - 100P)
marginal revenue MR = $20 - $0.02Q
marginal cost MC = $10

a. Calculate the output level (Q - number of rooms of rooms cleaned) at which profits are maximized. (Hint: remember that profits are maximized at that output where marginal revenue (MR) = marginal cost (MC))

b. In order to sell the amount computed in part A. above, at what price would the company have to offer its service? (Hint: which curve (equation) gives the relationship between the price of a good or service and how much of it is demanded?).

c. What is this firm's total revenue at the optimum price/output computed in parts A. and B.?

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Solution Summary

Optiaml output and price are derived for profit maximization. Revenue computation for the optimal level is also shown. The solution provides step by step details for computations.

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