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Worked Problem: Profit-Maximizing Price and Output Levels

Bow Wow Bazaar is a growing firm specializing in gourmet dog food and supplies in Florida resort communities. BWB's demand and cost information are as follows:

P = 4500 - Q
MR = 4500 - 2Q
TC = 150,000 + 400Q
MC = $400

where Q is output, P is price in dollars, MR is marginal revenue, TC is total cost and MC is marginal cost. All costs include a normal return of 12% on capital investment.

A. Determine the profit-maximizing price and output levels, and the profit earned.
B. Based on your results in Part A and assuming the firm operates in a monopolistically competitive industry, explain what will happen to this industry in the long run?
C. Determine the output level, price, and profits that will occur in long-run equilibrium. Assume a high-price, low-output scenario assuming a parallel shift of the firm's demand curve. Be sure to explain what you are doing and why. Hint: The slope of the ATC curve is -$150,000/Q2.
D. Calculate BWB's new long-run equilibrium demand curve.

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Solution Preview

A. BWB maximizes its profit at the level of output where MR = MC

Let MR = MC
4500 - 2Q = 400
4100 = 2Q
Q = 2050

P = 4500 - Q
P = 4500 - 2050
P = 2450

Profit = Total Revenue (TR) - TC
Profit = PQ - (150000 + 400Q)
Profit = (2450)(2050) - 150000 - (400)(2050)
Profit = 4052500

B. The firm is earning a positive economic profit, so other firms will enter the ...

Solution Summary

This solution illustrates mathematical calculations to find the profit-maximizing price and output levels for the Bow Wow Bazaar, a monopolistically competitive pet supply store. It shows how to predict what will happen to the industry in the long eun, and how to calculate the firm's long-run demand curve.