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Profit maximization for a shop using the MR= MC method

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Joe's Barber Shop has a daily total cost function of

TC = 100 + 4Q + Q^2

and the daily demand for his services is

Q = 50 - 2P

What is the profit maximizing price that Joe should charge for his services?

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Solution Summary

This solution shows how to calculate the profit-maximizing output and price for a barber shop that operates as a monopolistic competitor.

Solution Preview

Joe's maximum profit occurs where Marginal Revenue (MR) = Marginal Cost (MC).

Demand curve:
Q = 50 - 2P
Rearranging:
2P = 50 - Q
P = 25 - ...

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