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Maximizing profit by charging different prices in NY and LA

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A monopolistic firm operates in the U.S. No trade is possible between the NY market and the LA market. The firm has calculated the demand functions for each market as follows:

NY Market Pn = 150 - Qn
LA Market Pl = 50 - Ql

The company estimates its total cost function to be: TC = 40Q.

Calculate the following:

a. quantity, total revenue and profit when the company maximizes its profit and charges the same price in both markets.
b. quantity, total revenue and profit when the company charges different prices in each market and maximizes its total profit.

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Solution Summary

Given the demand functions that a firm faces in the New York and Los Angeles markets, this firm shows how to calculate the firm's maximum profit when it charges the same price in both markets, and when it charges different prices in each market.

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a) To find the joint demand function, first rearrange the separate demand functions:

Pn = 150 - Qn
Pl = 50 - Ql

Rearranging:
Qn = 150 - Pn
Ql = 50 - Pl

Add the demand functions:
Qtotal = 150 - Pn + 50 - Pl
Q = 200 - Pn - Pl

Pn = Pl, so:
Q = 200 - 2P

Rearranging:
2P = 200 - Q

So the joint demand function is:
P = 100 - Q/2

The firm maximizes its profit when Marginal Revenue ...

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