Question

A monopolistic firm operates in two separate markets. No trade is possible between market A and market B. The firm has calculated the demand functions for each market as follows:

     Market A p = 15 - Q; Market B p = 11 - Q

The company estimates its total cost function to be TC = 4Q. Calculate the following:

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

Answer 1

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(a) This cannot be defined since when the company maximizes its profit and charges the same price in both the markets the quantity, total revenue and the profit cannot be determined because they have the same set of values in both the markets.

(b) Now the given information,

Market A; p = 15-Q
Market B; p = 11-Q

Total revenue = Market A x Market B = 15Q-Q^2 + 11Q - Q^2 = 26Q-(2Q)^2 = 26-4Q
Therefore, Total Revenue = 26-4Q

Total Cost = 4Q

Now,
TR = TC
26-4Q = 4Q
26 = 8Q
8Q = 26
Q = 3.25

Substitute Q value in the total revenue equation, that implies
TR = 26(3.25) - 4(3.25)^2 = 84.5 - 42.25 = 42.25
TC = 4(3.25) = 13

Now, Profit = 42.25 - 13 = 29.25