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# How do you calculate the quantity, total revenue and profit when the monopolistic firm operates in two separate markets?

Profit Maximization
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A monopolistic firm operates in two seperate 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:

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.

Please show calculations it is very helpful for me as I have difficulty with the math.

#### Solution Preview

a. Quantity, total revenue and profit when the company maximizes its profit and charges the same price in both markets.

We write Qa = 15 - P
Qb = 11 - P
Then the total quantity is Q = Qa + Qb = 15 - P+ 11-P = 26-2P

Write Q = 26-2P into: P = 13 - 0.5Q
Then Revenue is TR= P * Q = (13 -0.5Q)*Q = 13Qa -0.5Qa^2
Marginal revenue is MR = dTR / dQ = 13- Q

Firm's marginal cost is MC = dTC / dQ = 4
in order to maximize the total profit, ...

#### Solution Summary

This solution show show to calculate quantity, total revenue and profit.

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