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Maximizing profit in separated markets

Ann McCutcheon is hired as a consultant to a firm producing ball bearings. This firm sells in two distinct markets, each of which is completely sealed off from the other. The demand curve for the firm's output in the first market is P1 =160 - 8Q1, where P1 is the price of the product and Q1 is the amount sold in the first market. The demand curve for the firm's output in the second market is P2 = 80 - 2Q2, where P2 is the price of the product and Q2 is the amount sold in the second market. The firm's marginal cost curve is 5 + Q, where Q is the firm's entire output (destined for either market). Managers ask Ann McCutcheon to suggest a pricing policy.
a. How many units of output should she tell managers to sell in the second market?
b. How many units of output should she tell managers to sell in the first market?
c. What price should managers charge in each market?

Solution Preview

Profit is maximized at the level of production where MR = MC.

The firm's MC is 5 + (Q1 + Q2).
To derive the MR curves in each market, we first calculate Total Revenue (TR).

TR1 = P1Q1
TR1 = (160 - 8Q1)Q1
TR1 = 160Q1 - 8Q1^2 (where ...

Solution Summary

This solution shows how a firm should set its price and output in each of two markets so as to maximize its profit in both markets.

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