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Profit maximization using third-degree price discrimination

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A. Explain what is meant by "third-degree" price discrimination. What conditions would have to hold for a firm to be able to engage in third-degree price discrimination? If these conditions hold, what general rule would a firm follow to maximize profits? How would its pricing policy be related to the elasticity of demand?

B. Suppose that a firm producing and installing air filters for heating systems has a different sales representative selling the filters to homeowners in each county. If any potential customer inquires about the pumps, the firm directs them to the representative in the county in which they live. No sales representative is allowed to sell an air filtering system to a homeowner outside his or her own county, and is not allowed to discuss pricing at all with a potential customer outside their own county. Company policy dictates that they must direct any inquiries to the sales representative in the homeowner's own county. Suppose also that in two different counties (County A and County B) the demand for these air filtration systems is:

Qa = 1000 - Pa
Qb = 600 - Pb

If the firm's marginal cost of producing the air filters is constant at $200, what price would the firm charge in each county in order to maximize profits?

C. Verify that the pattern of pricing across these two counties corresponds to the general statement that you made in part A. of this question by calculating the elasticity of demand at the profit-maximizing price in each county.

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Solution Summary

A detailed calculation of a firm's profit-maximizing price and output for the same product (air filters) in two different counties. Also, proof of the general relationship between pricing policy and price elasticity in markets where third-degree price discrimination can be practiced.

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A.
Third-degree price discrimination means charging different prices to different customers for the same product. For it to be effective, three conditions must be met:
1. The firm must have a downward-sloping demand curve.
2. Groups of customers with different price elasticities of demand must be separable.
3. The firm must be able to prevent resale of its product.

The firm maximizes its profits by setting its price such that Marginal Revenue = Marginal Cost. If the above conditions are met, the firm will ...

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