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Answer to Question #71434 in Microeconomics for Jessica

Question #71434
Suppose a monopolist is able to segment its market into 2 consumer groups based upon known differences in willingness to pay. Group A's demand function is given by P = 160 - 2Q and group B's demand function is given by P = 120 - Q. In addition, the marginal cost of producing and selling a unit to group A is the same as the marginal cost of producing and selling a unit to group B. Specifically, MC = 20. If the firm practices second degree (or multi-market) price discrimination, then total profit will be maximized by:
Expert's answer
Group A's demand function: P = 160 - 2Q, MR = TR' (P*Q)' = 160 - 4Q,
group B's demand function: P = 120 - Q. MR = TR' = 120 - 2Q,
MC = 20.
If the firm practices second degree (or multi-market) price discrimination, then total profit will be maximized at Q for which MR = MC at both markets. So:
For group A's market 160 - 2Q = 20, Q = 70 units.
For group B's market 120 - Q = 20, Q = 100 units.
Total profit-maximizing output is Q = 70 + 100 = 170 units.

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