Quiz 23. Group Pricing Ans

# Quiz 23. Group Pricing Ans - = 2 Q 1 Q 2 From the second...

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Shomu Banerjee ECON 201 GROUP PRICING ANSWERS A monopolist engages in third degree differential pricing (i.e., group pricing) across two markets with demand curves given by P 1 = 60 – 0.5 Q 1 and P 2 = 80 – Q 2 . Its cost function is given by C ( Q ) = Q 2 , where Q = Q 1 + Q 2 , implying that his marginal cost is MC = 2 Q = 2( Q 1 + Q 2 ). What are the profit-maximizing quantities ( Q 1 * and Q 2 * ) sold in each market and at what price ( P 1 * and P 2 * )? From the first demand curve, MR 1 = 60 – Q 1 and from the second demand curve, MR 2 = 80 – 2 Q 2 . Set each marginal revenue equal to the marginal cost: 60 – Q 1 = 2( Q 1 + Q 2 ) 80 – 2 Q 2

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Unformatted text preview: = 2( Q 1 + Q 2 ). From the second equation, Q 2 = 20 - (1/2) Q 1 . Substitute for Q 2 in the first equation and solve to obtain Q 1 * = 10 and Q 2 * = 15. From the respective demand equations, P 1 * =\$55 and P 2 * =\$65. Q 1 Q 2 Q = Q 1 + Q 2 1 2 3 4 1 2 3 4 M C D 2 D 1 M R 2 M R 1 1 2 3 4 8 6 4 2 8 6 4 2 8 6 4 2 \$ \$ \$ P 1 = 6-. 5 Q 1 M R 1 = 6-Q 1 P 2 = 8-Q 2 M R 2 = 8-2 Q 2 M C = 2 Q = 2 ( Q 1 + Q 2 ) Q 1 * = 1 P 1 * = \$ 5 5 Q 2 * = 1 5 P 2 * = \$ 6 5 M R 1 = M R 2 = M C...
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Quiz 23. Group Pricing Ans - = 2 Q 1 Q 2 From the second...

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