A monopolist sells in two markets. The demand curve for her product is given by

Question

A monopolist sells in two markets. The demand curve for her product is given by p1= 122 - 2x1 in the first market and p2 = 306 - 5x2 in the second market, whee xi is the quantity sold in market i and pi is the price charged in market i. She has a constant marginal cost of production, c= 6, and no fixed costs. She can charge different prices in the two makets. What is the profit-maximizing combination of quantities for this monopolist?

a. x1 = 58 and x2 = 32

b. x1 = 29 and x2 = 30

c. x1 = 59 and x2 = 29

d. x1 = 39 and x2 = 28

e. x1 = 49 and x2 = 40

(Please show work or explain. I already have the answer. Just need to know how to solve it)

Explanation / Answer

Revenue is pix1= 122x1-2x1^2 and p2x2= 306x-5x2^2.

So marginal revenue is (derivative) 122-4x1 and 306-10x2

Set equal to marginal cost (6) and solve for x

6= 122-4x1; x1= 29

6= 306-10x2; x2=30

b) is the answer.

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