25. Suppose a monopoly sells to two identifiably different types of customers, A

Question

25. Suppose a monopoly sells to two identifiably different types of customers, A and B, who are unable to practice arbitrage. The inverse demand curve for group A is PA 19 - QA, and the inverse demand curve for group B is PB 11 2QB. The monopolist is able to produce the good for either type of customer at a constant marginal cost of 1, and the monopolist has no fixed costs. If the monopolist practices group price discrimination, what are the profit maximizing prices and quantities for each type of customer?

Explanation / Answer

Pa = 19 - Qa

Total Revenue of A ( TR a) = Pa* Qa = 19 Qa - Qa2

Marginal Revenue of A (MRa) = 19 - 2 Qa

At Equilibrium MRa = Marginal Cost (MCa)

19 - 2 Qa = 1

2Qa = 18

Qa = 9

Pa = 19-9 = 10

Similarly Pb = 11 -2 Qb

Total Revenue of B (TRb) = 11 Qb - 2 Qb2

Marginal Revenue of B (MRb) = 11 -4 Qb

At Equilibrium MRb = MC

11-4 Qb = 1

4Qb = 10

Qb =2.5

Pb = 11 -2 (2.5) = 6

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