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 = 18 - QA, and the inverse demand curve for group B is PB = 10 - QB. The monopolist is able to produce the good for either type of customer at a constant marginal cost of 2, and the monopolist has no fixed costs. If the monopolist is able to practice group price discrimination, what would be the values of the elasticities of the two groups at the profit maximizing prices?

Customer A: (-) 1.25 or 1.25

Customer B: (-) 1.49 or 1.5

Explanation:

Pa = 18 - Qa

Total Revenue, TRa = Pa * Qa

TRa = (18 - Qa) * Qa

TRa = 18Qa - Qa^ (2)

Marginal Revenue, MRa = 18 - 2Qa

At equilibrium, MR = MC

18 - 2Qa = 2

2Qa = 16

Qa = 8

Substituting 'Qa' is demand equation

Pa = 18 - 8

Pa = $10

Pb = 10 - Qb

TRb = (10 - Qb) * Qb

TRb = 10Qb - Qb^ (2)

MRb = 10 - 2Qb

10 - 2Qb = 2

2Qb = 8

Qb = 4

Substituting 'Qb' in demand equation

Pb = 10 - 4

Pb = $6

Elasticity of demand of type A customer:

When quantity demanded is 0, price is $18

When quantity is 8, price is $10

Elasticity of demand of A:

= [ (8 - 0) : 8] : [ (10 - 18) : 10]

= 1 : - 0.8

= (-) 1.25 or 1.25

Elasticity of demand of type B customer:

Pb = $6, Qb = 4;

Pb = 10 - Qb

When Qb is zero, Pb = $10

Elasticity of demand of B:

= [ (4 - 0) : 4] : [ (6 - 10) : 6 ]

= 1 : (-0.67)

= (-) 1.49 or 1.5