You are the manager of a monopoly that sells a product to two groups of consumer

Question

You are the manager of a monopoly that sells a product to two groups of consumers in different parts of the country. Group 1’s elasticity of demand is -2, while group 2’s is -5. Your marginal cost of producing the product is $10.

a. Determine your optimal markups and prices under third-degree price discrimination. Instruction: Round your answers to two decimal places. Markup for group 1: Price for group 1: $ Markup for group 2: Price for group 2: $

b. Which of the following are necessary conditions for third-degree price discrimination to enhance profits.

Explanation / Answer

(a)

Lerner index (LI) = -1 / elasticity of demand

Group 1: - 1 / - 2 = 0.5

Group 2: - 1 / - 5 = 0.2

Again, LI = (P - MC) / P

Group 1: (P - 10) / P = 0.5

P - 10 = 0.5P

0.5P = 10

P = 20

Optimal mark-up = (P - MC) / MC = (20 - 10) / 10 = 10 / 10 = 1, or 100%

Group 2: (P - MC) / P = 0.2

(P - 10) / P = 0.2

P - 10 = 0.2P

0.8P = 10

P = 12.5

Optimal-markup = (12.5 - 10) / 10 = 2.5 / 10 = 0.25, or 25%

(b) Necessary conditions are:

(i) The monopolist can precisely estimate the price elasticity of demand for different consumer segments, and

(ii) No re-sale can take place between different customer segments.

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