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 -3, while group 2’s is -4. Your marginal cost of producing the product is $20.

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.

Instructions: You may select more than one answer.

A. At least one group has elasticity of demand greater than 1 in absolute value. B. We are able to prevent resale between the groups. C. At least one group has elasticity of demand less than one in absolute value. D. There are two different groups with different (and identifiable) elasticities of demand.

Explanation / Answer

P = MC/(1-1/|e|)

(P-MC)/P = 1/|e|

P = MC/(1-1/|e|) = MC |e|/(|e|-1)

(P-MC)/MC=1/(|e|-1)

Markup for group 1 = 1//(1-1/|e|) = 1/(1- 1/3) = 3/2

Price for group 1 = 20*3/2 = 30

Markup for group 2 = 1//(1-1/|e|) = 1/(1- 1/4) = 4/3

Price for group 2 = 20*4/3 = 80/3 = 26.66

b.

We are able to prevent resale between the groups

There are two different groups with different (and identifiable) elasticities of demand.

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