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 -4. Your marginal cost of producing the product is $40. a. Determine your optimal markups and prices under third-degree price discrimination. Instructions: Enter your responses rounded 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: In order to receive full credit, you must make a selection for each option. For correct answer(s), click the box once to place a check mark. For incorrect answer(s), click twice to empty the box. We are able to prevent resale between the groups. unchecked At least one group has elasticity of demand greater than 1 in absolute value. unanswered At least one group has elasticity of demand less than one in absolute value. unanswered There are two different groups with different (and identifiable) elasticities of demand.

Explanation / Answer

(a)

Lerner Index (LI) = - 1 / Elasticity of demand = (P - MC) / P, where P: Price

For group 1,

LI = - 1 / - 2 = 1/2

Therefore,

1/2 = (P - 40) / P

P = 2P - 80

P = $80

Mark-up = (P - MC) / MC = $(80 - 40) / $40 = $40 / $40 = 1 (= 100%)

For group 2,

LI = - 1 / - 4 = 1/4

Therefore,

1/4 = (P - 40) / P

P = 4P - 160

4P = 160

P = $40

(b) Following conditions are necessary:

- We are able to prevent resale

- There are two different groups with different and identifiable elasticities of demand

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