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 -5. 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.

At least one group has elasticity of demand greater than 1 in absolute value.

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

We are able to prevent resale between the groups.

At least one group has elasticity of demand less than one in absolute value.

Explanation / Answer

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

P: Price

MC: Marginal cost = $40

(a)

For group 1,

LI = (-1) / (-3) = 1/3

1/3 = (P - 40) / P

P = 3P - 120

2P = 120

P = $60.00

Markup (over MC) = (P - MC) / MC = $(60 - 40) / $40 = $20/$40 = 0.5 = 50.00%

For group 2,

LI = (-1) / (-5) = 1/5

1/5 = (P - 40) / P

P = 5P - 200

4P = 200

P = $50.00

Markup (over MC) = (P - MC) / MC = $(50 - 40) / $40 = $10/$40 = 0.25 = 25.00%

(b) Following conditions are necessary:

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

- We are able to prevent resale between groups

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