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 -5, while group 2’s is -6. Your marginal cost of producing the product is $20.

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.

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

Answer 1

(a)

Group 1

Ed = -5

MC = 20

Calculate Price (P) -

[P - MC]/P = -(1/Ed)

[P - 20]/P = -[1/(-5)]

[P - 20]/P = 1/5

5(P - 20) = P

5P - 100 = P

5P - P = 100

4P = 100

P = 100/4 = 25

Markup = Price - Marginal cost = 25 - 20 = 5

Thus,

Markup for Group 1 = $5

Price for Group 1 = $25

Group 2

Ed = -6

MC = 20

Calculate Price (P) -

[P - MC]/P = -(1/Ed)

[P - 20]/P = -[1/(-6)]

[P - 20]/P = 1/6

6(P - 20) = P

6P - 120 = P

6P - P = 120

5P = 120

P = 120/5 = 24

Markup = Price - Marginal cost = 24 - 20 = 4

Thus,

Markup for Group 2 = $4

Price for Group 2 = $24

(b)

The necessary conditions for the third degree price discrimination are as follows -

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

2. We are able to prevent resale between the groups.