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.
(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.
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