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. For incorrect answer(s), click twice to empty the box.

• We are able to prevent resale between the groups. yes or no
• At least one group has elasticity of demand greater than 1 in absolute value. yes or no
• At least one group has elasticity of demand less than one in absolute value. yes or no
• There are two different groups with different (and identifiable) elasticities of demand. yes or no

Answer 1

Under third degree price discrimination, monopolist maximizes profit according to the rule MR = MC
Where MR = P[1-(1/e)] and MC = $40

Group 1: Absolute value of e = 3
So, MR = MC gives
P[1-(1/3)] = 40
So, P(2/3) = 40
So, P = 40*(3/2) = $60
Mark up = P/MC = 60/40 = 1.5

Group 2: Absolute value of e = 5
So, MR = MC gives
P[1-(1/5)] = 40
So, P(4/5) = 40
So, P = 40*(5/4) = $50
Mark up = P/MC = 50/40 = 1.25

Markup for group 1: 1.5
Price for group 1: $60
Markup for group 2: 1.25
Price for group 2: $50

b.  

• We are able to prevent resale between the groups - yes
• At least one group has elasticity of demand greater than 1 in absolute value - no
• At least one group has elasticity of demand less than one in absolute value - no
• There are two different groups with different (and identifiable) elasticities of demand - yes

Two of the given four conditions are true. Elasticities must be different and resale should not be possible.