18). You are the manager of a monopoly that sells a product to two groups of con

Question

18).

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.  

Instruction: Round your answers 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: You may select more than one answer. Click the box with a check mark for the correct answers and click twice to empty the box for the wrong answers. You must click to select or deselect each option in order to receive full credit.

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

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

Explanation / Answer

a) Mark-up rule for monopolist

P = [E / (1 + E)] * MC

where
E = Own-price elasticity of demand for the firm's product
MC = Firm's marginal cost

Thus, for group 1,

P1 = [-2 / (1 - 2)] * $40

P1 = $80

(P – MC)/P is the mark-up over marginal cost as a proportion of price.

Mark-up for group 1 =($80 - $40) / $80 = 0.50

For group 2,

P2 = [-4 / (1 - 4)] * $40

P2 = $53.33

Mark-up for group 2 =($53.33 - $40) / $53.33 = 0.25

Thus,

Markup for group 1: 0.50
Price for group 1: $ 80

Markup for group 2:  0.25
Price for group 2: $ 53.33

b)

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

We are able to prevent resale between the groups.

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