Question

Suppose a monopolist is able to segment its market into 2 consumer groups based upon known differences in willingness to pay. Group A's demand function is given by P = 90 - 2Q and group B's demand function is given by P = 70 - 0.5Q. In addition, the marginal cost of producing and selling a unit to group A is the same as the marginal cost of producing and selling a unit to group B. Specifically, MC = 10. If the firm practices second degree (or multi-market) price discrimination, then total profit will be maximized by:
i. selling Q = 20 units at a price of P = $50 to members of group A
ii. selling Q = 40 units at a price of P = $10 to members of group A
iii. selling Q = 60 units at a price of P = $40 to members of group B
iv. selling Q = 80 units at a price of P = $30 to members of group B

Answer 1

Answer on Question 71435-Economics - Microeconomics

Suppose a monopolist is able to segment its market into 2 consumer groups based upon known differences in willingness to pay. Group A's demand function is given by $P = 90 - 2Q$ and group B's demand function is given by $P = 70 - 0.5Q$. In addition, the marginal cost of producing and selling a unit to group A is the same as the marginal cost of producing and selling a unit to group B. Specifically, $MC = 10$. If the firm practices second degree (or multi-market) price discrimination, then total profit will be maximized by:

i. selling $Q = 20$ units at a price of $P = \$50$ to members of group A

ii. selling $Q = 40$ units at a price of $P = \$10$ to members of group A

iii. selling $Q = 60$ units at a price of $P = \$40$ to members of group B

iv. selling $Q = 80$ units at a price of $P = \$30$ to members of group B

Solution.

The sales volumes of the monopoly in both markets are determined from the condition of maximizing profits under market segmentation: MR1 (q1) = MR2 (q2) = MC (Q), where $Q = q1 + q2$.

$$\begin{array}{l} MR_1 = \left((90 - 2q_1) \times q_1\right)' = 90 - 4q_1 = 10, \quad \Rightarrow q_1 = 20, P = 50 \\ MR_2 = \left((70 - 0.5q_2) \times q_2\right)' = 70 - q_2 = 10 \Rightarrow q_2 = 60, P = 40 \\ \end{array}$$

So, the right answers are

i. selling $Q = 20$ units at a price of $P = \$50$ to members of group A

i. selling $Q = 20$ units at a price of $P = \$50$ to members of group A

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