Suppose the demand curves for a product in two segmented markets are given by p1

Question

Suppose the demand curves for a product in two segmented markets are given by p1 = 12 Q1 and p2 = 24-2Q2. ptachya is a monopolist who produces the product at a marginal cost of $4 per unit. Suppose ptachya is unable to sort perfectly among his customers but is able tell one type of buyer apart from another. Suppose no resale is possible between the buyers in the two markets under group pricing. Then the price charged in each in each market and quantity sold equal p1 = $4; Q1 = 8;p2 = $10: Q2 = 7 p1 = $6; Q1 =6; p2 = $12: Q2 =8 p1 = $8; Q1 = 4; p2 = $14: Q2 = 5

Explanation / Answer

Profit in first market is ( 12 - Q1 - 4 ) * Q1

= 8Q1 - Q1^2

to maximize profit 8 - 2Q1 = 0 => Q1 = 4

Price is 12- 4 = 8 and profit is 8 - 4 = 4

Profit in market 2

( 24 - 2Q - 4 ) * Q

20Q - 2Q^2

to find maximum

4Q = 20

Q = 5

price is 24 - 2 * 5 = 14

profit is 14 - 4 = 10

Hence answer is

D) P1 = 8, Q1 = 4, P2 = 14, Q2 = 5

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