# One checks that at p 30 p 10 and p 0 profit equals 0

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cur at the kinks of the marginal revenue function. One checks that at P = 30, P = 10 and P = 0, profit equals 0, 40 , 000 and 0, respectively. Hence, P = 7 achieves the highest overall profit, namely Π 0 = 49 , 000. b) Demand from consumers of type 2 is Q 2 ( P ) = 6 , 000 - 200 P , for 0 P 30, 3

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and Q 2 = 0 otherwise. Marginal revenue in this market segment is MR 2 ( P ) = 6 , 000 - 400 P if 0 < P < 30, and MR 2 = 0 if P > 30, so the condition MR = MC is satisfied on { 15 } ∪ (30 , + ). Thus, P 2 = 15 achieves the highest profit in this market segment, namely Π 2 = 45 , 000. On the other hand, demand from consumers of type 1 is Q 1 ( P ) = 8 , 000 - 800 P , for 0 P 10, and Q 1 = 0 otherwise. Marginal revenue in this market seg- ment is MR 1 ( P ) = 8 , 000 - 1 , 600 P if 0 < P < 10, and MR 1 = 0 if P > 10, so the condition MR = MC is satisfied on { 5 } ∪ (10 , + ). Thus, P 1 = 5 achieves the highest profit in this market segment, namely Π 1 = 20 , 000. That the equilibrium price in market segment 2 exceeds that in market segment 1 may occur because consumers of type 2 have more inelastic demand than their type 1 counterparts. c) Without price discrimination, the consumer surplus is simply the area below the demand curve nodiscrimination, beyond the equilibrium price: CS 0 = + P 0 Q ( P )d P (4) = 10 7 (14 , 000 - 1 , 000 P )d P + 30 10 (6 , 000 - 200 P )d P (5) = 14 , 000 P - 500 P 2 10 7 + 6 , 000 P - 100 P 2 30 10 (6) = 56 , 500 . (7) With price discrimination, the consumer surplus is the sum of the consumer surpluses of both types. The consumer surplus of type 1 consumers is: CS 1 = 30 15 (6 , 000 - 200 P )d P = 6 , 000 P - 100 P 2 30 15 = 22 , 500 , (8) whereas the consumer surplus of type 2 consumers is: CS 2 10 5 (8 , 000 - 800 P )d P = 8 , 000 P - 400 P 2 10 5 = 10 , 000 . (9) So the change in consumer surplus amounts to: Δ CS = ( CS 1 + CS 2 ) - CS 0 = - 24 , 000 . (10) With price discrimination, the producer surplus is the sum of profits realized from selling to both types of consumers. So the change in producer surplus is:
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