Question: There are two types of consumers 1 and 2 with demands: P 1 (Q) = a b 1 Q P 2 (Q) = a

There are two types of consumers 1 and 2 with demands:

P₁(Q) = a – b₁Q

P₂(Q) = a – b₂Q

The monopolist has a marginal cost function given by

MC(Q)

a. Shows that if there is no price discrimination, then the profit maximizing price and quantity, (P*, Q*), satisfy

bib2 2(5+ b3) MC(Q') = a – 2 Q* bị + b2 a + MC(Q*) 2 P*:

b. Under third degree price discrimination, let (P₁, Q₁) and (P₂, Q₂) be the profit maximizing prices and quantities for consumers 1 and 2, respectively. Show that:

bib2 2(5+ b3) MC(Q') = a 2 Q* b + b2 a

That is, under this particular kind of demand system a monopolist that can practice third degree price discrimination will not benefit from doing so. It will choose prices that are the same for both customers and equal to the price level under no price discrimination.

bib2 2(5+ b3) MC(Q') = a 2 Q* b + b2 a + MC(Q*) 2 P*:

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