4) Apple released iPhone4 and suppose Apple has factories in the United States a

Question

4) Apple released iPhone4 and suppose Apple has factories in the United States and Europe.
Both factories have cost functions given by TC(Q)= 10Q. In the Europe, demand for iPhone4 is given by Q= 70-P, where P is the price charged in Europe.
In the United States, demand for iPhone4 is Q=110-P .

a. Apple can engage in third-degree price discrimination, (i.e. set two different prices in Europe and the US), what should be profit maximizing prices and output levels in Europe and the US?
b. Assume now that price discrimination is illegal, so that Apple can charge only a single price P (i.e. uniform pricing) on both continents.
What price will it charge, and what profits will it earn?
c. Will consumer and producer surplus be higher with price discrimination or without price discrimination?

Explanation / Answer

a)Europe demand Q= 70-P P= 70-Q Revenue PQ- 70Q-Q^2 Marginal Revenue 70- 2Q (derivative of revenue function) Marginal Cost 10 (derivative of cost function) Max profits is where marginal cost = marginal revenue so 10= 70-2Q 2Q=60 Q=30 Since P=70-Q P=40 Similarly in the U.S. Q=110-P P=110-Q PQ= 110Q- 2Q Marginal revenue =110-2Q 110-2Q= 10 Q= 50 P= 60 b)Uniform Pricing add the two demand curves Q=110-P Q= 70-P Q(total)= 180-2P 2P= 180-Q P= 90- Q/2 PQ= 90Q- Q^2/2 Marginal revenue= 90-Q 10= 90-Q Q=80 P= 90-40=50 Profits will be 80*50- 10*80= 3,200 c) Consumer surplus will be lower and producer surplus higher under price discrimination. The purpose of price discrimination is to capture some of the consumer surplus.

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