# What is the optimal price in each one of the markets?

Third Degree Price Discrimination. Consider a monopolist (say a local movie theatre in Fort Lauderdale) which has two distinct client groups, adults and seniors. The inverse demand for the adults is given by p (qA) = a bqA; and the inverse demand of retirees is given by p (qB) = a 3 b 3 qR: (a) Describe the demand function in the two markets graphically and then compute the demand elasticity in each market. (b) Compute the demand function q (p) under the assumption that the movie theater can only o§er a single price to both segments of the market. (Hint: at a given price add the demand of the adults and senior market. You need to go from the inverse demand function to the demand function.) Illustrate the aggregate demand function in contrast to the demand functions in each segment. Now compute the optimal price of the movie theatre when it can only o§er a single and common price to the market segments. Who goes to the movies and who doesnít? (c) Next we allow the movie theatre to o§er di§erent prices in each segment and customers cannot misrepresent their identity. What is the optimal price in each one of the markets? (d) Compare the welfare of the consumers and the revenue of the consumer after the introduction of di§erent prices across di§erent segments. Explain.

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