Consider a monopolist (say a local movie theatre in Fort Lauderdale) which has two distinct client...

 

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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(q) = a - bqA+ and the inverse demand of retirees is given by a b p(9B) = - 3 39B¹ (a) Compute the demand elasticity in each market in terms of p. (b) Compute the demand function q(p)under the assumption that the movie theater can only offer 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 offer a single and common price to the market segments. Who goes to the movies and who doesn't? (c) Next, we allow the movie theatre to offer different prices in each segment and customers cannot misrepresent their identity. What is the optimal price in each one of the markets? (d) Compare the consumers surplus under the single common price on both segments of the market with the consumers surplus under the introduction of different prices across different segments. (Calculate consumer surplus of each client group and analyze the difference.)< 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(q) = a - bqA+ and the inverse demand of retirees is given by a b p(9B) = - 3 39B¹ (a) Compute the demand elasticity in each market in terms of p. (b) Compute the demand function q(p)under the assumption that the movie theater can only offer 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 offer a single and common price to the market segments. Who goes to the movies and who doesn't? (c) Next, we allow the movie theatre to offer different prices in each segment and customers cannot misrepresent their identity. What is the optimal price in each one of the markets? (d) Compare the consumers surplus under the single common price on both segments of the market with the consumers surplus under the introduction of different prices across different segments. (Calculate consumer surplus of each client group and analyze the difference.)<