What price should theater charge to maximize profit


Question: In the short run, suppose that all the costs (except film rental and concessions) at a theater are fixed, and that each theater can seat 500 people per day,no more. The demand curve for tickets at this theater is P=8-.01q and the marginal revenue curve is MR=8-.02q where p is price in dollars per ticket and mr= marginal revenue from ticket sales and q= the number of people who buy per day. If each person who buys a ticket spends 50 cents at the concession stand for items that cost the theater 10 cents, if the theater must pay half of its ticket sales to rent the film, and if the theaters fixed costs are $1200 per day, what price should the theater charge for a ticket if it wants to maximize profit? how big will its profit be?

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Microeconomics: What price should theater charge to maximize profit
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