Question A.) 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?
I think that profit is maximized when p= mc which = 8-.01q=.1 or .01q=8-.1= .01q/7.9=790 but this doesn't make sense.
part B.) When some popular children's films were released, distributors insist on charging a minimum amount for admission. suppose that each child who comes to such a movie has $3, which is to cover admission and food. If the theater keeps 50 cents of every dollar spent on ticket sales( the rest goes to the distributor) and 77 cents of every dollar spent on food (the rest goes to the firms that supply them), derive an equation showing how the theater's profit per child varies with the price it charges. If you were the distributor, what price would you like to charge? (Assume that each child spends the entire $3 in the theater)
Marginal Revenue is determined.