You live in a town with 300 adults and 200 children,and you are thinking about putting on a play to entertain your neighbours and make some money. A play has a fixed cost of $2000, but selling an extra ticket has zero marginal cost.Here are the demand schedules for your two types of customer: Price: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 Adults: 0, 100, 200, 300, 300, 300, 300, 300, 300, 300, 300 Children: 0, 0, 0, 0, 0, 100, 200, 200, 200, 200, 200 a) To maximise profit,what price would you charge for an adult ticket? For a child's ticket? How much profit do you make? b) The city council passes a law prohibiting you from charging different prices to different customers. What price do you set for a ticket now? How much profit do you make? c) Who is worse off because of the law prohibiting price discrimination? Who is better off? (If you can, quantify the changes in welfare.) d) If the fixed cost of the play were $2500 rather than $2000, how would your answers to parts (a), (b) and (c) change?
Question
You live in a town with 300 adults and 200 children,and you are thinking about putting on a play to entertain your neighbours and make some money. A play has a fixed cost of $2000, but selling an extra ticket has zero marginal cost.Here are the demand schedules for your two types of customer:
Price: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
Adults: 0, 100, 200, 300, 300, 300, 300, 300, 300, 300, 300
Children: 0, 0, 0, 0, 0, 100, 200, 200, 200, 200, 200
a) To maximise profit,what price would you charge for an adult ticket? For a child's ticket? How much profit do you make?
b) The city council passes a law prohibiting you from charging different prices to different customers. What price do you set for a ticket now? How much profit do you make?
c) Who is worse off because of the law prohibiting price discrimination? Who is better off? (If you can, quantify the changes in welfare.)
d) If the fixed cost of the play were 2000, how would your answers to parts (a), (b) and (c) change?
Solution
a) To maximize profit, you would charge 4 for a child's ticket. At these prices, you would sell 200 adult tickets and 200 child tickets, generating a total revenue of 2000, you would make a profit of $400.
b) If you cannot charge different prices to different customers, you would set the ticket price at 2100. After subtracting the fixed cost of 100.
c) Adults are worse off because of the law prohibiting price discrimination, as they now have to pay 300 (300 adults * 0 (since they were not attending the play at the higher price).
d) If the fixed cost of the play were 2000, you would not make a profit in either scenario. In scenario (a), you would make a loss of 400. The welfare changes in part (c) would remain the same.
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