Question

You live in a town with 300 adults and 200 children, and you are thinking about putting on a play to entertain your neighbors 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 Adults Children
10 0 0
9 100 0
8 200 0
7 300 0
6 300 0
5 300 100
4 300 200
3 300 200
2 300 200
1 300 200

a. To maximize 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 $2,500 rather than $2,000 how would your answers to parts a, b, and c change?

Answer 1

Step-by-step explanation:

a) To maximise profit, we would charge a price of 7 for adults and a price of 4 for children.

Profit would be = 7 x 300 + 4 x 200

Profit = 2900

This is the maximum profit other than fixed cost

b) If we have to keep one price of the ticket, then it would be 7. This would yeild a profit of 2100

c) From the law, the adults dont get any benefit, rather the children are in best position of free ticket

d) Fixed cost wont effect the answers above as long as the price and numbers of participants wont change

Answer 2

a. To maximize profit, the price for an adult ticket would be $6, and for a child's ticket, $2. The profit made would be $3,000.

b. With the prohibition on charging different prices, a price of $5 for a ticket is set. The profit earned would be $2,500.

c. Due to the law prohibiting price discrimination, adults are worse off as they now pay the same price as children. Children are better off since they pay less than they would have under price discrimination. However, quantifying these changes in welfare requires detailed analysis.

d. If the fixed cost of the play increased to $2,500, the prices would need adjustment. The optimal prices for adults and children would likely increase, impacting profit margins and altering the welfare changes among adults and children.

Step-by-step explanation:

To maximize profit, the pricing strategy involves analyzing demand schedules to determine the prices that yield the highest revenue. The profit-maximizing prices are $6 for adult tickets and $2 for child tickets. Multiplying these prices by the corresponding quantity sold at each price level and deducting the fixed cost of $2000 results in a profit of $3,000.

However, if the city council restricts price discrimination, a single price must be set. In this scenario, the profit-maximizing price for a ticket, considering both adults and children, is $5, generating a profit of $2,500. This scenario assumes uniform pricing for both customer segments.

The law prohibiting price discrimination affects the welfare of adults and children differently. Adults, who would have paid a higher price under price discrimination, are worse off as they now pay the same as children. Children, benefiting from lower prices, are better off under uniform pricing. Quantifying the exact changes in welfare requires detailed analysis of consumer surplus changes due to price adjustments.

If the fixed cost of the play increased to $2,500, the profit-maximizing prices for both adults and children would likely need adjustment to cover the higher fixed cost, influencing the profit margins and, subsequently, the welfare changes among adults and children.