Question

There are 1,000 people in the town of Wilmington, who want to have a fireworks show on the 4th of July. Willingness to pay for each of the 100 individuals is P = 5.52 - 0.01Q, where Q is the amount of exploding rockets that shoot off during the show. The cost of each exploding rocket is $20.

1. How many rockets should the town of Wilmington purchase for its fireworks show?

2. How much should the town of Wilmington charge each individual in order to maximize consumer surplus?

3. Why is it unlikely that the optimal amount of rockets will be purchased no matter what system of payment is used?

Answer 1

Market demand (if all individuals are taken together) is P = 100(5.52 - 0.01Q) or P = 552 - Q

Marginal cost is 20 so optimal number of rocckets is 552 - Q = 20 or Q = 532. The price that maximizes consumer surplus is determined at P = MC so the price is $20 per rocket

Now it is unlikely that the optimal amount of rockets will be purchased no matter what system of payment is used because each individual has a maximum willingness to pay fixed at 5.52 so at a price of 20 per rocket, nobody will pay $20.