An amusement park is considering changing its pricing system from a pay-per-ride system to a single entrance fee entitling the entrant to unlimited rides. Assume that the park is not close to approaching the attendance capacity. The marginal value for rides for the typical entrant is listed below:
Quantity (# of rides) Marginal value ($)
1 $2.50
2 $2.00
3 $1.50
4 $1.00
5 $0.50
6 $0.10
7 $0
Note: we did not talk about this in the slides but a demand curve is sometimes referred to as a "willingness to pay" curve because it informs us how much consumers value additional units. In this context, the information above can allow us to construct a demand curve for rides. At a price of $2.50 per ride, how many rides would our consumer ride? If the price were $2.00 per ride, how many rides would our consumer ride? etc.
a. Assuming that the marginal cost is zero to provide the rides to those in attendance, what is the best pay-per-ride price (take make things convenient for the cashiers, consider only 50 cent increments)?
b. Instead of pay-per-ride, you implement an entrance fee (and unlimited rides). What is the profit-maximizing entrance fee?