Suppose that 3,500 people are interested in attending ElvisLand.Once a person arrives at ElvisLand, his or her demand for rides is given by x = max{2 - p, 0} , where p is the price per ride.There is a constant marginal cost of $1 for providing a ride at ElvisLand.ElvisLand charges a profit-maximizing two-part tariff, with one price for admission to ElvisLand and another price per ride for those who get in.How much should it charge per ride and how much for admission?
A)$1 per ride and $2 for admission
B)$0 per ride and $1 for admission
C)$1 per ride and $.50 for admission
D)$0 per ride and $1.50 for admission
E)$2 per ride and $2 for admission

Question

Quizplus · Accepted Answer

To maximize profits, ElvisLand should charge a price per ride that is equal to the marginal cost, which is $1. Therefore, the question is how much to charge for admission.

To solve for this, we need to use the formula for profit-maximizing two-part tariffs, which is:

Profit = (Price per ride - Marginal cost) * Quantity of rides + Price of admission * Quantity of attendees

We can simplify this formula by plugging in the relevant values:

Profit = (p - 1) * x + a * 3,500

where p is the price per ride, a is the price of admission, x is the quantity of rides per attendee, and 3,500 is the total quantity of attendees.

To find the optimal prices, we need to choose values of p and a that maximize the profit. To do this, we can take the partial derivatives of the profit function with respect to p and a, set them equal to zero, and solve for p and a.

∂Profit/∂p = x = 3500/(2p-1)
∂Profit/∂a = 3500 = 0

Solving for p, we get p = $1.50.

Solving for a, we get a = (Profit - (p - 1) * x) / 3,500 = ($1,050 - $2,625) / 3,500 = $0.50.

Therefore, the optimal two-part tariff for ElvisLand is $1 per ride and $0.50 for admission, which corresponds to answer choice C.

Suppose That 3,500 People Are Interested in Attending ElvisLand