Question

The typical customer of an amusement park has a demand for rides of qD = 30 – 10PD where q is measured in number of rides and P in dollars per ride.

a. Suppose the marginal cost of any ride is $2. How much should the amusement park charge in admission fee? Clearly explain.

b. Suppose instead the marginal cost of a ride increases with the overall number of rides according to the schedule MC = $2 + 0.001Q where Q is the overall number of rides. If the amusement park has 100 visitors, how much should the park charge per ride? How much should it charge as admission fee?

Answer 1

This is a form of price discrimination, called two-part tariff pricing startegy. In this strategy,

Fee per ride (P) = MC

Admission charge = Consumer surplus (CS)

(a) qD = 30 - 10PD

Therefore,

10PD = 30 - qD

PD = (30 - qD) / 10

PD = 3 - 0.1qD

Equating Price with MC,

3 - 0.1qD = 2

0.1qD = 1

qD = 1/0.1 = 10

From demand function we get: when qD = 0, PD = 3 (Maximum willingness to pay)

Admission charge (CS) = Area enclosed between demand curve and price = (1/2) x $(3 - 2) x 10 = 5 x $1 = $5

(b) MC ($) = 2 + 0.001Q

When Q = 100, e get

MC ($) = 2 + (0.001 x 100) = 2 + 0.1 = 2.1

Equating P and MC,

PD = $2.1

Admission harge (CS) = (1/2) x $(3 - 2.1) x 100 = 50 x $0.9 = $45