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 an example of two-part tariff pricing startegy where

Change per ride (P) = MC and Admission fee = Consumer surplus (CS)

(a) qD = 30 - 10PD

10PD = 30 - qD

PD = 3 - 0.1qD

Equating PD and MC,

3 - 0.1qD = 2

0.1qD = 1

qD = 10

From demand function, when qD = 0, PD = 3 (Reservation price)

Admission fee (CS) = Area between demand curve & price = (1/2) x $(3 - 2) x 10 = 5 x $1 = $5

(b) MC = 2 + 0.001Q

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

Equating PD with MC,

PD = $2.1

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