An amusement park, whose customer set is made up of two markets, adults and children, can be expressed in equation form as follows (where subscript A refers to the adult market, subscript C to the market for children, and subscript T to the two markets combined):
QA = 20 - 1PA
QC = 30 - 2PC
QT = 50 - 3PT
The marginal operating cost of each unit of quantity is $5. The owners of the amusement park wish to maximise profits.
a. Solve these equations for the maximum profit that the amusement park will attain when it charges different prices in the two markets and when it charges a single price for the combined market.
b. What is a two-part tariff? How can a firm determine an optimal two-part tariff it has two customers with different demand curves?