Question

Lisa and Maggie like to go to the only amusement park in town. Lisa’s demand for rides is given by Q(L) = 5 - P, and Maggie’s demand is Q(M) = 15 - 3P (P is the price per ride). The marginal cost for the park of each ride is 1 dollar.

(a) Suppose that the park charges P = 3 dollars per ride. What is the maximal entrance fee that the park can charge so that Lisa will choose to enter? How many rides Lisa would do in this case?

(b) What is the two-part tariff (entrance fee plus price per ride) that the park should choose in order to extract all the surplus from Lisa? What would be the profit that the park extracts from Lisa and Maggie together in this case?

(c) Repeat the previous item with the two-part tariff that extracts all the surplus from Maggie. Hint: When you compute the profit think whether Lisa would choose to enter the park in this case.

(d) Suppose that the park offers two options: Either you pay an entrance fee of 22 dollars and then a price per ride of 1 dollar, or you enter for free and then pay 4 dollars per ride. Which option would Lisa choose in this case? What about Maggie? What is the profit that the park extracts from the two girls?

Answer 1