Question

3. ZipCar is the only car sharing company in Burlington. There are two kinds of car users in Burlington: frequent users (F-types) and infrequent users (I-types). The weekly demand for car trips for a representative F-type is qF = 10 – p while the weekly demand for car trips for a representative I-type is qI = 8 – p. Suppose there are ten F-types and ten I-types in Burlington. ZipCar estimates that the marginal cost of each car trip is 2 and that it incurs a fixed cost of 100 per week. a. Suppose ZipCar adopts the simplest possible pricing strategy of setting a single uniform price for each car trip for any potential customer. To maximize profits, what price should ZipCar charge per trip and how many car trips will be made? Compute ZipCar’s profits under this uniform pricing scheme. b. Suppose ZipCar discovers that all F-type customers are men and all I-type customers are women. Assuming that ZipCar can charge a different price per car trip for women and men, what prices should it charge and how many car trips will be made by men and by women? Compute ZipCar’s profits under this new pricing scheme. c. ZipCar hires a management consultant who says that the company could earn more money by requiring all customers to pay a weekly membership fee and charging a price per car trip that just covers ZipCar’s marginal costs. If ZipCar is determined to service the entire market, what is the maximum price it can charge for a membership? What are ZipCar’s profits under this system? d. ZipCar likes this idea of charging all customers the same weekly membership fee and all customers the same price per ride. However, does the pricing scheme proposed by the management consultant maximize ZipCar’s profits? If not, what combination of membership fee and price per ride would maximize ZipCar’s profits. And how much profit would ZipCar earn? e. An economist tells ZipCar that the company could earn even more money by setting up two different membership categories, A and B. Category A members would pay a higher membership fee than Category B members, but would be entitled to purchase more trips per week (at a constant price per trip) than Category B members. Describe how these two membership categories should be structured. Specifically, how much should ZipCar charge for each type of membership and how many car trips should each membership package include to maximize its profits?

Answer 1

A. Under uniform pricing, we add the two demand equations and take a common price as p

Total quantity demanded = 18-2P

Total Revenue = 18P - 2P²

^{Marginal revenue = 18-4P =MC =2 (in equilibrium}  

^16=4P

^P=4

^{Quantity produced = 18-2(4)=10}

^{Profits =10(4-2)=20}

^{Taking differential prices}

For men, total revenue =10P-P²

Marginal revenue =10-2P =MC=2

P=4

Q =10-4=6

IN CASE OF FEMALES,

Total Revenue =8P - P²

MR =8-2P =MC =2

P=3

Q =8-3=5

PROFITS = 5(3)+4(6)-2(5+6)=39-22=17