Economics 160A: Industrial Organization
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Economics 160A: Industrial Organization
Practice Final Exam
1) You have been hired as a consultant for Caribou Coffee. Caribou faces two types of customers: type H are high demand and type L are low demand. The type L customers have the following inverse demand function for ounces of coffee (price is in cents per ounce): P = 35 – Q. Type H customers have an inverse demand of P = 45 – Q. Assume that the marginal cost of an ounce of coffee is 15 cents.
Initially, the firm tells you that it is able to identify customers of each type and that it would like to offer two drink sizes—one for each customer type.
a) What drink size should be offered to type L consumers, and at what price? What drink size should be offered to type H consumers, and at what price? (HINT: Think in terms of the total price.) (10 Points)
Continue with the same setup. But Caribou Coffee now tells you that it cannot identify the customers of each type. That is, when a customer walks in the door, Caribou does not know if he/she is type H or type L. You explain to Caribou that they can still design the prices of the small and large drinks so that the high demand consumers will voluntarily choose to buy the large drink and the low demand consumers will choose to consume the small drink. Intrigued, the firm asks for more details.
b) Suppose that Caribou offers the same size and price to the low types as it did in part a) above. If a type H consumer were to buy this small drink, how much surplus would she receive? (10 Points)
c) Given your calculation in (a), how much should the large drink cost? (10 Points)
d) Now let’s analyze the incentive to “degrade” the low type’s package. Suppose that Caribou Coffee reduces the number of ounces in the small drink by 2. By how much will Caribou have to reduce the price of the small drink so that the low types continue to buy? (10 Points)
e) By reducing the size of the small drink by 2 ounces, Caribou Coffee will be able to raise the price of high demand package. What is the highest price it can charge for the high demand package? (10 Points)
2) Suppose that Northwest Airlines has a monopoly on flights from Detroit to Minneapolis. Further suppose that customers are only willing to fly between 8:00 AM and 8:00 PM each day. Each consumer has an optimal flight time x. Across consumers, x is uniformly distributed between 8:00 AM and 8:00 PM. Each
consumer’s willingness to pay for a flight at her optimal time x is $200 (you may refer to this value as V). The disutility associated with a flight time 1 hour from her optimal flight time is $10. For simplicity, assume that the marginal cost of a flight is zero and that the firm sets the highest price that still provides the good to all customers.
a) If Northwest offers only one flight, at what time should the flight be and what price should Northwest charge? (10 Points)
b) If Northwest offers two flights, at what time should the flights be and what single price should Northwest charge? (10 Points)
3) There are two breweries in Ann Arbor, Arbor Brewing Company (ABC) and Grizzly Peak (GP). Each firm can choose to produce a low (L), medium (M), or high (H) quantity of beer. In a one-shot quantity game, their payoffs are given by the following game matrix (the first element in each pair of payoffs is the payoff of ABC, the second one is the payoff of GP):
a) Find the Nash Equilibrium (NE) of this game. (10 Points)
b) Suppose that ABC could commit to and publicly announce its strategy (L, M, or
H) before GP made its decision. What would ABC commit to? What is the most that ABC would be willing to pay to gain the ability to commit? (10 Points)
4) There are two firms in the market that compete in quantities (i.e., Cournot competition). The total cost of firm 1 is given by C₁(Q₁) = (Q₁)² , i.e., the total cost equals the level of production squared. The total cost of firm 2 is given by C2(Q2) = (Q2)² , i.e., the total cost equals the level of production squared. The market demand is given by the equation
P(Q₁ + Q₂) = 30 - (Q₁ + Q₂).
Find the equilibrium level of production of each firm and the equilibrium market price. (10 Points)
2022-03-15