ECONOMICS 121A INDUSTRIAL ORGANIZATION SPRING QUARTER 2009 PROFESSOR REQUENA PROBLEM SET 2
DUE: APRIL 17TH
PROBLEM 1 A food co-op sells a homogenous good, called groceries, with the quantity sold denoted by q. The co-op´s cost function is described by C (q ) = F + cq , where F denotes fixed costs and c is the constant per-unit variable cost. At the meeting of the co-op board, a young economist proposes the following marketing strategy for the co-op: Set a fixed membership fee, M, and a price per unit groceries, p M , that members pay. In addition, set a price per unit of groceries, p N , higher than p M at which the co-op will sell groceries to non-members. a. What must be true about the demand of different customers for this strategy to work? The consumers who join must have a higher demand for groceries than those who do not. Since they are willing to buy more groceries as a given price, the co-op would like to give them a quantity discount. b. What kinds of price discrimination does this strategy employ? This is an example of second price discrimination.
PROBLEM 2 A night club owner has both student and adult customers. The demand for drinks by a typical student is Q S = 18 − 3P . The demand for drinks by a typical adults is Q A = 10 − 2 P . There are equal number of students and adults. The marginal cost of each drink is $2. a. What price will the owner set if she cannot discriminate between the two groups? What will her total profit be at this price?
Aggregate demand is Q S + A
=
(18 − 3P) + (10 − 2 P) = 28 − 5 P , inverse demand is
+ + P = 28 / 5 − 1 / 5Q S A and marginal revenue is MR = 28 / 5 − 2 / 5Q S A
MR=MC, that is , 28 / 5 − 2 / 5Q S + A = 2 Q S + A = 9 Her profits without price discrimination: π = ( P − 2)Q = 16.2 →
b. If the club owner could separate the groups and practice third-degree price discrimination what price per drink would have charged to members of each group? What would be club´s owner profits?
If the club owner can price discriminate, she will equate marginal revenue and marginal cost for each group. That is, S S 6 − 2 / 3Q S = 2 Q =6 P =4 →
→
A 5−QA = 2 Q A = 3 P = 3.5 Hence, total profit with price discrimination is S A = ( 4 − 2)(6) + (3.5 − 2)(3) = 12 + 4.5 = 16.5 π + π →
→
c. If the owner can “card” patrons and determine who among them is a student and who is not and , in turn, can serve each market by offering a cover charge and a number of drink tokens to each group, what will be the cover charge and the number of tokens given to students be? What will be the cover charge and the number of tokens given to adults? What is the club owner´s profit under this regime?
In this scenario, the owner club can practice two-part pricing. For each group, the number of token will be equal to quantity demanded at price $2, which is the marginal cost of a drink. Number of tokens for students = 18 − 3(2) = 12 Number of tokens for the adults = 10 − 2(2) = 6 Now for each group, the cover charge should equal the consumer surplus received at the given number of tokens. That is, 1 Cover charge for students = (6 − 2)(12) + 2(12) = 48 2 1 Cover charge for an adult = (5 − 2)(6) + 2(6) = 21 2 Therefore, her profits = Total revenue – total cost of drinks = 1 1 (6 − 2)(12) + 2(12) + (5 − 2)(6) + 2(6) − 2(12) − 2(6) = 33 2 2
PROBLEM 3 A country club knows that all of its customers have a (inverse) demand curve for golf rounds of P = 500 – Q, per year. Furthermore, because it is so exclusive and there are not many members, the marginal cost of a round of golf is essentially zero. (a) Suppose the management of the country club charged just one uniform price. Calculate the optimal price and the per member profit that the country club earns.
Profit maximization:
π
= 500Q − Q
2
∂π →
∂Q
= 500 − 2Q =
0
→
Q U = 250
→
P
U
=
250
Total profits: 250*250 Per member profits= 250 (b) Now suppose the management took 121A and is interested in designing a two-part tariff (a fixed fee and a per golf round fee). What would be the fixed fee? What would be the per round fee? What would per member profits be? 1 (500 − 0) 2 = $125000 2 Profit per round = 0 Consequence: max demand = 500
Calculate the consumer surplus: CS Golf round fee=0
→
=
→
Q = 500 members Per member fee = $125000/500 = $250 Monopoly gets the entire consumer surplus.
PROBLEM 4 A university has determined that its students fall into two categories when it comes to room and board demand. University planners call these two types Sleepers and Eaters. The reservation prices for a dormitory room and the basic meal plan of the two types are as follows:
DORM ROOM MEAL PLAN
SLEEPERS $5,500 $2,500
EATERS $3,000 $6,000
Currently, the university offers students the option of selecting just the dorm room at $3,000, just the meal plan at $2,500, or both for a total price of $5,500. An economic consultant advises the university to stop offering the two goods separately and, instead, to sell them only as a single, combined room and board package. Explain the consultant´s strategy and determine what price the university should set for the combined product.
Answer: By allowing the student to pick and choose rather than buying a bundle, each group is getting one of the items at a price well below their reservation price. While the sleepers get no consumer surplus from the meal plan price of $2500, they get $2500 in consumer surplus from the dorm price of $3000 or the package price of $5500. Similarly, the eaters get surplus $3500 from the meal plan price of $2500 or the package price of $5500. By creating a bundle the university can capture a large amount of this consumer surplus.
Assuming all students need to sleep and eat, a package price of $8000 would significantly raise revenue. This would exhaust all the surplus of the sleepers and all but $1000 of the surplus of the eaters.