Econ 316: Industrial Organization
Logistics The due time is the beginning of class, for your specific class (i.e. 9:30 or 11:00AM). There are two ways to hand it in: 1. Email a readable copy of the homework to the CA. 2. Hand in at the beginning of class as you come in. The problem sets will be collected before the end of the reading reaction. We will accept problem sets up to exactly 48 hours late for full credit. In other words, you may submit the problem sets via email or at the beginning of class on Wednesdays and still receive full credit. However, problem sets submitted later than this will receive zero credit. Group work is encouraged. However, each person should write and submit his or her own answers. Copying answers from other students, from some third party or tutor, or from any other resource is not permitted. At the top of your problem set, include: ? Your group members’ names ? An estimate of how much time you spent on the problem set There are 20 possible points, plus five points of extra credit. Hotelling Model Problem H1 (8 points) In-N-Out Burger is trying to determine the optimal placement of its restaurants between San Jose and San Diego. Each consumer has a preferred restaurant location (x) and incurs travel disutility of $0.10 for every mile between x and the closest store. Each day, 5000 people between San Jose and San Diego might purchase from In-N-Out. They are uniformly distributed along the 500 miles between San Jose and San Diego. Consumers will buy one burger if the price plus travel disutility is less than $5. The marginal cost of a burger is $1 and the fixed cost of a store is $100 per day. Hint: This is a standard Hotelling monopoly model as described in lecture. Imagine that In-N-Out maximizes profits a. How many restaurants will In-N-Out build? b. What will be the price of a burger? In-N-Out is known to be socially minded. Imagine that it instead maximizes total surplus instead of profits. c. How many restaurants will In-N-Out build? d. What will be the price (or range or prices) of a burger? e. Explain the difference (or similarity) between (a) and (c). (3 sentences or less.) Problem H2 (3 points) Now, imagine that In-N-Out can deliver to consumers at their specific location x. Delivery costs are $0.10 per mile. Hint: This is Hotelling with delivery, as described in 7.4. Re-read 7.4 and it is straightforward to see how to proceed. a) What is the profit-maximizing price of a (delivered) burger? b) How many restaurants will In-N-Out build if it maximizes profits? c) How many restaurants will In-N-Out build if it maximizes total surplus? d) Explain the difference (or similarity) between (b) and (c). (3 sentences or less.) Bundling Problem B1 (4 points) Consider the bundling model from Section 8.1.1 of Pepall. Now assume that each good can beproduced at marginal cost 0.2 per unit. (So the bundle can be produced at 0.4 per bundle.) a) What price does the monopolist charge to sell each separately? What are profits? b) What price does the monopolist charge if bundling? What are profits? Problem B2 (5 points) Continue to consider the bundling model from Section 8.1.1, except: for this problem, the distributions of WTP R1 and R2 are no longer independent. (R 1 and R2 are still uniformly distributed on [0,1].) Case 1: First assume that R1 and R2 are perfectly negatively correlated, so R1+R2=1 for all consumers. a) What price does the monopolist charge to sell each separately? What are profits? What is consumer surplus? b) What price does the monopolist charge if bundling? What are profits? What is consumer surplus? Case 2: Now assume that R1 and R2 are perfectly positively correlated, so R1=R2 for all consumers. c) What price does the monopolist charge to sell each separately? What are profits? What is consumer surplus? (Hint: This problem does not require additional calculations.) d) What price does the monopolist charge if bundling? What are profits? What is consumer surplus? e) In three sentences or less, give the intuition for the difference between Case 1 and Case 2. Problem B3 (Extra Credit: 5 points) Bundling is not always more profitable than selling products separately. Assume that Time Warner Cable offers two goods, Standard Cable and Cinemax. There are two types of consumers (Jin and Hunt) that exist in equal proportions but differ in their willingness-to-pay for Standard Cable vs. Cinemax, per the table below: Jin Hunt Cinemax: $40 $W Standard Cable: $16 $24 Determine the values of W for which bundling would be more profitable than not bundling. Explain (in three sentences or less) what this says about major networks (CBS, NBS, ABC) are bundled into a Standard Cable package but Cinemax is not. (Hint: Notice that the two consumer types have different preferences if the goods are sold separately. Do preferences tend to differ more across consumers for Cinemax or for the major networks?)