EC 360 SPRING 2023: PROBLEM SET 6
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EC 360 SPRING 2023: PROBLEM SET 6
Assignment date: Apr 18, 2023
Due date: Apr 27, 2023
Total Points: 15 points
Note: Your score will be based on your overall performance in answering all questions in this problem set. Answers to speciÖc questions will not be individually graded. Show all logical steps in your arguments. Answers without any explanation will get zero credit. You are strongly encouraged to work in groups (of at most three students) and submit one homework per group. You are allowed to discuss the homework with other groups and consult any other resources (internet, other text books, etc.).
(1) Consider a retailer serving a market with a demand curve given by:
Q = 10 一 2P
The downstream retailer (R) purchases the input at price w from an upstream manufacturer M . The manufacturer has a cost function of C(Q) = 2Q. So, the marginal cost is $2. What is the retail price p, wholesale price w, and quantity sold in this market? What are proÖts for the retailer and manufacturer? If the downstream retailer and the upstream manufacturer were integrated to form a single Örm, what retail price would it set? How much proÖt would the integrated Örm make?
(2) As you may note, the vertical relation in Question 1 su§ers from a double marginal- ization problem. We now consider two solutions to this problem:
(a) Suppose the upstream manufacturer o§ers a two-part pricing to the retailer. The pricing stipulates a wholesale price w and an up-front fee T that the retailer must pay to the manufacturer. What wholesale price and up-front fee should the manufacturer o§er so as it maximize its proÖt? How much proÖt would the retailer and the manufacturer make?
(b) Suppose that the downstream retailer R makes take-it-or leave it o§ers w to the manufacturer, specifying the price at which it will purchase the good. The manufacturer can then supply as much, or as little of the good as she chooses. What is the outcome of this scenario in terms of retail price p, wholesale price w, and quantity sold in this market? What are proÖts for the retailer and manufacturer?
(3) We now consider two variations in the vertical relationship described in Question 1.
(a) Suppose that the antitrust authority is now considering a merger between the upstream and downstream Örms. What are the e§ects of this merger if at present it is the manufacturer who chooses the price to sell its good? What are the e§ects of this merger at present the retailer makes take-it-or-leave it o§ers? Would you approve it if you did not know who makes o§ers to whom?
(b) Suppose that a second retailer R2 now enters, and both retailers compete in prices (as in Bertrand competition) in the downstream retail market. Suppose as well that the manufacturer chooses the price w that it will sell its good. What is the retail price p, wholesale price w, and quantity sold in this market? What are proÖts for the retailers?
(4) (This question is based on the entry deterrance example discussed in class.) In the market for carbonated water in France, Perrier, an incumbent Örm faces threat of entry from another company Evian. Evian can enter either with a small capacity (S) or a large one (L). But before Evian enters, Perrier can choose its own capacity level and make it known to all potential entrants. Perrier has three options: it can open either 1, or 2, or 3 plants. The table below summarizes the proÖts of the two Örms given their production capacities. Keep in mind that even though we present this information in a tabular form, it is understood that Perrier moves Örst, and seeing that, Evian moves second. The Örst number in each cell is Perrierís proÖt and the second number is Evianís proÖt.
Evian
S
|
300, 0 |
140, 70 |
115, 90 |
|
350, 0 |
110, 50 |
90, 40 |
|
325, 0 |
100, 30 |
50, 0 |
(a) What is the optimal capacity for Perrier if Evian is not going to enter (i.e., if Evian is going to choose capacity 0)?
(b) Now suppose Evian is indeed planning to enter provided it could make a positive proÖt net of entry cost. What is the optimal capacity for Perrier if Evianís entry cost is $25? What if the entry cost rises to $45? What if it further rises to $55? In which case do we have entry accommodation? When do we see entry deterrence? When do we see blockaded entry?
2023-04-28