1 Problem Set #4 – ECON 121A, Fall Quarter 2022 Name:_______________________
Due: Monday, November 14 at 11:59pm. Problem sets are to be turned in through Grade scope
In order to receive credit, you must show your work and explain your answer in
words.
1. Suppose there are two firms in a market where the market demand of a product is
given by: P(Q) = 60 – Q
Q = q1 + q2
The costs of each firm are: c(qi) = 10qi + 25
Firm 1 is the quantity leader and firm 2 is the quantity follower .
The firms are selling identical products.
a. What are the profits of each firm in a regular Stackelberg setting? Show all of your work.
b. Suppose that firm 1 decides that it is going to produce 44 units. Will this increase its
profits relative to part ‘a’ above? Show your work.
c. Is there another quantity that firm 1 should produce in order to increase its profits?
Assume that firm 2 will leave the market if its profits are less than or equal to 0.
2. What is the main difference in the reaction functions when firms compete by setting quantity versus when firms compete by setting price? Briefly explain. You do not need to write down any equations representing the reaction functions.
3. The following tree diagram depicts the example we did in class of Davistech and Aggietech.
Recall that Davistech is the incumbent firm and Aggietech is thinking of entering the market.
However, there is uncertainty regarding whether Davistech is a low-cost or high-cost
producer. All Aggietech sees is what price Davistech charges .
a. What is the rationale behind Davistech pretending to be a low-cost producer even when it’s a high-cost producer?
b. As the probability (p) of Davistech being a low-cost producer increases, how would this affect the other firm, Aggietech?
4. Suppose there is a sandwich shop selling lemonade and sandwiches separately.
The marginal cost of lemonade is $2 and the marginal cost of sandwiches is $3. There is a new potential entrant in the lemonade market with a marginal cost of $1. Assume the lemonade is identical from either place.
The table below depicts the valuation for lemonade and sandwiches of different consumers.
Consumer Value of
Lemonade
Value of
Sandwich
1 1.0 2.0
2 1.5 5.5
3 3.4 4.6
4 4.0 4.0
5 4.5 7.0
6 5.0 9.0
7 3.0 4.0
a. Suppose the entrant sells lemonade for $2 while the incumbent sells lemonade for $3.
How many consumers will buy lemonade and who will they buy it from?
b. What would happen if the incumbent stops selling lemonade and sandwiches separately, but bundles them and sells the bundle for $6.50. Which consumers will buy lemonade for $2 and which will buy the bundle for $6.50?
5. Suppose the market demand for tires is given by P = 100 – 2Q
There are two firms: Q = q1 + q2
The marginal cost of producing each tire is 20, there are no fixed costs, and the firms are producing identical products. The firms usually compete in a Cournot type setting by choosing the quantity they are going to produce simultaneously.
a. How many units should each firm produce if they form a cartel? What would the profits of each firm be?
b. How much profits will a firm gain by deviating from the agreed upon quantity in part ‘a’?
Assume the non-deviating firm continues to produce the amount agreed upon in part ‘a’.
c. Why will a cartel never sustain itself when the interaction between the two firms is for a finite number of periods?
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