Homework has SIX questions and it is due Tuesday, March 29, at the beginning of class.

1. Suppose two firms 1 and 2 compete in quantities and face a demand curve p = 100 - q. Suppose firm 1 has a constant marginal cost of 10 while firm 2 has a constant marginal cost of 40. Suppose they produce quantities simultaneously.

a. Find quantity produced by each firm in a Cournot equilibrium.

b. Find the market price and the consumer surplus. Suppose the firms merge, and form a single new firm that will operate at a constant marginal cost of 10.

c. Find the price charged by this new, single firm. d. Find the consumer surplus at this new price. Is it higher or lower than above?

2. Consider the same two firms as above with marginal costs 10 and 40, facing a demand p = 100 - q.

a. Find the market price and quantities produced if firm 1 moved first, followed by firm 2

b. Find the market price and quantities produced if firm 2 moves first, followed by firm 1.

c. Which of (a) or (b) would the consumers prefer? Explain.

3. Consider a Stackelberg game with three firms (1, 2 and 3) where firm 1 moves first and firm 3 moves last. What quantities will they choose if they have zero costs and the demand curve is p = 100 - q?

4. Consider a simultaneous move quantity-setting game with two firms facing a demand curve p = 100 - q. Both firms have marginal cost of 20. Suppose one firm maximizes profit and the other maximizes revenue, but both take into account the other firm's action while making its decision.

a. Find the quantities sold by each firm and the market price.

b. Who makes higher profit?

c. How would your answers change if each firm had a constant marginal cost of 60 (rather than 10)?

5. Consider two firms competing in prices and selling a homogeneous product. The market demand curve is p = 100 - q and the constant marginal costs of the two firms are 10 and 20 respectively. Also, suppose all prices should be integer numbers. Find the prices the two firms choose if they move simultaneously.

6. Consider two firms competing in prices and selling two products that are imperfect substitutes. They both have zero marginal costs and the demands faced by them are given by Q1 = 100 -4 p1 +2 p2 . Q2 =100-5p2 +p1

a. Find the reaction function for each firm. b. Using the reaction functions, find the optimal prices, quantities and profits for each firm. c. If firm 1 now has a marginal cost increase, how would the price charged by each firm change, and how would the profits change?

d. Suppose the two firms merge, and while the new entity still sells both products, it maximizes the
joint profit obtained from the two products. What would be the new prices set by the merged entity for each product?