Question

Two duopolists have the following market demand and cost structures.

P = 2000 – 2Q; MR= 2000-4Q

MC is constant at 400, and FC=0

1. If the firms cooperate to set quantity, what will cartel quantities, prices, and profits be? Make sure to identify each firm’s q, P and profits as well [6]
2. One firm cheats to lower its price by $100. What happens to the quantity and profits of this firm? If the other firm does not reduce its price and consumers have perfect information, what happens to the profits of the other firm? [3+2]
3. If the other firm now also lowers their price by the same amount, and both firms agree to take half of the market, calculate individual profit for each firm. [5]
4. Does either firm have a dominant strategy? You can assume they each have an option of charging the profit maximizing price (see (a)) or the “cheating on cartel” price. Explain your answer. [5]
5. If the firms continue to undercut each other, what will the price become? Is this a strange result? [4]

Answer 1