ECON 101 University of California Los Angeles Equilibrium Prices and Profits Problems

1 Problem 1

Two rms – rm 1 and rm 2 – share a market for a speci c product. Both have zero marginal

cost. They compete in the manner of Bertrand and the market demand for the product is given

by: q = 20 ?? minfp1; p2g.

1. What are the equilibrium prices and pro ts?

2. Suppose the two rms have signed a collusion contract, that is, they agree to set the same

price and share the market equally. What is the price they would set and what would be

their pro ts?

For the following parts, suppose the Bertrand game is played for in nitely many times with

discount factor for both rms 2 [0; 1).

3. Let both players adopt the following strategy: start with collusion; maintain the collusive

price as long as no one has ever deviated before; otherwise set the Bertrand price. What is

the minimum value of for which this is a SPNE.

4. Suppose the policy maker has imposed a price

oor p = 4, that is, neither rm is allowed to

set a price below $4. How does your answer to part 3 change? Is it now larger or smaller?

Explain.