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