EC332, Fall 2009, Prof. Jordi Jaumandreu
Problem set #4 .
1. (Cabral) In a market with annual demand
= 100
−
, there are two
fi
rms,
A and B, that make identical products. Because their products are identical, if
one charges a lower price than the other, all consumers will want to buy from
the lowerpriced
fi
rm. If they charge the same price, consumers are indi
ff
erent
and end up splitting their purchases about evenly between the
fi
rms. Marginal
cost is constant and there are no capacity constraints.
a. What are the singleperiod Nash equilibrium prices,
and
?
b What prices would maximize the two
fi
rms’ joint pro
fi
ts?
Assume that one
fi
rm cannot observe the other’s price until after it has set
its own price for the year.
Assume further that both
fi
rms know that if one
undercuts the other, they will revert forever to the noncooperative behavior
you described in a.
c If the interest rate is 10%, is one repeatedgame Nash equilibrium for both
fi
rms to charge the price you found in part b? What if the interest rate is 110%?
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 Spring '10
 tack
 Economics, Equilibrium, Game Theory, Cabral, repeatedgame nash equilibrium

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