2. Consider a monopolist facing the demand curve p = 10 Q. The monopolist can ch

Question

2. Consider a monopolist facing the demand curve p = 10 Q.
The monopolist can
choose either of the following cost functions:
c1(q) = 3q
or
c2(q) = 10 + q.
a) Which cost function does the monopolist choose?
b) Now suppose that there is a second rm with cost function c1 (q) above. Whichever
cost function rm 1 chooses, the second rm will observe this choice and then have the
option of entering the market or not. If he does not enter, rm 1 remains a monopolist
with the chosen cost function. If rm 2 does enter, he pays an entry cost of $4 and the
two rms compete as Cournot duopolists. More precisely, whichever cost function rm 1
chose, we have a pure strategy Nash equilibrium in quantity choices. Which cost function
does rm 1 choose now? Put dierently, what is the subgame perfect equilibrium of this
game?

Explanation / Answer

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