1
$\begingroup$

Firms A and B are in an oligopoly. They both face the linear market demand curve $X=A-\alpha P$, where $X$ is total market demand, and $P$ is price. Assume constant marginal costs $C_{A}$ and $C_{B}$, where $C_{B}<C_{A}$.

What will be the SPNE outcome if firm A sets price first? Is the following correct?

So long as firm A sets $P>C_{B}$, then it will get 0 profits (as firm B will profitably undercut and take all market demand). Therefore, it is indifferent between any $P>C_{B}$. If, however, A sets $P \leq C_{B}$, then firm B will not be able to profitably undercut, and so market demand will be split between the two firms, at some $P \leq C_{B}$. But then firm A will be making negative profits, and so can profitably deivate to setting some P>$C_{B}$.

Is this analysis correct? Or can firm A set some $p\leq C_{B}$ in an SPNE?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
-1
$\begingroup$

Your logic is correct. You need one more step. Using the same logic you can show that, in any SPNE, firm $A$ must set a price greater than the price that maximizes $B$'s profits. Firm $B$ then chooses such price.

Improve this answer
$\endgroup$
2
  • $\begingroup$ (-1) Answer is false. $\endgroup$
    – Giskard
    Jun 10, 2020 at 22:07
  • $\begingroup$ @Giskard I believe you, but it would be more useful if you tell me why so that I can fix it. $\endgroup$
    – brunosalcedo
    Jun 10, 2020 at 22:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.