<p>Your logic is correct. You need one more step. Using the same logic you can show that, in any SPNE, firm <span class="math-container">$A$</span> must set a price greater than the price that maximizes <span class="math-container">$B$</span>'s profits. Firm <span class="math-container">$B$</span> then chooses such price. </p>

CC BY-SA 4.0
2020-06-10T22:07:45.333Z
(-1) Answer is false.
Giskard
CC BY-SA 4.0
2020-06-10T22:24:02.753Z
@Giskard I believe you, but it would be more useful if you tell me why so that I can fix it.
brunosalcedo
CC BY-SA 4.0
2020-06-10T21:09:33.983Z
2020-06-10T21:09:33.983Z
brunosalcedo
<p>Firms A and B are in an oligopoly. They both face the linear market demand curve <span class="math-container">$X=A-\alpha P$</span>, where <span class="math-container">$X$</span> is total market demand, and <span class="math-container">$P$</span> is price. Assume constant marginal costs <span class="math-container">$C_{A}$</span> and <span class="math-container">$C_{B}$</span>, where <span class="math-container">$C_{B}&lt;C_{A}$</span>.</p>

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

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

<p>Is this analysis correct? Or can firm A set some <span class="math-container">$p\leq C_{B}$</span> in an SPNE?</p>

<microeconomics><game-theory><industrial-organisation>
Sequential price setting SPNE
George
# Sequential price setting SPNE

(Asked by: username_0 on 2020-06-10)

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}.

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?

**Tags:** microeconomics, game-theory, industrial-organisation

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## 1 answers

### Answer by username_1 on 2020-06-10. Score: -1

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.

> **Comments:**
> **username_2**: (-1) Answer is false.  
> **username_1**: @Giskard I believe you, but it would be more useful if you tell me why so that I can fix it.  

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