<p>Consider a market served by two firms, firm <span class="math-container">$1$</span> and firm <span class="math-container">$2$</span>. Suppose that the (inverse) demands for the two firms are given by
<span class="math-container">$P_1=1-q_1-aq_2$</span>
<span class="math-container">$P_2=1-q_2-aq_1$</span> with <span class="math-container">$a$</span> belongs to <span class="math-container">$(0,1)$</span>.
In addition, suppose that the two firms face the same constant marginal costs equal to <span class="math-container">$c$</span> where <span class="math-container">$0&lt;c&lt;1$</span>
Suppose that both firms strategically choose prices to maximize own profits and firm <span class="math-container">$1$</span> chooses its price before firm <span class="math-container">$2$</span>. Using
• Derive and describe the best response functions of the two firms
• Derive and describe the prices, quantities and profits in equilibrium</p>

CC BY-SA 4.0
2023-11-06T23:20:33.427Z
You first write down the profit functions for both firms.  Then you calculate for a given $q_1$ the value $q_2$ that maximizes the profit of firm $2$. This will give you $q_2$ as a function of $q_1$. Plug the solution into the profit function of firm $1$ and solve the resulting profit maximization problem in a single variable, $q_1$. This gives you the choice of $q_1$. Plug it into your previous solution for firm 2 to get theiroptimal quantity. The rest should be easy.
Michael Greinecker
CC BY-SA 4.0
2023-11-08T19:24:26.737Z
Have you checked this post in wikipedia about Stackelberg competition? 

https://en.wikipedia.org/wiki/Stackelberg_competition

It is simple and veryhelpful!
Oliver Queen
<price><model>
How do I find the best response for a Stackberg duopoly with price leadership, specifically for the question below
Aarav
# How do I find the best response for a Stackberg duopoly with price leadership, specifically for the question below

(Asked by: username_0 on 2023-11-06)

Consider a market served by two firms, firm $1$ and firm $2$. Suppose that the (inverse) demands for the two firms are given by
$P\_1=1-q\_1-aq\_2$
$P\_2=1-q\_2-aq\_1$ with $a$ belongs to $(0,1)$.
In addition, suppose that the two firms face the same constant marginal costs equal to $c$ where $0<c<1$
Suppose that both firms strategically choose prices to maximize own profits and firm $1$ chooses its price before firm $2$. Using
• Derive and describe the best response functions of the two firms
• Derive and describe the prices, quantities and profits in equilibrium

**Tags:** price, model

> **Comments:**
> **username_1**: You first write down the profit functions for both firms.  Then you calculate for a given $q_1$ the value $q_2$ that maximizes the profit of firm $2$. This will give you $q_2$ as a function of $q_1$. Plug the solution into the profit function of firm $1$ and solve the resulting profit maximization problem in a single variable, $q_1$. This gives you the choice of $q_1$. Plug it into your previous solution for firm 2 to get theiroptimal quantity. The rest should be easy.  
> **username_2**: Have you checked this post in wikipedia about Stackelberg competition?   https://en.wikipedia.org/wiki/Stackelberg_competition  It is simple and veryhelpful!  

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## 0 answers

