<p>Yes, you can have different marginal costs in a Cournot model. Here is a simple example:</p>
<p>Two firms with marginal costs of <span class="math-container">$c_1$</span> and <span class="math-container">$c_2$</span> competing in quantities where inverse demand is <span class="math-container">$p=A-b(q_1+q_2)$</span>. Firms are maximizing:
<span class="math-container">$$\max_{q_i} \; (A-b(q_1 + q_2))q_i - c_i q_i$$</span>
Taking a derivative and solving you can find unique quantities, e.g.
<span class="math-container">$$q_1 = \frac{A+2b(c_1 -A) - c_2}{4b^2 -1}$$</span></p>
<p>You mention that marginal costs are often given as &quot;fixed&quot;. This is often done for simplicity. It can be challenging to solve a Cournot model with increasing/decreasing returns and an equilibrium may not exist.</p>

CC BY-SA 4.0
2022-10-29T20:53:55.610Z
May I ask do you use some apps to write formulas?
Nick
CC BY-SA 4.0
2022-10-29T20:56:45.347Z
No, you can find more information about how to write math (LaTeX) on Stack Exchange here: https://economics.stackexchange.com/editing-help#latex
Fića
CC BY-SA 4.0
2022-10-29T20:49:48.587Z
2022-10-29T20:49:48.587Z
Fića
<p>I am confused that If the marginal costs of the two firms are different, is it still a Cournot model?
I saw many examples that  give a fixed marginal cost of the products.</p>

<microeconomics>
A Cournot question
Nick
# A Cournot question

(Asked by: username_0 on 2022-10-29)

I am confused that If the marginal costs of the two firms are different, is it still a Cournot model?
I saw many examples that give a fixed marginal cost of the products.

**Tags:** microeconomics


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## 1 answers

### Answer by username_1 on 2022-10-29. Score: 2 | Accepted answer

Yes, you can have different marginal costs in a Cournot model. Here is a simple example:

Two firms with marginal costs of $c\_1$ and $c\_2$ competing in quantities where inverse demand is $p=A-b(q\_1+q\_2)$. Firms are maximizing:
$$\max\_{q\_i} \; (A-b(q\_1 + q\_2))q\_i - c\_i q\_i$$
Taking a derivative and solving you can find unique quantities, e.g.
$$q\_1 = \frac{A+2b(c\_1 -A) - c\_2}{4b^2 -1}$$

You mention that marginal costs are often given as "fixed". This is often done for simplicity. It can be challenging to solve a Cournot model with increasing/decreasing returns and an equilibrium may not exist.

> **Comments:**
> **username_0**: May I ask do you use some apps to write formulas?  
> **username_1**: No, you can find more information about how to write math (LaTeX) on Stack Exchange here: https://economics.stackexchange.com/editing-help#latex  

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