<p>First, there is an error in your last equation: You forgot to divide <span class="math-container">$2q$</span> by <span class="math-container">$b$</span>. But that doesn't help here, because the problem is that you are mixing things up. Your equation for <span class="math-container">$p$</span> describes the demand curve of the market, but in a competitive market individual firms are by assumption <em>price takers</em>, so they treat the price <span class="math-container">$p$</span> as a constant. Then, <span class="math-container">$R=pq$</span> and therefore <span class="math-container">$MR=p$</span>. (What you calculated is the <span class="math-container">$MR$</span> curve of a <em>monopolist</em> instead.)</p>
<p>Given this, and remembering that the profit maximizing <span class="math-container">$q$</span> is the one where <span class="math-container">$MR=MC$</span>, you can substitute <span class="math-container">$p$</span> for <span class="math-container">$MR$</span> and get that the supplied quantity <span class="math-container">$q$</span> is the one where <span class="math-container">$p=MC$</span>.</p>

CC BY-SA 4.0
2021-11-05T09:36:18.593Z
Thank you for the explanation. It makes sense now.
RadDragon
CC BY-SA 4.0
2021-11-05T08:39:56.163Z
2021-11-05T08:39:56.163Z
VARulle
<p>I am real learning microeconomics with a bit more math under my belt, but could not understand why the MR=P in competitive markets.
This was my attempt at reasoning
Given,
<span class="math-container">$R= P*q$</span><br />
For a linear demand curve <span class="math-container">$q=a-bp$</span><br />
<span class="math-container">$p= a-q/b$</span><br />
<span class="math-container">$R= aq-q^2/b$</span><br />
<span class="math-container">$MR= dR/dq$</span><br />
<span class="math-container">$MR=a-2q/b$</span><br />
Which doesn't seem equal to price<br />
I have two questions<br />
a) How did I go wrong ?<br />
b) How do we go from this to the MC curve being the supply curve mathematically ?</p>

<microeconomics><perfect-competition>
Supply and Demand Curves under Perfect Competition
RadDragon
# Supply and Demand Curves under Perfect Competition

(Asked by: username_0 on 2021-11-05)

I am real learning microeconomics with a bit more math under my belt, but could not understand why the MR=P in competitive markets.
This was my attempt at reasoning
Given,
$R= P\*q$  
For a linear demand curve $q=a-bp$  
$p= a-q/b$  
$R= aq-q^2/b$  
$MR= dR/dq$  
$MR=a-2q/b$  
Which doesn't seem equal to price  
I have two questions  
a) How did I go wrong ?  
b) How do we go from this to the MC curve being the supply curve mathematically ?

**Tags:** microeconomics, perfect-competition

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## 1 answers

### Answer by username_1 on 2021-11-05. Score: 0 | Accepted answer

First, there is an error in your last equation: You forgot to divide $2q$ by $b$. But that doesn't help here, because the problem is that you are mixing things up. Your equation for $p$ describes the demand curve of the market, but in a competitive market individual firms are by assumption *price takers*, so they treat the price $p$ as a constant. Then, $R=pq$ and therefore $MR=p$. (What you calculated is the $MR$ curve of a *monopolist* instead.)

Given this, and remembering that the profit maximizing $q$ is the one where $MR=MC$, you can substitute $p$ for $MR$ and get that the supplied quantity $q$ is the one where $p=MC$.

> **Comments:**
> **username_0**: Thank you for the explanation. It makes sense now.  

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