<p>There is no issue with the cost function.</p>
<p><span class="math-container">$p$</span> only equals <span class="math-container">$MC$</span> at the equilibrium and not for every quantity, as you have written. For example, if I produce <span class="math-container">$q=3$</span>, the price will not be <span class="math-container">$12$</span>.</p>
<p>To find the equilibrium price and quantity you should specify a demand function, so that you can find the point <span class="math-container">$(p,q)$</span> at which <span class="math-container">$MR=MC$</span>.</p>

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2022-10-13T18:06:45.573Z
Oh right! I see the details now. I assumed $p$ but I have to ensure that $p$ is determined wrt the demand function. So while we assume it an exogenous variable, to calculate the market price, we have to consider it in terms of $D(p)$. Once the market price is determined, then everything I wrote works (including treating $p$ as a constant). Is that correct?
Patricia
CC BY-SA 4.0
2022-10-13T17:17:58.470Z
2022-10-13T17:17:58.470Z
Fića
<p>Can <span class="math-container">$C(q) = 2q^2$</span> be the long-run cost in a perfectly competitive market? It appears that if <span class="math-container">$p$</span> is the long-run price, then <span class="math-container">$p = MC = 4q$</span> and profit turns out to be <span class="math-container">$\pi(q) = 0.125p^2 &gt; 0$</span>. In fact, the quantity is fixed while in a competitive market, any quantity should work.</p>

<microeconomics>
Long run profit example
Patricia
# Long run profit example

(Asked by: username_0 on 2022-10-13)

Can $C(q) = 2q^2$ be the long-run cost in a perfectly competitive market? It appears that if $p$ is the long-run price, then $p = MC = 4q$ and profit turns out to be $\pi(q) = 0.125p^2 > 0$. In fact, the quantity is fixed while in a competitive market, any quantity should work.

**Tags:** microeconomics

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## 1 answers

### Answer by username_1 on 2022-10-13. Score: 0 | Accepted answer

There is no issue with the cost function.

$p$ only equals $MC$ at the equilibrium and not for every quantity, as you have written. For example, if I produce $q=3$, the price will not be $12$.

To find the equilibrium price and quantity you should specify a demand function, so that you can find the point $(p,q)$ at which $MR=MC$.

> **Comments:**
> **username_0**: Oh right! I see the details now. I assumed $p$ but I have to ensure that $p$ is determined wrt the demand function. So while we assume it an exogenous variable, to calculate the market price, we have to consider it in terms of $D(p)$. Once the market price is determined, then everything I wrote works (including treating $p$ as a constant). Is that correct?  

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