<blockquote>
<p>In most models, perfect competition implies that MC = P, shouldn't it be the average cost that is equal to price instead?</p>
</blockquote>
<p>No, you can verify it yourself mathematically.  In perfect competition firms take price <span class="math-container">$p$</span> as fixed so the profit function is given by:</p>
<p><span class="math-container">$$\Pi = pq -c(q)$$</span></p>
<p>Where <span class="math-container">$q$</span> is quantity produced and <span class="math-container">$c$</span> is cost function. Because firm is is a <em>price taker</em> in perfect competition it cannot control price only quantity, so firm choice variable is <span class="math-container">$q$</span>.</p>
<p>Now if firm <em>maximizes profit</em> we take derivative of profit function wrt <span class="math-container">$q$</span> to find  first order condition for profit maximization which is:</p>
<p><span class="math-container">$$p-c'(q)=0 \implies p=c'(q)$$</span></p>
<p><span class="math-container">$c'(q)$</span> is unambiguously marginal cost not average cost (which would be <span class="math-container">$c(q)/q$</span>). So it is indeed a marginal cost not average cost.</p>
<blockquote>
<p>If the Average Cost is greater than the Marginal Cost, firms are losing money when they sell at their price P = MC.</p>
</blockquote>
<p>It is possible for perfectly competitive firm to have economic loss in a short-run even if it maximizes profit.</p>
<p>There is not much that firm can do here. Perfectly competitive firm cannot charge higher price than exogenously given (from the point of view of the firm) market price without loosing all customers. So <span class="math-container">$p$</span> is fixed, <span class="math-container">$q$</span> is already set optimally so that profit is maximized (the maximum value of profit can still be negative number). Only other option is to shut down production altogether, but by assumption that can happen only in long-run since in microeconomics short run is defined as a time period when firm dont have enough time to enter/exit market.</p>

CC BY-SA 4.0
2022-01-28T15:38:31.863Z
2022-01-28T15:38:31.863Z
1muflon1
<p>in the short run, firms fix the price of goods based on their variable costs and ignore the fixed cost. so while pricing goods profit-maximizing firms ensure P=MC at least, where p=price and MC=marginal cost. but in long run, it should produce at a point where its average cost(AC) is minimum.</p>
<p>similarly, in the perfect market condition, we assume that there are no fixed costs which increases the barrier of entry for a new firm. so no fixed cost means, variable costs or marginal cost(MC) will be the same as average cost(AC). thus in perfect market P=MC.</p>

CC BY-SA 4.0
2022-01-30T22:20:42.757Z
No fixed costs *increases* the barrier of entry?
Herr K.
CC BY-SA 4.0
2022-01-29T17:39:11.193Z
2022-01-29T17:39:11.193Z
Sumit Kumar Jha
<p>In most models, perfect competition implies that MC = P, shouldn't it be the average cost that is equal to price instead?</p>
<p>If the Average Cost is greater than the Marginal Cost, firms are losing money when they sell at their price P = MC.</p>

CC BY-SA 4.0
2022-01-28T15:50:58.423Z
Does this answer your question? [Why is Marginal Cost = Price better than Marginal Cost > Price for maximizing profit?](https://economics.stackexchange.com/questions/28959/why-is-marginal-cost-price-better-than-marginal-cost-price-for-maximizing-pr)
Giskard
<microeconomics><perfect-competition>
Why Marginal Cost (MC) equal Market Price (PC)?
Kien
# Why Marginal Cost (MC) equal Market Price (PC)?

(Asked by: username_0 on 2022-01-28)

In most models, perfect competition implies that MC = P, shouldn't it be the average cost that is equal to price instead?

If the Average Cost is greater than the Marginal Cost, firms are losing money when they sell at their price P = MC.

**Tags:** microeconomics, perfect-competition

> **Comments:**
> **username_1**: Does this answer your question? [Why is Marginal Cost = Price better than Marginal Cost > Price for maximizing profit?](https://economics.stackexchange.com/questions/28959/why-is-marginal-cost-price-better-than-marginal-cost-price-for-maximizing-pr)  

---

## 2 answers

### Answer by username_2 on 2022-01-28. Score: 1 | Accepted answer

> In most models, perfect competition implies that MC = P, shouldn't it be the average cost that is equal to price instead?

No, you can verify it yourself mathematically. In perfect competition firms take price $p$ as fixed so the profit function is given by:

$$\Pi = pq -c(q)$$

Where $q$ is quantity produced and $c$ is cost function. Because firm is is a *price taker* in perfect competition it cannot control price only quantity, so firm choice variable is $q$.

Now if firm *maximizes profit* we take derivative of profit function wrt $q$ to find first order condition for profit maximization which is:

$$p-c'(q)=0 \implies p=c'(q)$$

$c'(q)$ is unambiguously marginal cost not average cost (which would be $c(q)/q$). So it is indeed a marginal cost not average cost.

> If the Average Cost is greater than the Marginal Cost, firms are losing money when they sell at their price P = MC.

It is possible for perfectly competitive firm to have economic loss in a short-run even if it maximizes profit.

There is not much that firm can do here. Perfectly competitive firm cannot charge higher price than exogenously given (from the point of view of the firm) market price without loosing all customers. So $p$ is fixed, $q$ is already set optimally so that profit is maximized (the maximum value of profit can still be negative number). Only other option is to shut down production altogether, but by assumption that can happen only in long-run since in microeconomics short run is defined as a time period when firm dont have enough time to enter/exit market.


---

### Answer by username_3 on 2022-01-29. Score: 0

in the short run, firms fix the price of goods based on their variable costs and ignore the fixed cost. so while pricing goods profit-maximizing firms ensure P=MC at least, where p=price and MC=marginal cost. but in long run, it should produce at a point where its average cost(AC) is minimum.

similarly, in the perfect market condition, we assume that there are no fixed costs which increases the barrier of entry for a new firm. so no fixed cost means, variable costs or marginal cost(MC) will be the same as average cost(AC). thus in perfect market P=MC.

> **Comments:**
> **username_4**: No fixed costs *increases* the barrier of entry?  

---

