<p>Your intuition is correct (assuming that you mean <span class="math-container">$MC &lt; P$</span> rather than <span class="math-container">$MC &gt; P$</span> as you wrote). For a given level of production, profits are indeed higher when <span class="math-container">$MC &lt; P$</span> than when <span class="math-container">$MC = P$</span>, as you'd expect from an increase in the price holding everything else constant. </p>

<p>So why do we say that a firm in a competitive market maximizes profit by setting <span class="math-container">$P = MC$</span>? Because we're not looking at <em>an increase in the price holding everything else constant</em>, we're looking at <em>a change in the quantity, holding price constant</em>.</p>

<p>It may help to think first about the traditional model of monopoly, where a monopolist will maximize profit by choosing a quantity <span class="math-container">$Q$</span> that sets <span class="math-container">$MC = MR$</span>, i.e. marginal cost = marginal revenue. Then, because they're a monopolist, they can sell that quantity <span class="math-container">$Q$</span> at a price <span class="math-container">$P &gt; MR$</span> (and so we get <span class="math-container">$P &gt; MR = MC$</span> or <span class="math-container">$P &gt; MC$</span>). This is because the monopolist has some control over their price: they can choose to go high price/low quantity or low price/high quantity. In the process of selling an additional unit, their revenue goes up (<span class="math-container">$MR$</span>) by <em>less</em> than the price (<span class="math-container">$MR &lt; P$</span>), since they're moving towards the "low price/high quantity" end of the scale - they get paid the price <span class="math-container">$P$</span> by selling an additional unit, but they had to lower their price too and so make less on the other units they sell, making <span class="math-container">$MR &lt; P$</span>.</p>

<p>That takes us back to the competitive market. In the competitive market, each firm has no control over the price and so there's no price/quantity tradeoff - whatever quantity they pick, the price stays the same. So, in a competitive market, <span class="math-container">$P = MR$</span> by definition. So when they maximize their profit by choosing a quantity that sets <span class="math-container">$MR = MC$</span>, since <span class="math-container">$P = MR$</span> we get <span class="math-container">$P = MR = MC$</span> or <span class="math-container">$P = MC$</span>.</p>

<p>Intuitively, the reason the firm in the competitive market doesn't shoot for <span class="math-container">$P &gt; MC$</span> is that the price is real darn stubborn. You can't coax it to go higher by picking a lower quantity (like you could if you were a monopoly). So it's not "I'd like to pick a price higher than my <span class="math-container">$MC$</span>" because you can't pick a price. Instead, it's "I may as well continue producing more and more until my <span class="math-container">$MC$</span> meets the price". So, for a firm in a competitive market, profit is maximized at <span class="math-container">$P = MC$</span>.</p>

CC BY-SA 4.0
2019-04-24T09:52:47.120Z
2019-04-24T09:52:47.120Z
NickCHK
<p>Isn't MC>P a better aim? Given the revenue you earn from each unit is more than cost in producing each unit? </p>

CC BY-SA 4.0
2019-04-24T05:31:49.323Z
I think you mean MC < P, don't you? i.e. marginal cost less than price? (not greater than)
410 gone
CC BY-SA 4.0
2019-04-24T05:45:08.667Z
Also, aim in terms of what...? My aim is to have MC = \$0, P = \$10 billion and Q = 1, but perhaps that is not possible given the model?
Giskard
CC BY-SA 4.0
2019-04-24T08:28:52.987Z
The MC is not the cost of producing each unit. Rather, it is the change in total cost when you produce one more unit.
David
<microeconomics>
Why is Marginal Cost = Price better than Marginal Cost > Price for maximizing profit?
Kal
# Why is Marginal Cost = Price better than Marginal Cost > Price for maximizing profit?

(Asked by: username_0 on 2019-04-24)

Isn't MC>P a better aim? Given the revenue you earn from each unit is more than cost in producing each unit?

**Tags:** microeconomics
> **Comments:**
> **username_1**: I think you mean MC < P, don't you? i.e. marginal cost less than price? (not greater than)  
> **username_2**: Also, aim in terms of what...? My aim is to have MC = \$0, P = \$10 billion and Q = 1, but perhaps that is not possible given the model?  
> **username_3**: The MC is not the cost of producing each unit. Rather, it is the change in total cost when you produce one more unit.  

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## 1 answers

### Answer by username_4 on 2019-04-24. Score: 1

Your intuition is correct (assuming that you mean $MC < P$ rather than $MC > P$ as you wrote). For a given level of production, profits are indeed higher when $MC < P$ than when $MC = P$, as you'd expect from an increase in the price holding everything else constant.

So why do we say that a firm in a competitive market maximizes profit by setting $P = MC$? Because we're not looking at *an increase in the price holding everything else constant*, we're looking at *a change in the quantity, holding price constant*.

It may help to think first about the traditional model of monopoly, where a monopolist will maximize profit by choosing a quantity $Q$ that sets $MC = MR$, i.e. marginal cost = marginal revenue. Then, because they're a monopolist, they can sell that quantity $Q$ at a price $P > MR$ (and so we get $P > MR = MC$ or $P > MC$). This is because the monopolist has some control over their price: they can choose to go high price/low quantity or low price/high quantity. In the process of selling an additional unit, their revenue goes up ($MR$) by *less* than the price ($MR < P$), since they're moving towards the "low price/high quantity" end of the scale - they get paid the price $P$ by selling an additional unit, but they had to lower their price too and so make less on the other units they sell, making $MR < P$.

That takes us back to the competitive market. In the competitive market, each firm has no control over the price and so there's no price/quantity tradeoff - whatever quantity they pick, the price stays the same. So, in a competitive market, $P = MR$ by definition. So when they maximize their profit by choosing a quantity that sets $MR = MC$, since $P = MR$ we get $P = MR = MC$ or $P = MC$.

Intuitively, the reason the firm in the competitive market doesn't shoot for $P > MC$ is that the price is real darn stubborn. You can't coax it to go higher by picking a lower quantity (like you could if you were a monopoly). So it's not "I'd like to pick a price higher than my $MC$" because you can't pick a price. Instead, it's "I may as well continue producing more and more until my $MC$ meets the price". So, for a firm in a competitive market, profit is maximized at $P = MC$.


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