<p>In the model of perfect competition firms do not set prices. They are price takers, i.e. they choose their quantities taking the price as given. The price is determined by the intersection of the market supply and demand curves.</p>
<p>Given the above, your questions about a firm's choice of price don't really make sense - at least not in the context of the model of perfect competition.</p>
<p>A price-taking firm considers the price <span class="math-container">$p$</span> as a constant and chooses its quantity <span class="math-container">$q$</span>. Its profit is <span class="math-container">$pq-C(q)$</span> where <span class="math-container">$C$</span> is the cost function. If the firm's profit-maximizing quantity <span class="math-container">$q^*$</span> is positive then it satisfies <span class="math-container">$p=C'(q^*)=MC(q^*)$</span> (mathematically, this is the first-order condition for maximization of the profit function).</p>
<hr />
<p>Moving away from the model of perfect competition, consider a price-setting firm. For simplicity, suppose it is a monopolist.</p>
<p>Let the inverse demand be given by <span class="math-container">$P(q)$</span>, where <span class="math-container">$P$</span> is a decreasing function of <span class="math-container">$q$</span> (demand is downward sloping). Here <span class="math-container">$P(q)$</span> is the willingness to pay for the <span class="math-container">$q$</span>th unit of output.</p>
<p>If the monopolist wishes to go from selling <span class="math-container">$q$</span> units of output to <span class="math-container">$q+1$</span>, and it is unable to price discriminate, then it would have to reduce the price on all the units to <span class="math-container">$P(q+1)$</span>. Since <span class="math-container">$P(q+1)&lt;P(q)$</span>, it would not be able to increase its price and sell the <span class="math-container">$q+1$</span>th unit if its price for the <span class="math-container">$q$</span>th unit was already equal to the willingness to pay of the <span class="math-container">$q$</span>th unit. So the scenario you ask about where a firm raises its price to sell an extra unit does not arise.</p>
<p>Also, note that if the monopolist could perfectly price discriminate (i.e. if it were able to identify who is willing to pay what and if it could prevent resale), then it could <em>reduce</em> the price on the <span class="math-container">$q+1$</span>th unit while maintaining the prices on the first <span class="math-container">$q$</span> units.</p>

CC BY-SA 4.0
2024-12-03T14:45:24.100Z
I should probably rephrase it, when I meant MC is seen as the supply curve I meant it in the sense that if the firm was given the choice of how much they were willing to sell and at what price > that would be mapped out as the MC curve. Obviously in reality the quantity and price the actually sell it at will be different ie profit max points for monopolies, so at that price level they are selling a lot less quantity than they would actually be willing to sell for the price(but the market obviously would not be willing to buy all of it).
j jose
CC BY-SA 4.0
2024-12-03T14:47:28.637Z
Same with perfect competition, i am aware the firms cant set the price themselves, but I am saying that the MC curve just describes what quantities a firm IS willing to supply at any given price level. So I know they cant change the price but only quantity, I was just stating what amount of Q the firm wouldn't mind selling at each price level (ie the MC curve)
j jose
CC BY-SA 4.0
2024-11-28T14:36:18.243Z
2024-11-28T15:41:24.830Z
2024-11-28T15:41:24.830Z
smcc
<p>As another answer says the argument is applicable under perfect competition on a perfect market. These two assumptions are foundations in the developed neoclassical models often taught in introductory macroeconomics courses. They are an important part of the school of thought sometimes called marginalists.</p>
<p>The reality is of course a lot more complicated which more modern theories of economics accept.</p>

CC BY-SA 4.0
2024-11-28T22:16:51.663Z
2024-11-28T22:16:51.663Z
ghellquist
<p>As far as I know, we view the supply curve for a firm as the MC curve, of course, firms would want to produce at the profit maximising point but say they had to produce amounts below and or above this then, the price they would be willing to assign for those quantities would be shown at the MC level for that quantity.</p>
<p>But I never actually knew what the argument for this was, all I ever hear is that if a firm wants to go from Q to Q+1 there will be a marginal cost for that extra good and so the firm wants to recover that and so, as a result, they price all the goods at q+1 to be the same as the MC value. But that MC value was for the extra unit &gt;&gt; Why would the firm then price all the goods at the q+1 level to be the MC level since that extra cost was really only created by that extra good?</p>
<p>Is there a mathematical reasoning behind this or is it just for the sake of practicality?</p>

<marginal><cost-functions><theory-of-the-firm>
Why is supply equal to the MC curve for firms
j jose
# Why is supply equal to the MC curve for firms

(Asked by: username_0 on 2024-11-28)

As far as I know, we view the supply curve for a firm as the MC curve, of course, firms would want to produce at the profit maximising point but say they had to produce amounts below and or above this then, the price they would be willing to assign for those quantities would be shown at the MC level for that quantity.

But I never actually knew what the argument for this was, all I ever hear is that if a firm wants to go from Q to Q+1 there will be a marginal cost for that extra good and so the firm wants to recover that and so, as a result, they price all the goods at q+1 to be the same as the MC value. But that MC value was for the extra unit >> Why would the firm then price all the goods at the q+1 level to be the MC level since that extra cost was really only created by that extra good?

Is there a mathematical reasoning behind this or is it just for the sake of practicality?

**Tags:** marginal, cost-functions, theory-of-the-firm

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## 2 answers

### Answer by username_1 on 2024-11-28. Score: 2

In the model of perfect competition firms do not set prices. They are price takers, i.e. they choose their quantities taking the price as given. The price is determined by the intersection of the market supply and demand curves.

Given the above, your questions about a firm's choice of price don't really make sense - at least not in the context of the model of perfect competition.

A price-taking firm considers the price $p$ as a constant and chooses its quantity $q$. Its profit is $pq-C(q)$ where $C$ is the cost function. If the firm's profit-maximizing quantity $q^\*$ is positive then it satisfies $p=C'(q^\*)=MC(q^\*)$ (mathematically, this is the first-order condition for maximization of the profit function).

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Moving away from the model of perfect competition, consider a price-setting firm. For simplicity, suppose it is a monopolist.

Let the inverse demand be given by $P(q)$, where $P$ is a decreasing function of $q$ (demand is downward sloping). Here $P(q)$ is the willingness to pay for the $q$th unit of output.

If the monopolist wishes to go from selling $q$ units of output to $q+1$, and it is unable to price discriminate, then it would have to reduce the price on all the units to $P(q+1)$. Since $P(q+1), it would not be able to increase its price and sell the $q+1$th unit if its price for the $q$th unit was already equal to the willingness to pay of the $q$th unit. So the scenario you ask about where a firm raises its price to sell an extra unit does not arise.

Also, note that if the monopolist could perfectly price discriminate (i.e. if it were able to identify who is willing to pay what and if it could prevent resale), then it could *reduce* the price on the $q+1$th unit while maintaining the prices on the first $q$ units.

> **Comments:**
> **username_0**: I should probably rephrase it, when I meant MC is seen as the supply curve I meant it in the sense that if the firm was given the choice of how much they were willing to sell and at what price > that would be mapped out as the MC curve. Obviously in reality the quantity and price the actually sell it at will be different ie profit max points for monopolies, so at that price level they are selling a lot less quantity than they would actually be willing to sell for the price(but the market obviously would not be willing to buy all of it).  
> **username_0**: Same with perfect competition, i am aware the firms cant set the price themselves, but I am saying that the MC curve just describes what quantities a firm IS willing to supply at any given price level. So I know they cant change the price but only quantity, I was just stating what amount of Q the firm wouldn't mind selling at each price level (ie the MC curve)  

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### Answer by username_2 on 2024-11-28. Score: 0

As another answer says the argument is applicable under perfect competition on a perfect market. These two assumptions are foundations in the developed neoclassical models often taught in introductory macroeconomics courses. They are an important part of the school of thought sometimes called marginalists.

The reality is of course a lot more complicated which more modern theories of economics accept.


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