<p>I’m guessing what this means is that if <span class="math-container">$C$</span> is the cost function and <span class="math-container">$x$</span> represents the number of units of a good produced, marginal cost at production level <span class="math-container">$x_0$</span> is <em>not</em> the cost of producing the <span class="math-container">$(x_0)$</span>th unit. And, importantly, if goods are not sold in <em>discrete</em> amounts, it’s not quite the cost of producing the next “unit” either.</p>

<p>If the good is produced in discrete amounts (that is, if <span class="math-container">$x \in \mathbb{N}$</span>), then marginal cost at production level <span class="math-container">$x_0$</span> is defined as <span class="math-container">$C(x_{0}+1) - C(x_0)$</span>. For example, marginal cost when <span class="math-container">$15$</span> goods have been produced is the additional cost of producing the <span class="math-container">$16$</span>th good, not the <span class="math-container">$15$</span>th good.</p>

<p>More often than not, though, economists assume the good is continuous (e.g., milk, for instance). In that case, marginal cost at production level <span class="math-container">$x_0$</span> is the derivative of the cost function at <span class="math-container">$x = x_0$</span>, i.e., <span class="math-container">$C'(x_0)$</span>. That means it's the cost of producing an additional <em>incremental</em> amount of the good (i.e., the “instantaneous rate of change” of the cost with respect to quantity). </p>

CC BY-SA 4.0
2019-12-24T12:24:04.403Z
2019-12-24T12:29:26.370Z
2019-12-24T12:29:26.370Z
Tejas Subramaniam
<p>The full quote from the <a href="http://docshare01.docshare.tips/files/13925/139258369.pdf" rel="noreferrer">cited reference</a> (p. 181) is</p>

<blockquote>
  <p>Marginal cost is <em>not</em> the cost of producing the "last" unit of output. The cost of producing the last unit of output is the same as the cost of producing the first or any other unit of output and is, in fact, the <em>average</em> cost of output. <strong>Marginal cost (in the finite sense) is the increase (or decrease) in cost resulting from the production of an extra increment of output, which is not the same thing as the "cost of the last unit."</strong></p>
</blockquote>

<p>I think the boldfaced part is the important part that the Wikipedia editor left out.</p>

<p>What you have in mind is correct. Suppose we can produce 4 hats for the cost of \$8, and 5 hats for the cost of \$15, then the authors are saying that if you choose to produce 5 hats instead of 4, then it would cost you \$7 more. That's the marginal cost.</p>

<p>They argue that it's not <em>right</em> to say that, having chosen to produce 5 hats, that the cost of producing the 5th hat is \$7.</p>

<p>To me, this is a very minor distinction.</p>

CC BY-SA 4.0
2019-12-11T08:58:01.183Z
Thanks a lot, that clears things up. Isn't it incorrect to say that the cost of producing the first or any unit is the same as the last, as the cost of producing each unit changes? And why is that considered the average cost of output, not marginal?
Chris Mason
CC BY-SA 4.0
2019-12-11T10:35:32.337Z
The point is that once you choose to produce 5 hats, all you know is it would cost you \$15, or \$3 per hat on average. This is the same for any of those five hats as you can't distinguish them; you can't say that the fifth hat costs \$7. In short, the authors argue that marginal cost applies when you choose how many to produce. Once you choose that quantity, all hats are the same.
Art
CC BY-SA 4.0
2019-12-11T11:22:07.023Z
But isn't the statement still incorrect?it writes the cost of producing the last output is the same as the first and any other unit. Won't the cost of the last hat change due to diminishing returns? And isn't the ATC different for each hat?
Chris Mason
CC BY-SA 4.0
2019-12-11T12:03:49.800Z
ATC would be the same for each hat, once you decided how many hats to produce. ATC would be different for different quantities of hats you decide to produce.
Art
CC BY-SA 4.0
2019-12-11T16:27:56.663Z
@CyrusMason Universe A: You buy 4 hats' worth of fabric for \$8 and make 4 hats. How much did each hat cost to make? Universe B: You buy 5 hats' worth of fabric for \$15 and make 5 hats. How much did each hat cost to make?
Criticize SE actions means ban
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2019-12-11T16:37:56.117Z
or @user253751 you buy 8 hats worth of fabric for $15, but only make 5
Chris H
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2019-12-12T06:12:32.623Z
tl;dr: marginal cost is `C(N + 1) - C(N)`, not `C(N) - C(N - 1)` where C is the total cost to produce N units. In many cases, for large k, `C(k + 1) / C(k) ≈ 1`, so there is no distinction. This is not always the case though.
MooseBoys
CC BY-SA 4.0
2019-12-11T08:11:59.173Z
2019-12-11T08:11:59.173Z
Art
<p>I am slightly confused about this wikipedia article. en.wikipedia.org/wiki/Marginal_cost</p>

<p>It states that marginal cost is not the cost of producing the next or last unit.</p>

<p>Why is this the case? I thought that was precisely the definition of marginal cost.</p>

<p>I also hear marginal cost defined as cost of the last unit. What is meant by this? If quantity is increased by 5, is the marginal cost the cost of the 5th unit only?</p>

CC BY-SA 4.0
2019-12-11T08:11:32.073Z
The reason why it is not the cost of the last unit is actually explained in the article: mc are the **additional** costs incurred by producing an extra unit. This includes the cost of the next unit but also the costs of the reduced productivity in all other units due to the law of diminishing returns.
Maarten Punt
CC BY-SA 4.0
2019-12-11T09:15:25.687Z
@MaartenPunt but isn't it incorrect to state that the cost of producing the last unit of output is the same as the cost of producing the first or any other unit of output, because isn't the cost of producing an extra unit changing?
Chris Mason
<microeconomics>
Why is marginal cost not the cost of producing the last unit?
Chris Mason
# Why is marginal cost not the cost of producing the last unit?

(Asked by: username_0 on 2019-12-11)

I am slightly confused about this wikipedia article. en.wikipedia.org/wiki/Marginal\_cost

It states that marginal cost is not the cost of producing the next or last unit.

Why is this the case? I thought that was precisely the definition of marginal cost.

I also hear marginal cost defined as cost of the last unit. What is meant by this? If quantity is increased by 5, is the marginal cost the cost of the 5th unit only?

**Tags:** microeconomics

> **Comments:**
> **username_1**: The reason why it is not the cost of the last unit is actually explained in the article: mc are the **additional** costs incurred by producing an extra unit. This includes the cost of the next unit but also the costs of the reduced productivity in all other units due to the law of diminishing returns.  
> **username_0**: @MaartenPunt but isn't it incorrect to state that the cost of producing the last unit of output is the same as the cost of producing the first or any other unit of output, because isn't the cost of producing an extra unit changing?  

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## 2 answers

### Answer by username_3 on 2019-12-11. Score: 14 | Accepted answer

The full quote from the [cited reference](http://docshare01.docshare.tips/files/13925/139258369.pdf) (p. 181) is

> Marginal cost is *not* the cost of producing the "last" unit of output. The cost of producing the last unit of output is the same as the cost of producing the first or any other unit of output and is, in fact, the *average* cost of output. **Marginal cost (in the finite sense) is the increase (or decrease) in cost resulting from the production of an extra increment of output, which is not the same thing as the "cost of the last unit."**

I think the boldfaced part is the important part that the Wikipedia editor left out.

What you have in mind is correct. Suppose we can produce 4 hats for the cost of \$8, and 5 hats for the cost of \$15, then the authors are saying that if you choose to produce 5 hats instead of 4, then it would cost you \$7 more. That's the marginal cost.

They argue that it's not *right* to say that, having chosen to produce 5 hats, that the cost of producing the 5th hat is \$7.

To me, this is a very minor distinction.

> **Comments:**
> **username_0**: Thanks a lot, that clears things up. Isn't it incorrect to say that the cost of producing the first or any unit is the same as the last, as the cost of producing each unit changes? And why is that considered the average cost of output, not marginal?  
> **username_3**: The point is that once you choose to produce 5 hats, all you know is it would cost you \$15, or \$3 per hat on average. This is the same for any of those five hats as you can't distinguish them; you can't say that the fifth hat costs \$7. In short, the authors argue that marginal cost applies when you choose how many to produce. Once you choose that quantity, all hats are the same.  
> **username_0**: But isn't the statement still incorrect?it writes the cost of producing the last output is the same as the first and any other unit. Won't the cost of the last hat change due to diminishing returns? And isn't the ATC different for each hat?  
> **username_3**: ATC would be the same for each hat, once you decided how many hats to produce. ATC would be different for different quantities of hats you decide to produce.  
> **username_4**: @CyrusMason Universe A: You buy 4 hats' worth of fabric for \$8 and make 4 hats. How much did each hat cost to make? Universe B: You buy 5 hats' worth of fabric for \$15 and make 5 hats. How much did each hat cost to make?  
> **username_5**: or @user253751 you buy 8 hats worth of fabric for $15, but only make 5  
> **username_6**: tl;dr: marginal cost is `C(N + 1) - C(N)`, not `C(N) - C(N - 1)` where C is the total cost to produce N units. In many cases, for large k, `C(k + 1) / C(k) ≈ 1`, so there is no distinction. This is not always the case though.  

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### Answer by username_2 on 2019-12-24. Score: 0

I’m guessing what this means is that if $C$ is the cost function and $x$ represents the number of units of a good produced, marginal cost at production level $x\_0$ is *not* the cost of producing the $(x\_0)$th unit. And, importantly, if goods are not sold in *discrete* amounts, it’s not quite the cost of producing the next “unit” either.

If the good is produced in discrete amounts (that is, if $x \in \mathbb{N}$), then marginal cost at production level $x\_0$ is defined as $C(x\_{0}+1) - C(x\_0)$. For example, marginal cost when $15$ goods have been produced is the additional cost of producing the $16$th good, not the $15$th good.

More often than not, though, economists assume the good is continuous (e.g., milk, for instance). In that case, marginal cost at production level $x\_0$ is the derivative of the cost function at $x = x\_0$, i.e., $C'(x\_0)$. That means it's the cost of producing an additional *incremental* amount of the good (i.e., the “instantaneous rate of change” of the cost with respect to quantity).


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