# Why is marginal cost not the cost of producing the last unit?

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?

• 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 Dec 11 '19 at 8:11
• @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 Dec 11 '19 at 9:15

The full quote from the cited reference (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.

• 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 Dec 11 '19 at 8:58
• 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 Dec 11 '19 at 10:35 • 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 Dec 11 '19 at 11:22 • 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 Dec 11 '19 at 12:03 • or @user253751 you buy 8 hats worth of fabric for$15, but only make 5 – Chris H Dec 11 '19 at 16:37

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).