<p>The marginal output in all production functions explains the degree of increase in production following (1) the addition of one more unit of labor, (2) an additional unit of capital, or (3) <strong>a productivity gain of one of the production factors</strong> - the parameter A.</p>
<p>Generally, it is assumed that the returns are constant, so the production function can be rewritten as:</p>
<p><span class="math-container">$Y=F(AK, AL) = AF(K,L) $</span></p>
<p>meaning that if you double the quantity of input, the quantity of output doubles as well.</p>
<p>The expression <span class="math-container">$F(AK)$</span> refers the efficient capital while  <span class="math-container">$F(AL)$</span> refers to the efficient labor. You can see that if you increase the efficiency of one factor, it increases the output too. To know at which rate, you got to measure the marginal productivity :</p>
<p><span class="math-container">$\frac{\partial Y}{\partial AL}$</span> or <span class="math-container">$\frac{\partial Y}{\partial AK}$</span></p>

CC BY-SA 4.0
2024-01-31T12:48:45.080Z
2024-01-31T12:48:45.080Z
justaneconomist
<p>The parameter <span class="math-container">$A$</span> typically refers to total factor productivity which is a measure of how much output is created per unit of input.</p>
<p>If you rearrange your equation you can see this more clearly:</p>
<p><span class="math-container">$$A=\frac{F(K,L)}{K^aL^{1-a}}$$</span></p>
<p>Naturally as <span class="math-container">$A$</span> grows so will your output. In &quot;words&quot;, <span class="math-container">$A$</span> measures the portion of your production that <span class="math-container">$K^aL^{1-a}$</span> does not explain.</p>

CC BY-SA 4.0
2022-09-08T14:14:14.830Z
Hi, thankyou for your answer! However, I don't think that A corresponds to the marginal productivity of a factor. Am I wrong?
student
CC BY-SA 4.0
2022-09-08T06:52:07.883Z
2022-09-08T06:58:09.883Z
2022-09-08T06:58:09.883Z
Eli J
<p>I don't understand its importance in this production function.</p>
<p>I know that the productivity parameter is A in the function:</p>
<p><span class="math-container">$F(K,L) = AK^α L^{(1-α)} $</span></p>
<p>So what could it be?</p>
<p>Thank you!</p>

CC BY-SA 4.0
2022-09-08T07:08:34.637Z
Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
Giskard
<macroeconomics><labor-economics><international-economics>
Why is the 'marginal productivity of a factor' of any relevance in the Cobb-Douglas production function?
student
# Why is the 'marginal productivity of a factor' of any relevance in the Cobb-Douglas production function?

(Asked by: username_0 on 2022-09-08)

I don't understand its importance in this production function.

I know that the productivity parameter is A in the function:

$F(K,L) = AK^α L^{(1-α)} $

So what could it be?

Thank you!

**Tags:** macroeconomics, labor-economics, international-economics

> **Comments:**
> **username_1**: Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.  

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## 2 answers

### Answer by username_2 on 2024-01-31. Score: 0

The marginal output in all production functions explains the degree of increase in production following (1) the addition of one more unit of labor, (2) an additional unit of capital, or (3) **a productivity gain of one of the production factors** - the parameter A.

Generally, it is assumed that the returns are constant, so the production function can be rewritten as:

$Y=F(AK, AL) = AF(K,L) $

meaning that if you double the quantity of input, the quantity of output doubles as well.

The expression $F(AK)$ refers the efficient capital while $F(AL)$ refers to the efficient labor. You can see that if you increase the efficiency of one factor, it increases the output too. To know at which rate, you got to measure the marginal productivity :

$\frac{\partial Y}{\partial AL}$ or $\frac{\partial Y}{\partial AK}$


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### Answer by username_3 on 2022-09-08. Score: 0

The parameter $A$ typically refers to total factor productivity which is a measure of how much output is created per unit of input.

If you rearrange your equation you can see this more clearly:

$$A=\frac{F(K,L)}{K^aL^{1-a}}$$

Naturally as $A$ grows so will your output. In "words", $A$ measures the portion of your production that $K^aL^{1-a}$ does not explain.

> **Comments:**
> **username_0**: Hi, thankyou for your answer! However, I don't think that A corresponds to the marginal productivity of a factor. Am I wrong?  

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