<p><strong>Constant returns of scale</strong></p>

<p>As observed above, in mathematical terms the function is homogeneous of degree 1. But in terms of economic theory, this is called a production function with constant returns of scale.</p>

<p>It means that if you change the inputs in a determinate proportion, the output varies in the same proportion. </p>

CC BY-SA 3.0
2016-01-29T05:05:23.773Z
2016-01-29T05:05:23.773Z
Joao Luiz Pacheco
<p>Such a function is called <a href="https://en.wikipedia.org/wiki/Homogeneous_function" rel="nofollow">homogeneous</a> of degree 1.</p>

CC BY-SA 3.0
2016-01-28T19:12:15.793Z
2016-01-31T13:59:56.497Z
2016-01-31T13:59:56.497Z
Oliv
<p>I believe the following is the multiplicative property of bilinearity:</p>

<p>$$ Y=F(K,AL) $$
$$ c_1 F(K,AL) = F(c_1 K, AL) $$
$$ c_2 F(K,AL) = F(K, c_2 AL) $$</p>

<p>But when we have multiplied through the production function with a constant we have done so through each term as below</p>

<p>$$ c_3 F(K,AL) = F(c_3 K, c_3 AL) $$</p>

<p>e.g.</p>

<p>$$ \frac{1}{AL} F(K,AL) = F\left( \frac{K}{AL} , \frac{AL}{AL} \right) = F(k,1) = f(k) $$</p>

<p>What is the name of this property?</p>

<production-function>
Is a production function bilinear?
Sunhwa
# Is a production function bilinear?

(Asked by: username_0 on 2016-01-28)

I believe the following is the multiplicative property of bilinearity:

$$ Y=F(K,AL) $$
$$ c\_1 F(K,AL) = F(c\_1 K, AL) $$
$$ c\_2 F(K,AL) = F(K, c\_2 AL) $$

But when we have multiplied through the production function with a constant we have done so through each term as below

$$ c\_3 F(K,AL) = F(c\_3 K, c\_3 AL) $$

e.g.

$$ \frac{1}{AL} F(K,AL) = F\left( \frac{K}{AL} , \frac{AL}{AL} \right) = F(k,1) = f(k) $$

What is the name of this property?

**Tags:** production-function

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## 2 answers

### Answer by username_2 on 2016-01-28. Score: 7 | Accepted answer

Such a function is called [homogeneous](https://en.wikipedia.org/wiki/Homogeneous_function) of degree 1.


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### Answer by username_1 on 2016-01-29. Score: 4

**Constant returns of scale**

As observed above, in mathematical terms the function is homogeneous of degree 1. But in terms of economic theory, this is called a production function with constant returns of scale.

It means that if you change the inputs in a determinate proportion, the output varies in the same proportion.


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