<p>According to the following definition:</p>

<pre><code>q-complements/substitutes (q is for quantity).
Input x and y are complements if the marginal product of x is increasing in quantity of y.
Input x and y are substitutes if the marginal product of x is decreasing in quantity of y. 
</code></pre>

<p>Complements are sometimes called "imperfect substitute". See, for instance,<a href="https://economics.mit.edu/files/11574" rel="nofollow noreferrer">this paper</a> (Autor et al. 2003), page 1286-1287.</p>

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2019-03-22T03:51:39.887Z
Are you sure that definition of q-complements and substitutes applies to production functions? I thought it applied to inverse demand functions.

I believe imperfect substitutes just means there is input substitutability, but the two inputs are not perfect substitutes (MRTS is not a constant).
dlnB
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2019-03-22T09:27:25.290Z
See, for instance, [this paper](https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.20160696) (AER, 2018). Pag 1503, footnote 19, they say:

"For instance, with a constant returns to scale production function and two factors, capital and labor are q−complements. Thus, capital-augmenting technologies always increase the marginal product of labor."
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<microeconomics><production-function>
What is the difference between imperfect substitutes and complements in a production function?
Tecon
# What is the difference between imperfect substitutes and complements in a production function?

(Asked by: username_0 on 2019-03-21)

According to the following definition:
q-complements/substitutes (q is for quantity).
Input x and y are complements if the marginal product of x is increasing in quantity of y.
Input x and y are substitutes if the marginal product of x is decreasing in quantity of y. 

Complements are sometimes called "imperfect substitute". See, for instance,this paper (Autor et al. 2003), page 1286-1287.

**Tags:** microeconomics, production-function
> **Comments:**
> **username_1**: Are you sure that definition of q-complements and substitutes applies to production functions? I thought it applied to inverse demand functions.  I believe imperfect substitutes just means there is input substitutability, but the two inputs are not perfect substitutes (MRTS is not a constant).  
> **username_0**: See, for instance, [this paper](https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.20160696) (AER, 2018). Pag 1503, footnote 19, they say:  "For instance, with a constant returns to scale production function and two factors, capital and labor are q−complements. Thus, capital-augmenting technologies always increase the marginal product of labor."  

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## 0 answers

