# What is the difference between imperfect substitutes and complements in a production function?

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.

• 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 Mar 22 at 3:51
• See, for instance, this paper (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." – Tecon Mar 22 at 9:27