Linearity of Aggregate Production Functions

TL;DR

This paper proves that when individual firms have constant-returns-to-scale production functions, the aggregate production function is linear on some domain, providing a microeconomic foundation for linearity in aggregate production.

Contribution

It establishes a theoretical proof linking individual firm production functions to the linearity of the aggregate production function.

Findings

Aggregate production function is linear on some domain.

Provides microeconomic foundation for linear aggregate production.

Theoretical proof connecting individual and aggregate production functions.

Abstract

We prove that when individual firms employ constant-returns-to-scale production functions, the aggregate production function defined by the maximum achievable total output given total inputs is always linear on some part of the domain. Our result provides a microfoundation for the linear production function.