Zipf's law and maximum sustainable growth

TL;DR

This paper demonstrates that Zipf's law naturally emerges from Gibrat's rule under a balance condition and signifies the optimal resource allocation for maximum sustainable economic growth.

Contribution

It reveals that Zipf's law results from a balance condition in firm growth dynamics and links it to the economy's optimal resource allocation for sustainable growth.

Findings

Zipf's law arises from Gibrat's rule under a balance condition.

Zipf's law indicates the maximum sustainable growth rate.

The law reflects optimal resource allocation in the economy.

Abstract

Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all firm levels, yields Zipf's law under a balance condition between the effective growth rate of incumbent firms (which includes their possible demise) and the growth rate of investments in entrant firms. Remarkably, Zipf's law is the signature of the long-term optimal allocation of resources that ensures the maximum sustainable growth rate of an economy.