Typical properties of large random economies with linear activities

TL;DR

This paper analyzes the typical properties of large random economies with linear technologies using statistical mechanics, revealing phase transitions and the influence of technological change on economic criticality.

Contribution

It provides a complete statistical description of equilibria in large random economies and identifies phase transitions driven by technological efficiency.

Findings

Two regimes separated by a phase transition

Endogenous technological change pushes economy toward criticality

Characterization of equilibrium properties in large economies

Abstract

We study the competitive equilibrium of large random economies with linear activities using methods of statistical mechanics. We focus on economies with $C$ commodities, $N$ firms, each running a randomly drawn linear technology, and one consumer. We derive, in the limit $N,C\to\infty$ with $n=N/C$ fixed, a complete description of the statistical properties of typical equilibria. We find two regimes, which in the limit of efficient technologies are separated by a phase transition, and argue that endogenous technological change drives the economy close to the critical point.