# May's Instability in Large Economies

## TL;DR

This paper explores how large economies tend to become marginally stable due to complex interactions among firms, leading to systemic risks and power-law distributions of failures, similar to phenomena observed in ecosystems.

## Contribution

It extends Robert May's stability analysis to economic networks, demonstrating that increasing size and heterogeneity induce instability and systemic crises.

## Key findings

- Large economic networks tend to become dysfunctional as they grow.
- Heterogeneity and reduced substitutability increase systemic risk.
- Small shocks can trigger large avalanches of defaults, explaining business cycle volatility.

## Abstract

Will a large economy be stable? Building on Robert May's original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in which inputs for production are not easily substitutable, as in several real-world supply chains. Relying on results from Random Matrix Theory, we argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong or when substitutability of their production inputs is reduced. At marginal stability and for large heterogeneities, we find that the distribution of firm sizes develops a power-law tail, as observed empirically. Crises can be triggered by small idiosyncratic shocks, which lead to "avalanches" of defaults characterized by a power-law distribution of total output losses. This scenario would naturally explain the well-known "small shocks, large business cycles" puzzle, as anticipated long ago by Bak, Chen, Scheinkman and Woodford.