A study of a debt-influenced equilibrium of the Keen model

TL;DR

This paper analyzes a debt-influenced equilibrium in the Keen model, revealing a stable state where debt can become negative, implying income sources beyond labor.

Contribution

It constructs an example demonstrating a stable equilibrium with negative debt, expanding understanding of the Keen model's possible states.

Findings

Stable equilibrium with negative debt identified

Debt can become negative, indicating non-labor income sources

Equilibrium state shows collapse of wages and employment

Abstract

The Keen model is a mathematical model that describes the dynamic evolution of wages, employment, and debt based on the known Minsky's Financial Instability Hypothesis. It consists of three first order nonlinear ordinary differential equations. There exists an equilibrium state that corresponds to a collapse of both wage and employment but certain debts remain. In this paper, we construct an example in which this equilibrium appears to be stable. More interestingly, the debt becomes negative, which indicates some source of income without laboring.