An analysis of the Keen model for credit expansion, asset price bubbles and financial fragility

We analyze the system of differential equations proposed by Keen to model Minsky’s financial instability hypothesis. We start by describing the properties of the well-known Goodwin model for the dynamics of wages and employment. This is followed by Keen’s extension to include investment financed by debt. We determine the several possible equilibria and study their local stability, discussing the economical interpretation behind each condition. We then propose a modified extension that includes the role of a Ponzi speculator and investigate its effect on the several equilibria and their stability. All models are amply illustrated with numerical examples portraying their various properties.