1.Introduction

In contrast to the mainstream（Neoclassical）teaching that the capitalist economy is inherently stable, a representative American Post Keynesian economist Hyman Minsky（1919—1996）proposed the financial instability hypothesis, which means that the financially-dominated capitalist economy is inherently unstable（cf. Minsky 1975,1982,1986）.It seems that the credibility of Minsky's hypothesis has been rapidly increasing in recent times, since we experienced the Japanese long term deflationary depression in the 1990s and the 2000s after the bubbly prosperity in the 1980s, the Latin American and Asian currency crises in the 1980s and the 1990s, and the global financial crises in USA and Europe that were initiated by the so called“subprime mortgage crisis”of the US economy in 2008 after the prosperous period of the US economy in the 1990s and the 2000s.It looks as if the world economy in recent 30 years has been faithfully tracing Minsky's scenario of financial instability hypothesis.

In this paper, we shall try to present some formal mathematical models that are inspired by Minsky's idea. This paper is organized as follows. In section 2, we restate Minsky's financial instability hypothesis by referring to Minsky's own writings.In section 3, we interpret Asada's（2001）very simple fixed price dynamic model that is expressed by a Lotka-Volterra type two-dimensional system of nonlinear differential equations, which can reflect Minsky's perspective of financially-driven business cycle that is called“Minsky cycle”.In section 4, we interpret the extended three-dimensional model by introducing price flexibility following Asada's（2004）procedure, and show that the increase of price flexibility tends to destabilize rather than stabilize the macroeconomic system in this model contrary to the teaching of the mainstream macroeconomics.

Minsky's financial instability hypothesis means that the financially-driven capitalist economy is inherently unstable. But, according to Minsky（1986）, the stability/instability of the system is by no means independent of the macroeconomic policies of the government and the central bank.That is to say, the appropriate policy mix of the fiscal and monetary policies by the government and the central bank can contribute to“stabilize an unstable economy”if we quote from the title of Minsky's（1986）book.In sections 5 and 6, we present the further extended higher dimensional models that can study the effects of monetary and fiscal stabilization policies analytically.These models are designed to study theoretically what kind of policy mix is appropriate or inappropriate from the point of view of macroeconomic stabilization.We also argue that the analytical conclusions that are derived from these models are quite consistent with the experience of the Japanese economy under the serious deflationary depression in the 1990s and the 2000s, which is called the“lost twenty years”.Section 7 is devoted to some concluding remarks.