Goodwin's Non-Linear Model and Technological Progress

Jan Kodera and Miloslav Vosvrda

Centre for Economic Dynamics and Econometrics in Prague, the Czech Republic
kodera@vse.cz, vosvrda@utia.cas.cz

Abstract

Contemporary economics contains mainly two approaches for an exploration of fluctuations of economic activity indicators. The first approach explores these fluctuations as an expression of the environment that is uncertain in principle by the random external shocks. The second approach demonstrates these fluctuations as the expression of the deterministic dynamic process producing more complex behaviour of the economic system. A purpose of this paper is to derive, from traditional Goodwin’s model, the predator-prey model with a specific function for the technological progress. This model contains both a system of differential equations and system of stochastic differential equations. Bases of this system are the following variables: a rate of employment, a share of labour, and different forms of a variable rate of the technological progress. Three versions of the non-linear form of Goodwin's accelerator are introduced as a models allowing for technological progress. The first version with embodied exogenous technological progress gives nonlinear oscillations. The second version assumes the technological progress as an endogenous variable described by the specific differential equation. Introducing this equation for technological progress we get not only the enlarged Goodwin model but even more complex dynamics. The third version introduces a stochastic technological progress. Our task is to present the traditional Goodwin model and to show how endogenous technological progress, considered inside this model, changes the behaviour of this model. Systems behaviour is illustrated by numerical examples.