Goodwin Accelerator Model Revisited with Piecewise Linear Delay Investment

Abstract

It is well-known that Goodwin ’ s nonlinear delay accelerator model can generate diverse oscillations ( i.e ., smooth and sawtooth oscillations). It is, however, less-known what conditions are needed for these dynamics to emerge. In this study, using a piecewise linear investment function, we solve the governing delay differential equation and obtain the explicit forms of the time trajectories. In doing so, we detect conditions for persistent oscillations and also conditions for the birth of such cyclic dynamics.