Comparative Analysis of Goodwin's Business Cycle Models

We compare the behavior of solutions of Goodwin’s business cycle equation in the form of neutral delay differential equation with fixed delay (NDDE model) and in the form of the differential equations of 3rd, 4th and 5th orders (ODE model’s). Such ODE model’s (Taylor series expansion of NDDE in powers of θ) are proposed in N. Dharmaraj and K. Vela Velupillai [6] for investigation of the short periodic sawthooth oscillations in NDDE. We show that the ODE’s of 3rd, 4th and 5th order may approximate the asymptotic behavior of only main Goodwin’s mode, but not the sawthooth modes. If the order of the Taylor series expansion exceeds 5, then the approximate ODE becomes unstable independently of time lag θ.