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.
References
[1]
Goodwin, R. (1951) The Nonlinear Accelerator and the Persistence of Business Cycles. Econometrica, 19, 1-17. https://doi.org/10.2307/1907905
[2]
Matsumoto, A. and Szidarovszky, F. (2018) Goodwin Accelerator Model Revisited with Fixed Time Delays. Communications in Nolinear Science and Numerical Simulation, 58, 233-248. https://doi.org/10.1016/j.cnsns.2017.06.024
[3]
Matsumoto, A. (2009) Note on Goodwin's Nonlinear Acceleration Model with an Investment Delay. Journal of Economic Dynamics and Control, 33, 832-842. https://doi.org/10.1016/j.jedc.2008.08.013
[4]
Strotz, R., McAnulty, J. and Naines, J. (1953) Goodwin’s Non Linear Theory of the Business Cycle: An Electro-Analog Solution. Econometrica, 2, 390-411. https://doi.org/10.2307/1905446
[5]
Antonova, A., Reznik, S. and Todorv, M. (2013) Relaxation Oscillation Properties in Goodwin's Business Cycle Model. International Journal of Computational Economics and Econometrics, 3, 390-411. https://doi.org/10.1504/IJCEE.2013.058495
[6]
Freedman, H. and Kuang, Y. (1991) Stability Switches in Linear Scalar Neutral Delay Equations. Funkcialaj Ekvacioj, 34, 187-209.
