Goodwin Accelerator Model Revisited with Piecewise Linear Delay Investment - Advances in Pure Mathematics

APM > Vol.8 No.2, February 2018

Goodwin Accelerator Model Revisited with Piecewise Linear Delay Investment ()

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Download as PDF (Size: 1024KB) PP. 178-217

DOI: 10.4236/apm.2018.82010 641 Downloads 1,476 Views Citations

Author(s)

Akio Matsumoto¹, Keiko Nakayama², Ferenc Szidarovszky³

Affiliation(s)

¹Department of Economics, International Center for Further Development of Dynamic Economic Research, Chuo University, Hachioji, Japan.
²Department of Economics, Chukyo University, Nagoya, Japan.
³Department of Applied Mathematics, University of Pécs, Pécs, Hungary.

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.

KEYWORDS

Nonlinear Accelerator, Investment Delay, Successive Integration, Smooth and Kinked Solutions, Numerical Analysis

Share and Cite:

Matsumoto, A. , Nakayama, K. and Szidarovszky, F. (2018) Goodwin Accelerator Model Revisited with Piecewise Linear Delay Investment. Advances in Pure Mathematics, 8, 178-217. doi: 10.4236/apm.2018.82010.

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