Multiple periodicities in an extended Goodwin model with mechanization, independent investment, and disequilibrium: Toward a Marxian-Keynesian synthesis
Author
John Cajas Guijarro
Title
Multiple periodicities in an extended Goodwin model with mechanization, independent investment, and disequilibrium: Toward a Marxian-Keynesian synthesis
Description
Mathematical supplement to accompany Cajas Guijarro (2026): "Multiple periodicities in an extended Goodwin model with mechanization, independent investment, and disequilibrium: Toward a Marxian-Keynesian synthesis". Structural Change and Economic Dynamics, 77: 357-386. https://doi.org/10.1016/j.strueco.2026.02.003
Category
Academic Articles & Supplements
Keywords
endogenous cycles, multiple periodicities, Goodwin model
URL
http://www.notebookarchive.org/2026-02-bivbt4x/
DOI
https://notebookarchive.org/2026-02-bivbt4x
Date Added
2026-02-25
Date Last Modified
2026-02-25
File Size
12.99 megabytes
Supplements
Rights
CC BY 4.0

Multiple periodicities in an Extended Goodwin Model with Mechanization, Independent Investment, and Disequilibrium: Toward a Marxian-Keynesian Synthesis
Multiple periodicities in an Extended Goodwin Model with Mechanization, Independent Investment, and Disequilibrium: Toward a Marxian-Keynesian Synthesis
John Cajas Guijarro
This notebook proposes an extended Goodwin model that synthesizes Marxian and Keynesian dynamics into a unified four - dimensional framework.The model integrates endogenous technical change via mechanization, investment behavior driven by effective demand, and goods market disequilibrium. We develop two three - dimensional closures - a Classical - Marxian and a Keynesian - Kaleckian formulation - each capable of generating persistent endogenous cycles. These are then combined into a Marxian - Keynesian (MK) system, which exhibits complex dynamics including multiple periodicities. This result points to the potential for interacting oscillatory modes and long - run fluctuations even with relatively simple behavioral rules. Numerical simulations suggest that the MK synthesis captures rich endogenous fluctuations without relying on exogenous shocks and may exhibit chaotic dynamics under future extensions.
Clean all
In[]:=
ClearAll["Global`*"]
In[]:=
dlog[fun_]:=D[Distribute[Log[fun],Equal],t]//FullSimplify;solve1[eqns_,vars_]:=(Solve[eqns,vars][[1,1]]//FullSimplify)/.{RuleEqual};
General framework
Classical-Marxian (CM) closure
Local stability indicators (CM)
Parametrization (M)
Numerical simulations (CM)
Online Appendix: Simulation of a closed cycle
Bifurcation
Online Appendix: Sensitivity analysis
Keynesian-Kaleckian (K) Closure
Local stability indicators (K)
Parameterization (K)
Numerical simulation (K)
Online Appendix: Simulation of a closed cycle
Bifurcation
Sensitivity analysis
MK synthesis
Stability indicators (MK)
Parameterization (MK)
Numerical simulation 1 (MK)
Bifurcation parameters
Resonance
Cite this as: John Cajas Guijarro, "Multiple periodicities in an extended Goodwin model with mechanization, independent investment, and disequilibrium: Toward a Marxian-Keynesian synthesis" from the Notebook Archive (2026), https://notebookarchive.org/2026-02-bivbt4x
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