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Dynamics in a nonlinear Keynesian good market model.
Ahmad Naimzada1, Marina Pireddu2
1Department of Economics, Quantitative Methods and Management, University of Milano-Bicocca, U7 Building, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy.
Chaos (Woodbury, N.Y.)
|April 5, 2014
Summary
Introducing nonlinearity into the Keynesian income-expenditure model reveals complex dynamics. This study explores stability, bifurcations, and chaotic behaviors, including multistability, with and without government spending.
Area of Science:
- Economics
- Dynamical Systems Theory
Background:
- The standard Keynesian income-expenditure model typically exhibits linear dynamics.
- Nonlinearities are crucial for understanding complex economic phenomena and emergent behaviors.
Purpose of the Study:
- To investigate the emergence of diverse dynamical behaviors in the Keynesian income-expenditure model with introduced nonlinearity.
- To analyze the impact of nonlinearity on stability, bifurcations, and attractors, considering both endogenous and exogenous government spending scenarios.
Main Methods:
- Utilized a sigmoidal functional form for the income adjustment mechanism to bound income variation.
- Employed analytical and numerical tools to examine stability conditions, bifurcations, and periodic/chaotic dynamics.
- Investigated global dynamics, focusing on multistability and the coexistence of different attractors.
Main Results:
- Demonstrated that nonlinearity can generate a rich variety of dynamical behaviors, including periodic and chaotic attractors.
- Identified conditions for bifurcations and complex dynamics within the modified Keynesian model.
- Observed phenomena of multistability, where different types of attractors coexist.
Conclusions:
- The introduction of nonlinearity significantly enriches the dynamic possibilities of the Keynesian income-expenditure model.
- The findings highlight the importance of considering nonlinear adjustments and their implications for economic stability and predictability.
- The study provides insights into complex economic dynamics, including chaos and multistability, relevant for macroeconomic modeling.
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