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Stability analysis in economic dynamics: A computational approach

Author

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  • Halkos, George
  • Tsilika, Kyriaki

Abstract

Modern microeconomics and macroeconomics study dynamic phenomena. Dynamics could predict future states of an economy based on its structural characteristics. Economic dynamics are modeled in discrete and continuous time context, mainly via autonomous difference and differential equations. In this study, we use Xcas and Mathematica as software tools, in order to generate results concerning the dynamic properties of the solutions of the difference and differential equation(s) models and determine whether an economic equilibrium exists. Our computational approach does not require solving the difference or differential equation(s) and makes no assumptions for initial conditions. The results provide quantitative information based on the qualitative properties of the mathematical solutions. The computer codes are fully presented and can be reproduced as they are in computational-based research practice and education. The relevant output of CAS software is created in a way as to be interpreted without the knowledge of advanced mathematics.

Suggested Citation

  • Halkos, George & Tsilika, Kyriaki, 2012. "Stability analysis in economic dynamics: A computational approach," MPRA Paper 41371, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41371
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    References listed on IDEAS

    as
    1. George E HALKOS & George PAPAGEORGIOU, 2010. "Dynamic Optimization In Natural Resources Management," Journal of Advanced Research in Management, ASERS Publishing, vol. 1(2), pages 92-97.
    2. Champsaur, Paul & Dreze, Jacques H & Henry, Claude, 1977. "Stability Theorems with Economic Applications," Econometrica, Econometric Society, vol. 45(2), pages 273-294, March.
    3. Tesfatsion, Leigh & Judd, Kenneth L., 2006. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers Archive 10368, Iowa State University, Department of Economics.
    4. Marco Ratto, 2008. "Analysing DSGE Models with Global Sensitivity Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 115-139, March.
    5. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    6. Halkos, George & Papageorgiou, George, 2008. "Extraction of non-renewable resources: a differential game approach," MPRA Paper 37596, University Library of Munich, Germany.
    7. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    8. Orlando Gomes, 2012. "Transitional Dynamics in Sticky-Information General Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 39(4), pages 387-407, April.
    9. Halkos, George, 2011. "Cyclical and constant strategies in renewable resources extraction," MPRA Paper 34654, University Library of Munich, Germany.
    10. Wei-Bin Zhang, 2005. "Differential Equations, Bifurcations, and Chaos in Economics," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5827, February.
    11. Folsom, Roger Nils & Boger, Dan C & Mullikin, Harry C, 1976. "Stability Conditions for Linear Constant Coefficient Difference Equations in Generalized Differenced Form," Econometrica, Econometric Society, vol. 44(3), pages 575-591, May.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Halkos, George & Tsilika, Kyriaki, 2014. "Perspectives on integrating a computer algebra system into advanced calculus curricula," MPRA Paper 63898, University Library of Munich, Germany.
    2. Halkos, George & Tsilika, Kyriaki, 2012. "Constructing a Generator of Matrices with Pattern," MPRA Paper 43614, University Library of Munich, Germany.
    3. George Halkos & Kyriaki Tsilika, 2015. "Programming Identification Criteria in Simultaneous Equation Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 157-170, June.

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    More about this item

    Keywords

    Stability conditions; software tools; economic equilibrium;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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