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From constrained optimization to constrained dynamics: extending analogies between economics and mechanics

Author

Listed:
  • Erhard Glötzl

    (Johannes Kepler University Linz)

  • Florentin Glötzl

    (Vienna University of Economics and Business)

  • Oliver Richters

    (Carl von Ossietzky University of Oldenburg
    ZOE, Institute for future-fit economies)

Abstract

Economic equilibrium models have been inspired by analogies to stationary states in classical mechanics. To extend these mathematical analogies from constrained optimization to constrained dynamics, we formalize economic (constraint) forces and economic power in analogy to physical (constraint) forces and the reciprocal value of mass. Agents employ forces to change economic variables according to their desire and their power to assert their interest. These ex-ante forces are completed by constraint forces from unanticipated system constraints to yield the ex-post dynamics. The differential-algebraic equation framework seeks to overcome some restrictions inherent to the optimization approach and to provide an out-of-equilibrium foundation for general equilibrium models. We transform a static Edgeworth box exchange model into a dynamic model with procedural rationality (gradient climbing) and slow price adaptation, and discuss advantages, caveats, and possible extensions of the modeling framework.

Suggested Citation

  • Erhard Glötzl & Florentin Glötzl & Oliver Richters, 2019. "From constrained optimization to constrained dynamics: extending analogies between economics and mechanics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(3), pages 623-642, September.
    • Handle: RePEc:spr:jeicoo:v:14:y:2019:i:3:d:10.1007_s11403-019-00252-7
    DOI: 10.1007/s11403-019-00252-7
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    Cited by:

    1. Glötzl, Erhard, 2022. "General Constrained Dynamic (GCD) models with intertemporal utility functions," MPRA Paper 112387, University Library of Munich, Germany.
    2. Richters, Oliver, 2021. "Modeling the out-of-equilibrium dynamics of bounded rationality and economic constraints," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 846-866.
    3. Asad Zaman, 2020. "New Directions in Macroeconomics," International Econometric Review (IER), Econometric Research Association, vol. 12(1), pages 1-23, April.
    4. Richters, Oliver, 2020. "Between bounded rationality and economic imperatives: essays on out-of-equilibrium dynamics," EconStor Theses, ZBW - Leibniz Information Centre for Economics, number 228534, September.
    5. Oliver Richters & Erhard Glötzl, 2020. "Modeling economic forces, power relations, and stock-flow consistency: a general constrained dynamics approach," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 43(2), pages 281-297, April.
    6. Krecik, Markus, 2024. "Preference dynamics: A procedurally rational model of time and effort allocation," Discussion Papers 2024/1, Free University Berlin, School of Business & Economics.
    7. Glötzl, Erhard, 2022. "Macroeconomic General Constrained Dynamic models (GCD models)," MPRA Paper 112385, University Library of Munich, Germany.
    8. Glötzl, Erhard, 2022. "A simple General Constrained Dynamics (GCD) model for demand, supply and price shocks," MPRA Paper 112386, University Library of Munich, Germany.

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    More about this item

    Keywords

    Disequilibrium dynamics; Lagrangian mechanics; Behavioral microeconomics; Constrained dynamics; Edgeworth box; Tatonnement;
    All these keywords.

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • B00 - Schools of Economic Thought and Methodology - - General - - - History of Economic Thought, Methodology, and Heterodox Approaches
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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