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

  • Erhard Glötzl
  • Florentin Glötzl
  • Oliver RichtersEmail author
Regular Article


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.


Disequilibrium dynamics Lagrangian mechanics Behavioral microeconomics Constrained dynamics Edgeworth box Tatonnement 

JEL Classification

A12 B00 C62 D50 



EG, FG, and OR in alphabetical order. We thank Amit Bhaduri, Armon Rezai, Friedrich Schneider, Galo Nuno, Hans-Michael Trautwein, Heinz D. Kurz, Jakob Kapeller, Michael-Gregor Miess, Peter Fleissner, and an anonymous reviewer for their helpful comments. All errors and omissions are our own. OR acknowledges funding from Ev. Studienwerk Villigst. Declarations of interest: none.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for the Comprehensive Analysis of the EconomyJohannes Kepler University LinzLinzAustria
  2. 2.Institute for Ecological Economics, Department for SocioeconomicsVienna University of Economics and BusinessViennaAustria
  3. 3.International Economics, Department of EconomicsCarl von Ossietzky University of OldenburgOldenburg (Oldb)Germany
  4. 4.ZOE, Institute for future-fit economiesBonnGermany

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