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

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 to the modeling framework.