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

Since the beginnings of modern economics, economists sought to emulate the revolution in physics initiated by Newton's 'Principia' (1687). Concepts from mechanics have influenced economic models both in terms of methodology and content. The aim of this theoretical paper is to put forward a novel economic modeling framework that extends the analogies between economics and classical mechanics from constrained optimization to constrained dynamics. We introduce the concepts of economic forces and economic power that bear striking resemblance to physical forces and the reciprocal value of mass. In this setup, the change of a variable is determined by the forces agents employ to change it according to their desire, their power to assert their interest, and constraint forces emerging from system constraints. The approach is based on a genuine dynamic out-of-equilibrium analysis and can incorporate heterogeneous agents, prisoner's dilemma situations, and behavioral assumptions different from rationality and utility maximization. Thereby, it seeks to overcome some restrictions inherent to approaches based on optimization under constraint and provide an out-of-equilibrium foundation for equilibrium models. We transform a static textbook exchange model into a dynamic model, and reflect on advantages, extensions and caveats of our modeling approach.