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

Abstract

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.

Modeling the out-of-equilibrium dynamics of bounded rationality and economic constraints

“…General Constrained Dynamics (Glötzl, 2015;Glötzl et al, 2019) is an economic framework, describing the interaction of bounded rational agents that exert economic forces to improve their situation (gradient climbing) subject to the economic constraints. Adapting the concept of constrained dynamics from Lagrangian mechanics (Flannery, 2011;Lagrange, 1788), it carries on an "unfinished business" (Leijonhufvud, 2006, pp.…”

“…Adapting the concept of constrained dynamics from Lagrangian mechanics (Flannery, 2011;Lagrange, 1788), it carries on an "unfinished business" (Leijonhufvud, 2006, pp. 26-30) of the early neoclassicals such as Irving Fisher (1892) or Vilfredo Pareto (1897): Inspired by the description of stationary states in classical mechanics, they derived an economic theory of static equilibrium (Glötzl et al, 2019;Grattan-Guinness, 2010;Mirowski, 1989;Pikler, 1955). Despite some efforts, they were unable to describe analogously the adaptive processes that were thought to converge to the states analyzed in static theory (Donzelli, 1997;Leijonhufvud, 2006;McLure and Samuels, 2001).…”

“…Introduced by Glötzl et al (2019), GCD models extend the historical analogies between general equilibrium models and Newtonian physics: Similar to the forces of interacting bodies under constraint from Lagrangian mechanics, the modeling approach depicts the economy from the perspective of economic forces and economic power. Economic force corresponds to the desire of agents to change certain variables, while economic power captures their ability to assert their interest to change them.…”

Modeling economic forces, power relations, and stock-flow consistency: a general constrained dynamics approach

“…The Lagrange closure from classical mechanics introduces K additional variables (Lagrangian multipliers λ k ) and additional constraint forces to solve the system while respecting the constraints. Glötzl et al (2017) show how constraints add constraint forces to the equations of motion, guaranteeing that identities hold without the need to explicitly define a priori which variables determine others. The constraint forces can be modeled in analogy to classical mechanics by Lagrange multipliers λ k and the gradient of Z k .…”

New Directions in Macroeconomics

“…Economists have failed to benefit from the revolution in computing power, which enables us to move beyond pen and paper calculations of over-simplified formulae describing the economy. For example, Glötzl et. al.…”