Applications of a constrained mechanics methodology in economics

Janová, Jitka

doi:10.1088/0143-0807/32/6/001

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…In today's dynamic equilibrium models, the static optimization is replaced by a dynamic problem of optimal control. Similar to the calculation of motion in mechanics (Janová, 2011), variational calculus is used to maximize (or minimize) a specific Lagrangian function. The Euler-Lagrange equation describes the inter-temporal trade-off.…”

Section: Introductionmentioning

confidence: 99%

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

Glötzl

Richters

2019

J Econ Interact Coord

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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.

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Section: Introductionmentioning

confidence: 99%

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

Glötzl

Richters

2019

J Econ Interact Coord

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Computationally efficient algorithms for Brownian dynamics simulation of long flexible macromolecules modeled as bead-rod chains

Moghani

Khomami

2017

Phys. Rev. Fluids

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Logistic oscillator model for gross domestic product

Vallejo-Castañeda,

Quezada-Téllez,

Gutiérrez-Corona

et al. 2024

Int. J. Mod. Phys. C

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In this paper, a logistic oscillator model is presented to analyze the economic cycles of five selected economies: Mexico, Brazil, Canada, China and the United States. This selection was made taking as reference their level of economic development and their geographical position. The proposed model is an extension of the production Phillip’s model (1959), which considers autonomous expenses dependent on time. It should be noted that the logistic oscillator combines the dynamics of a forced damped oscillator, whose restoring force incorporates Verhulst’s logistic equation. The data used are the production levels of The Organization for Economic Cooperation and Development (OECD) at nominal prices of the mentioned nations. The results obtained show terms of no economic damping with explosive tendency. China shows greater nondamping with an explosive trend, as does Mexico. The countries with the greatest oscillatory behavior are Brazil and Canada. Additionally, those showing exponential dynamics are China and the USA. The fitting of the logistic oscillator to the data is significant given the level of the determination coefficient. Therefore, the results indicate that the model can be useful in formulating economic policy criteria, since it allows one to predict the evolution of the economic cycle in the future.

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Applications of a constrained mechanics methodology in economics

Cited by 3 publications

References 17 publications

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

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

Computationally efficient algorithms for Brownian dynamics simulation of long flexible macromolecules modeled as bead-rod chains

Logistic oscillator model for gross domestic product

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