Related papers: Applications of a constrained mechanics methodolog…
The correctness of Harrods model in the differential form is studied. The inadequacy of exponential growth of economy is shown; an alternative result is obtained. By example of Phillips model, an approach to correction of macroeconomic…
The correctness of Harrods model in the differential form is studied. The inadequacy of exponential growth of economy is shown; an alternative result is obtained. By example of Phillips model, an approach to correction of macroeconomic…
Vakonomic mechanics has been proposed as a possible description of the dynamics of systems subject to nonholonomic constraints. The aim of the present work is to show that for an important physical system the motion brought about by…
The analogies between economics and classical mechanics can be extended from constrained optimization to constrained dynamics by formalizing economic (constraint) forces and economic power in analogy to physical (constraint) forces in…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
This survey (re)introduces reinforcement learning methods to economists. The curse of dimensionality limits how far exact dynamic programming can be effectively applied, forcing us to rely on suitably "small" problems or our ability to…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
The conventional economic approaches explore very little about the dynamics of the economic systems. Since such systems consist of a large number of agents interacting nonlinearly they exhibit the properties of a complex system. Therefore…
System dynamics is a methodology that is widely used in many academic fields. It explains the behavior of social and economic systems with models that capture complex causality and feedback effects. This 'practice paper' discusses the…
This article is a follow-up of a short essay that appeared in Nature 455, 1181 (2008) [arXiv:0810.5306]. It has become increasingly clear that the erratic dynamics of markets is mostly endogenous and not due to the rational processing of…
We explore the nonlinear dynamics of a macroeconomic model with resource constraints. The dynamics is derived from a production function that considers capital and a generalized form of energy as inputs. Energy, the new variable, is…
Nowadays, there is an increasing concern about the unsustainability of the take-make-dispose paradigm upon which traditional production and consumption systems are built. The concept of circular economy is gaining attention as a potential…
Classical economics has developed an arsenal of methods, based on the idea of representative agents, to come up with precise numbers for next year's GDP, inflation and exchange rates, among (many) other things. Few, however, will disagree…
This paper presents a conceptual model describing the medium and long-term co-evolution of natural and socio-economic subsystems of Earth. An economy is viewed as an out-of-equilibrium dissipative structure that can only be maintained with…
We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of…
The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from…
We develop a tractable macroeconomic model that captures dynamic behaviors across multiple timescales, including business cycles. The model is anchored in a dynamic capital demand framework reflecting an interactions-based process whereby…
The monograph is concerned with some key problems of the theory of nonlinear economic dynamics. The authors' concept consists in analyzing the problem of structural instability of economic systems within the framework of the synergetic…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…