A statistical field approach to capital accumulation

Autor: Marc Wambst, Aïleen Lotz, Pierre Gosselin
Přispěvatelé: Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Cerca Trova, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Rok vydání: 2021
Předmět:
Physics - Physics and Society
Economics and Econometrics
Multi-Agent Model
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
FOS: Physical sciences
Distribution (economics)
Physics and Society (physics.soc-ph)
01 natural sciences
Phase Transition
010305 fluids & plasmas
FOS: Economics and business
E1
Microeconomics
Capital accumulation
Interaction Agents JEL Classification: C02
0502 economics and business
0103 physical sciences
Economics
Capital Accumulation
[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat]
050207 economics
Business and International Management
Ex- change Space
[QFIN]Quantitative Finance [q-fin]
business.industry
Field (Bourdieu)
Market clearing
Statistical Field Theory
05 social sciences
Depreciation (economics)
Crowding out
C60
[PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]
Capital (economics)
8. Economic growth
E00
Economic model
Path Integrals
General Finance (q-fin.GN)
Quantitative Finance - General Finance
business
Zdroj: Journal of Economic Interaction and Coordination
Journal of Economic Interaction and Coordination, Springer Verlag, 2021, 16 (5)
ISSN: 1860-7128
1860-711X
DOI: 10.1007/s11403-021-00330-9
Popis: International audience; This paper presents a model of capital accumulation for a large number of heterogenous producer-consumers in an exchange space in which interactions depend on agents' positions. Each agent is described by his production, consumption, stock of capital, as well as the position he occupies in this abstract space. Each agent produces one differentiated good whose price is fixed by market clearing conditions. Production functions are Cobb-Douglas, and capital stocks follow the standard capital accumulation dynamic equation. Agents consume all goods but have a preference for goods produced by their closest neighbors. Agents in the exchange space are subject both to attractive and repulsive forces. Exchanges drive agents closer, but beyond a certain level of proximity, agents will tend to crowd out more distant agents. The present model uses a formalism based on statistical field theory developed earlier by the authors. This approach allows the analytical treatment of economic models with an arbitrary number of agents, while preserving the system's interactions and complexity at the individual level. Our results show that the dynamics of capital accumulation and agents' position in the exchange space are correlated. Interactions in the exchange space induce several phases of the system. A first phase appears when attractive forces are limited. In this phase, an initial central position in the exchange space favors capital accumulation in average and leads to a higher level of capital, while agents far from the center will experience a slower accumulation process. A high level of initial capital drives agents towards a central position, i.e. improve the terms of their exchanges: they experience a higher demand and higher prices for their product. As usual, high capital productivity favors capital accumulation, while higher rates of capital depreciation reduce capital stock. In a second phase, attractive forces are predominant. The previous results remain, but an additional threshold effect appears. Even though no restriction was imposed initially on the system, two types of agents emerge, depending on their initial stock of capital. One type of agents will remain above the capital threshold and occupy and benefit from a central position. The other type will remain below the threshold, will not be able to break it and will remain at the periphery of the exchange space. In this phase, capital distribution is less homogenous than in the first phase.
Databáze: OpenAIRE
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