Kinetic wealth-exchange model of economic growth
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Quevedo Vega, David Santiago
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En esta tesis se propone un modelo cinético de intercambio de riqueza con crecimiento
económico (KWEMEG) en el que se explora el efecto del ahorro de la producción, los im-
puestos con beneficio tributario y la aversión al intercambio, sobre las distribuciones de
riqueza y de dinero. Este modelo se obtiene a partir de una extensión al formalismo mi-
croeconómico del modelo de Chakraborti y Chakrabarti (CCM), donde las preferencias de
consumo se describen mediante funciones de utilidad tipo Cobb-Douglas. Al maximizar es-
tas funciones, sujetas a ciertas restricciones sobre el consumo, se obtienen reglas generales
de interacción entre agentes económicos, caracterizadas por la emergencia de un régimen
conservativo, donde la riqueza total se mantiene constante en el tiempo y las interacciones
entre agentes se reducen a meros intercambios monetarios; y un régimen no conservativo,
en el cual la riqueza crece exponencialmente, induciendo un efecto de crecimiento económi-
co a tasa constante. Como casos particulares del KWEMEG se presentan por separado en
esta tesis tres nuevos modelos en el contexto de la econofı́sica, que extienden el CCM. Su
dinámica macroscópica se estudia analı́ticamente en todos los casos, utilizando la ecuación
cinética de Boltzmann; y numéricamente por medio de simulaciones de Monte Carlo. Esto
permite ajustar las distribuciones emergentes a densidades de probabilidad tipo gamma, y
establecer relaciones analı́ticas para sus parámetros, ası́ como para el ı́ndice de Gini, con el
cual se estudia el nivel de desigualdad en las distribuciones. Adicionalemente, en el régimen
no conservativo es posible estudiar distribuciones auto-semejantes utilizando una aproxima-
ción de campo medio, que abre la puerta a la discusión sobre la posible existencia de colas
de Pareto. Como un resultado general, al agregar en el modelo un efecto relacionado con el
ingreso por salario, se obtiene como una propiedad emergente la Segunda ley fundamental del
capitalismo, de Piketty. Las ideas propuestas en este trabajo atan algunos de los problemas
de la economı́a moderna con el discurso tradicional de los modelos cinéticos de intercambio
y proponen un puente que conecta de forma efectiva la microfundamentación basada en la
maximización de la función de utilidad y los modelos no conservativos. Ambos resultados
son novedosos en el contexto de la econofı́sica.
This thesis proposes a Kinetic wealth-exchange model of economic growth (KWEMEG) which explores the effects of saving of production, tax benefits with redistribution, and exchange aversion, over the wealth and the money distributions. The model is achieved extending the microeconomic formalism of the Chakraborti and Chakrabarti model (CCM), based on the Cobb-Douglas utility functions describing the preferences for consumption. The maximization of this functions, subjected to certain constraints over consumption leads to general rules of interaction between economic agents that induces the emergence of a conservative regime, where the total wealth of the system remains constant in time, and the interactions between agents are reduced to mere monetary exchanges; and a non-conservative regime, where the wealth and income increase exponentially, inducing an effect of economic growth with a constant rate. The particular cases of the KWEMEG set three new models in the context of econophysics that extend the CCM. All the cases are presented separately in the thesis, and their macroscopic dynamics are studied using the Boltzmann kinetic equation and Monte Carlo simulations, which allows to fit the emergent distributions to the gamma probability density function and to establish analytical relations for its parameters and the evolution of the economic inequality in terms of the Gini index. In addition, it is possible to study a mean field approach for self-similar distributions that allows to discuss the possibility of Pareto tails in the non-conservative regime. As a general result, the model leads to Piketty’s second fundamental law of capitalism as an emergent property, by adding an effect of income due to salary. The ideas developed in this work tie some of the problems of modern economics with the traditional speech of kinetic exchange models of markets, and propose an effective bridge between the microfoundation based on the maximization of the utility function and the non-conservative models. Both results are new in the context of econophysics.
This thesis proposes a Kinetic wealth-exchange model of economic growth (KWEMEG) which explores the effects of saving of production, tax benefits with redistribution, and exchange aversion, over the wealth and the money distributions. The model is achieved extending the microeconomic formalism of the Chakraborti and Chakrabarti model (CCM), based on the Cobb-Douglas utility functions describing the preferences for consumption. The maximization of this functions, subjected to certain constraints over consumption leads to general rules of interaction between economic agents that induces the emergence of a conservative regime, where the total wealth of the system remains constant in time, and the interactions between agents are reduced to mere monetary exchanges; and a non-conservative regime, where the wealth and income increase exponentially, inducing an effect of economic growth with a constant rate. The particular cases of the KWEMEG set three new models in the context of econophysics that extend the CCM. All the cases are presented separately in the thesis, and their macroscopic dynamics are studied using the Boltzmann kinetic equation and Monte Carlo simulations, which allows to fit the emergent distributions to the gamma probability density function and to establish analytical relations for its parameters and the evolution of the economic inequality in terms of the Gini index. In addition, it is possible to study a mean field approach for self-similar distributions that allows to discuss the possibility of Pareto tails in the non-conservative regime. As a general result, the model leads to Piketty’s second fundamental law of capitalism as an emergent property, by adding an effect of income due to salary. The ideas developed in this work tie some of the problems of modern economics with the traditional speech of kinetic exchange models of markets, and propose an effective bridge between the microfoundation based on the maximization of the utility function and the non-conservative models. Both results are new in the context of econophysics.