RAMSEY’S CONJECTURE OF SOCIAL STRATIFICATION AS FISHER’S SELECTION PRINCIPLE

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Abstract

Ramsey’s conjecture of social stratification states that wealth in a population of households is concentrated among the most frugal agents, who discount consumer spending with the lowest discount factor. Ramsey’s conjecture can be viewed as stating that Fisher’s principle of natural selection holds in a population of households. In this paper, based on Duesenberry’s hypothesis, discount factors are formed depending on the capital distribution among the agents. The behavior of households is described by Ramsey-type models of a rational representative consumer. For the corresponding optimal control problems, we construct solutions in the form of synthesis, which are used to model the dynamics of a household population. Theorems for a household population are proved that justify the validity of Ramsey’s conjecture. The influence of consumer loans on the social stratification of households is studied.

About the authors

G. S. Parastaev

Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University; Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences

Email: parastaew1996@yandex.ru
Moscow, 119991 Russia; Moscow, 119333 Russia

A. A. Shananin

Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University; Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences; Moscow Institute of Physics and Technology (National Research University); Moscow Center for Fundamental and Applied Mathematics; Peoples’ Friendship University of Russia (RUDN University)

Email: alexshan@yandex.ru
Moscow, 119991 Russia; Moscow, 119333 Russia; Moscow oblast, 141701 Russia; Moscow, 119991 Russia; Moscow, 117198 Russia

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