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.
Key words:optimal control synthesis, discount factor, relative income hypothesis, Ramsey’s conjecture, Lyapunov function.
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