Tolstoy’s dream and the quest for statistical equilibrium in economics and the social sciences

Abstract

The meaning of the notion of statistical equilibrium in economics is discussed as well as its relevance for economic theory. A simple agent-based model of taxation and redistribution is presented. Its invariant equilibrium distribution is the generalized P´olya sampling distribution. It turns out that the expected wealth distribution is the dichotomous Pólya whose continuous limit is the Beta distribution and whose appropriate thermodynamic limit is the Gamma distribution, often found in describing empirical data. The shape parameter of the Gamma distribution is the inverse of the wealth preferential attachment α−1.