Equal opportunities lead to maximum wealth inequality

Abstract

If wealthier people have advantages in having higher returns than poor, inequality will unequivocally increase, but is equal opportunity enough to prevent it? According to several models in economics and econophysics, no. They all display wealth concentration as a peculiar feature of its dynamics, even though no individual can have repeating gains advantage. Here, generalizing these particular models, we present a rigorous analytical demonstration, using master equation formalism, that any fair market that gives each agent the same expected return conducts the system to maximum inequality.

A constraint on the dynamics of wealth concentration

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In [1] the authors show that under minimal hypothesis, in a free, growing economy the wealth concentration as measured by the Gini coefficient G t is bounded to reach its maximum, G t → 1. Under their hypothesis the wealth growth is on average proportional to the wealth itself, thus leaving no room for a salary component independent of the individual's wealth.

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