A constraint on the dynamics of wealth concentration

TL;DR

This paper establishes necessary and sufficient inequalities to prevent infinite wealth concentration in stochastic growth models, highlighting the importance of labor income in controlling inequality without relying on equilibrium concepts.

Contribution

It generalizes previous results by providing broad inequalities applicable to various models, emphasizing the additive growth component's role in inequality regulation.

Findings

Necessary proportional labor income growth to avoid wealth runaway.

Inequalities hold across models without requiring equilibrium wealth distribution.

Highlights the additive component's role in limiting inequality growth.

Abstract

In the context of a large class of stochastic processes used to describe the dynamics of wealth growth, we prove a set of inequalities establishing necessary and sufficient conditions in order to avoid infinite wealth concentration. These inequalities generalize results previously found only in the context of particular models, or with more restrictive sets of hypotheses. In particular, we emphasize the role of the additive component of growth - usually representing labor incomes - in limiting the growth of inequality. Our main result is a proof that in an economy with random wealth growth, with returns non-negatively correlated with wealth, an average labor income growing at least proportionally to the average wealth is necessary to avoid a runaway concentration. One of the main advantages of this result with respect to the standard economics literature is the independence from the concept of an equilibrium wealth distribution, which does not always exist in random growth models. We analyze in this light three toy models, widely studied in the economics and econophysics literature.