  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.
