  We demonstrate by mathematical analysis and systematic computer simulations
that redistribution can lead to sustainable growth in a society. The human
capital dynamics of each agent is described by a stochastic multiplicative
process which, in the long run, leads to the destruction of individual human
capital and the extinction of the individualistic society. When agents are
linked by fully-redistributive taxation the situation might turn to individual
growth in the long run. We consider that a government collects a proportion of
income and reduces it by a fraction as costs for administration (efficiency
losses). The remaining public good is equally redistributed to all agents. We
derive conditions under which the destruction of human capital can be turned
into sustainable growth, despite the losses from the random growth process and
despite the administrative costs. Sustainable growth is induced by
redistribution. This effect could be explained by a simple portfolio-effect
which re-balances individual stochastic processes.
  The findings are verified for three different tax schemes: proportional tax,
taking proportional more from the rich, and proportionally more from the poor.
We discuss which of these tax schemes is optimal with respect to maximize
growth under a fixed rate of administrative costs, or with respect to maximize
the governmental income. This leads us to some general conclusions about
governmental decisions, the relation to public good games, and the use of
taxation in a risk taking society.
