Redistribution spurs growth by using a portfolio effect on risky human capital

We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. In accordance with economic models of risky human capital, we assume that dynamics of human capital is modeled as a multiplicative stochastic process which, in the long run, leads to the destruction of individual human capital. 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. Sustainable growth is induced by redistribution despite the losses from the random growth process and despite administrative costs. Growth results from a portfolio effect. 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 performs better with respect to maximize growth under a fixed rate of administrative costs, and with respect to maximize the governmental income. This leads us to some general conclusions about governmental decisions, the relation to public good games with free-riding, and the function of taxation in a risk taking society.