The Fractal Nature of Wealth Inequality when the Probability of Success is State-dependent

This dissertation investigates wealth inequality/polarization properties related to the features of the invariant distribution of wealth in an innovative economy characterized by uninsurable individual risk. In this model we assume that there is a sequence of successive generations of altruistic individuals who take decisions about consumption and bequest on their accumulated wealth out of a stochastic income at the utility cost of learning a new technology at every generation. In particular, in this model there are only two states of nature describing the achievements of economic agents at period t: "success" and "failure". By using the theory of Iterated Function Systems with state-dependent probabilities (IFSSDP) we describe the dynamics and the invariant distribution of an economy with (possibly) polarized wealth distribution in the long run. We will show through a numerical algorithm how an intense technological progress makes the support of the wealth distribution converge to a fractal Cantor-like set. Such invariant distribution implies the disappearance of the middle class, with a "gap" between a high and a low wealth clusters. Such a gap represents an unequivocal sign of wealth polarization and is more likely to appear at a faster pace of technology growth.