Towards a stochastic model with heterogeneous agents and class division

We present a simple stochastic model in which heterogeneous agents accumulate wealth belonging to the capitalist or the working class, with profits generated by a stochastic multiplicative process and wages by an additive one. Class selection is based on a random process depending on wealth distribution and the profit rate. In general, playing the role of capitalist rises the probability of accumulating more and more wealth that, in turn, increases the probability to play again the role of the capitalist in following periods. This may give rise to an amplification mechanism leading to a persistent division in social classes. A scenario analysis is performed to explore the sensitivity of results to alternative assumptions on the propensity to consume/save and the fraction of wealth invested by capitalists in the risky process.