The Distribution of Wealth with Imperfect Altruism
In this paper, we study the distribution of wealth in an economy with infinitely lived families. Individual generations of each family may or may not be altruistic. This is represented as a preference shock which follows a first-order Markov process within each family, a feature representing imperfect altruism. Altruistic individuals care about the welfare of their children and are likely to leave bequests; selfish ones do not. This results in a non-trivial distribution of wealth among families at any point in time. We study an economy with a risk-free, linear production technology and show that a stationary distribution of wealth exists. This distribution is discrete and approximates the pareto distribution under additional restrictions. We also charac- terize conditions on the production technology which yields perpetual growth with increasing inequality.