A dynamic model of the distribution of wealth among households and nations

Stiglitz once showed that, in general, aggregate wealth is asymptotically uniformly distributed among individuals. However, in his formulation household saving is not the outcome of utility maximization over time. Constructing a simple dynamic general equilibrium model in which household saving is choice-theoretically determined, we show that given initial holdings of wealth there is a unique and stable steady state distribution of wealth and that the distribution of wealth becomes more even (resp. uneven) as time goes by if the total wealth is initially greater (resp. smaller) than its steady state level. We also study the response of the steady state equilibrium to the changes in initial distribution of wealth and the rate of time preference, and to several types of technological improvements.