Distribution of Income and Wealth Among Individuals

TLDR

In a simple growth model with linear savings, constant reproduction, homogeneous labor, and equal inheritance, a stable balanced growth path leads asymptotically to equal wealth and income, though a transient period of inequality can occur. The paper investigates the forces driving inequality. The authors analyze how different tax regimes affect the speed of wealth equalization and illustrate the time scales involved with a simple example. The main conclusions hold under various savings functions and reproduction rates, leaving asymptotic equality unchanged.

Abstract

We begin by considering a simple model of accumulation, with a linear savings function, a constant reproduction rate, homogeneous labor, and equal division of wealth among one's heirs. In such an economy, if the balanced growth path is stable, all wealth and income is asymptotically evenly distributed, with the possible exception, in the case of negative savings at zero income, of a group with zero wealth. In the process of accumulation, there may, however, be a period during which wealth becomes less evenly distributed. We then show that the basic conclusions are unaltered under a variety of alternative savings assumptions, where savings is a function of wealth or of the distribution of income, or where savings is a nonlinear concave function of income, and that variable rates of reproduction make no difference at least to the asymptotic results. The effects of alternative taxes on the speed of equalization are investigated in Section 4, and in Section 5 we consider a simple example to see the order of magnitudes of time that are involved in the equalization process. In the remaining sections of the paper, we investigate the forces for inequality: