Changes in income distribution over time in a one-sector neoclassical setting

Abstract

This paper, which is aimed at explaining the endogeneous changes in the income distribution as an economy grows, extends Darity's model and applies it to the Gini decomposition equation developed by Fei, Ranis and Kuo. It defines two types of families, the rich and the poor, both being allowed to own labor and capital but the former being assumed to own more capital and have a higher savings rate than the latter. Total supply is produced according to a neoclassical production function. Consumption demand is determined by the pattern of income distribution, and the excess of total supply over consumption is available for investment, which is an addition to the physical capital stock as well as an increase in the wealth of the rich and poor families. Over time, both families become more wealthy as the economy grows according to enlarged production capacities, meanwhile the wage rate rises and the return to capital falls as capital deepening proceeds. These, along with the distribution of factor ownership between the poor and the rich family, determines the pattern of income distribution. It is then found that: (a) as the economy grows from an initial low-level per capita income towards a long-run steady-state equilibrium, the changes in income distribution over time may follow a variety of patterns, depending mainly on the magnitude of the elasticity of substitution and the situation of the initial position; and (b) only if (i) the initial distribution of the ownership of capital is comparable to or slightly more concentrated in the hands of the rich family than its long-run steady level, and (ii) the elasticity is less than one, will the changes in income distribution over time be consistent with the Kuznets inverted-U pattern.