Econophysics and Economics of Games, Social Choices and Quantitative Techniques pp 192-203 | Cite as

# A Model of Income Distribution

## Abstract

This paper determines the distribution of income that maximizes aggregate saving when the economy meets the restrictions that the mean income and level of social welfare are given. Presuming that the aggregate demand in the economy consists of the sectoral demand components, consumption and investment, the determined distribution is the one of a given total, that maximizes the funds that can be generated for investment without any loss of welfare. The saving function is assumed to be of Keynesian type: the marginal propensity to save is less than unity and the average propensity to save is increasing with income. The social welfare function we employ here is the single parameter Gini social welfare function introduced by Donaldson and Weymak (1983). If social welfare is assumed to be measured by the Gini social welfare function, then for a simple saving function, the resulting distribution turns out to be the Pareto. We also present an alternative unrestricted maximization of the aggregate saving function and look for the underlying income density function.We finally demonstrate that the Pareto income distribution is completely identifiable for the prespecified levels of welfare and the mean of the income distribution.

## Keywords

Social Welfare Income Distribution Pareto Distribution Social Welfare Function Inequality Index## Preview

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