A Model of Income Distribution.pdf

Abstract

In the modles discussed in this paper the distribution of incomes between an enumerable infinity of income ranges is assumed to develop by means of a stochastic process. In most models the stochastic matric is assumed to remain constant through time. Under these circustamces, and provided certain other conditions are satisfied, the distribution will tend towards a unique equilibrium distribution dependent upon the stochastic matric but not on the initial distribution. It is found that under fairly general conditions, provided the prospects of change of income as described by the matrix are in a certain sense independent of income for incomes above some limit then the Paresto curve of the equilibrium distribution will be asymptotic to a straight line. This result is preserved even wgen some of the effects of age on income are allowed for, and also when allowance is made for the effect of an occupational stratification of the population. Some consideration is also given to the fact that changes in the income distribution may cause the stochastic matrix itself to change. Some discussion is also given of cases where the Pareto curve of the equilibrium distribution is not asymptotic to a straight line.