The Personal Distribution of Income

Steindl, Josef

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Document type:: Works

Collection:: Josef Steindl Collection

Title:: The Personal Distribution of Income

Author:: Steindl, Josef

Scope:: Typoskript, 14 Seiten, mit handschriftlichen Anmerkungen

Year of publication:: 1990

Source material date:: [vermutlich um 1990]

Language:: English

Related work:: Steindl, Josef: The Personal Distribution of Income. In: Steindl, Josef: Economic Papers 1941-88. London: Macmillan, 1990, S. 356-371

Topic:: Stochastic processes and size distribution

Shelfmark:: S/M.52.10

Access:: Free access

5 distribution is apparently relatively stable although so many elements relevant to it are changing day by day; the explanation is that the stability lies in the distribution of wealth, education, training etc which change only slowly. In the present paper we shall confine ourselves to the consideration of wealth and thus consider only the income of the wealthy. 4 The dependence of income on wealth. In the following we shall initially consider the income of the wealthy as flowing from wealth. They have,of course,not only unearned but also earned income, and the two are not easy to distinguish even apart from lack of suitable data. But as a first step we may pretend that all their income is interest or profit. Instead of a matrix of income transitions we have now to consider a matrix wealth-income,which shows for each amount of wealth the corresponding probability of different incomes. The basis of the analysis is thus the conditional distribution of income,given the wealth. Economically speaking this is the probability of a certain rate of return to wealth, or profit rate. From this, if we know it,we can derive the distribution of income,provided we know the distribution of wealth. But the distribution of wealth is known; It follows the Pareto law over a fairly wide range and its pattern can also be explained theoretically (see the preceding paper in this volume ). Denoting wealth by W ,let us write for the density of the wealth distribution p*(W) = c W a-1 dW or,putting w = In W p(w) = c e -aw dw for w > 0 p(w) = 0 for w < 0. (7) If Y denotes income and y = In Y ,the conditional density function of income can b^ represented in the form f*(y- w),the density of a certain return on wealth. Even without knowing this function we might manage to derive the distribution of income from that of wealth provided we can make certain assumptions about independence.We shall provisionally assume that the distribution of the rate of return is independent of the amount of wealth. The method will be to "mix" the conditional distribution of income given the wealth (the distribution of return) with the density function of wealth. For the purposes of this calculation we shall replace the density f*(y-w) by the mirror function f(w-y) which is also independent of

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