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, 24 Seiten, mit handschriftlichen Ergänzungen bei mathematischen Formeln

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

Shelfmark:: S/M.52.11

Access:: Free access

10 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 wealth. The two functions are symmetric and have the same value.In fact, the only difference is in the dimension:while f* refers to the rate of return per year, f refers to the number of yearly incomes contained in the wealth (the reciprocal value of the return). We calculate then the density of income q(y) by mixing the function f(w-y) with the density of wealth: q(Y) = oo f(w-y) e-aw dw = c 0(a) e-ay for w > y > 0 q(y) = 0 for w < y.(8) where 0(a) is the Laplace transform of f(w). The above mixture is a Laplace transform of f(w) shifted to the right by y. The Laplace transform requires that the argument of the function f be non-negative. We have therefore to assume that w > y (we shall show later how this restriction can be relaxed). Equation (8) shows that the Pareto pattern of the wealth distribution is reproduced in the income

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