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

1 THE PERSONAL DISTRIBUTION OF INCOME When D.G.Champernowne showed how you can explain by means of a stochastic process why the pattern of the Pareto distribution is found with such great regularity in various fields he very naturally chose as an example the distribution of income,because that is the classical case.It seems to me that the approach is more easily applied to firm,towns,or wealth. The case of income is the hardest,so that the great pioneering paper (Champernowne 1953) while fully demonstrating a new method has not entirely disposed of the special problem to which it was directed. Champernowne's Model. I shall give a simplified version of Champernowne's model which will throw a new light on its relation to other models of the Pareto law. With Champernowne the income of a person is the state of the system,and its evolution is described by a Markov chain.The stochastic matrix of probabilities of income transitions from one year to the next,in desperate simplification, looks as follows: income in year t+i income in year t 0 1 2 3 4 5 6 q P q p q p q p q p q p We now re-interpret this matrix so that the states of the system are not the incomes but the stages in a hierarchy or the seniority,a kind of'age",which,however,as we shall see later,is linked to the income.Let us assume only two alternative possibilities of transition for a person in this system:Either a rise from one stage in one year to 0 1 2 3 4 5

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