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

5 1 relates here to the rank in an economic hierarchy linked to income.As promotion is assumed to be automatic the "age" k of the system ,or "spent life time" is geometrically distributed.Since the income is also an exponential function of k the Pareto law results from an elimination of k from the two exponential functions. It is natural to object here that Champernowne's model (Champernowne 1953)has been drastically simplified in the above argument. In his model there are more alternatives:People can either rise one step in the ladder or stay in the same state or recess to a lower state,although the possibilities of movement are limited to a certain range.The steady state solution which Champernowne obtains for his model is, however,essentially the same as the simplified case treated above. Champernowne assumes that the probability of transitions from state k-v to state k is independent of k and depends only on v.That means that the transitions depend on the size of the jump but not on where it starts from or where it ends. On this basis the following equation for the steady state is established: 1 X k = S p v X k _ v . (5) -n In terms of generating function the equation becomes

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