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Konvolut The Personal Distribution of Income 1

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Works

Document type:
Works
Collection:
Josef Steindl Collection
Title:
Konvolut The Personal Distribution of Income 1
Author:
Steindl, Josef
Scope:
Konvolut aus handschriftlichen und maschinenschriftlichen Blättern (insgesamt 71)
Year of publication:
ohne Datum
Language:
German English
Note:
Titel fingiert. - 2 Kopien einer unveröffentlichten Version des Artikels "The Personal Distribution of Income" von August/September 1972 mit handschrifltichen Anmerkungen und Anstreichungen, zusätzlich einzelne Blätter mit teils handgeschriebenen und -gezeichneten Formeln, Tabellen und Diagrammen.
Related work:
Steindl, Josef: The Distribution of Wealth after a Model of Wold and Whittle. In: Steindl, Josef: Economic Papers 1941-88. London: Macmillan, 1990, S. 328-355 Steindl, Josef: The Pareto Distribution. In: Steindl, Josef: Economic Papers 1941-88. London: Macmillan, 1990, S. 321-327 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
JEL Classification:
D31 [Personal Income, Wealth, and Their Distributions]
Shelfmark:
S/M.23.1
Rights of use:
All rights reserved
Access:
Free access

Full text

8 
provided we ’«crow the distribution of wealth. But the distribution 
of wealth is known: It follows the Pareto law - over a fairly 
wide range - and its pattern has also been explained 
theoretically / i3/- 
Denoting wealth by 
of the wealth distribution 
p* - c W“*” 1 dtf 
Tf , let us 
write 
for the density 
or putting w » ln W 
p( w) = c e ~ cLc** 
for w -^ > 
0 
(4) 
p(w) => 0 
for w <. 
0 
If Y denotes income and y= ln T the conditional 
density function of income can be represented in the form 
f*(y-w), the density of a certain return on wealth. Sven without 
knowing this f’unction 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. 
In terms of random variables, if ^ and 'Xj 
denote income, wealth and the rate of return, we have 
If the random variables wealth and the rate of return are independent, 
their sum can be represented by a convolution of the corresponding 
density functions, and we shall in this way obtain the 
distribution of income. 
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 : 
TTnile the former refers to a rate of return per year, the reciprocal 
value refers to the number of years income contained in the wealth ). 
The calculation of the density of income q(y) 
proceeds then by mixing the function f(w-y) with the density, 
of wealth:
	        

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Steindl, J. (ohne Datumohne Datum). Konvolut The Personal Distribution of Income 1.
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