Full text: Konvolut The Personal Distribution of Income 1

extent an inversion of the other; in addition, each will be 
influenced by the dispersion of the values round the other 
regression line. 
Thus . each of the regression lines will 
represent a compromise between the two underlying relations 
the weight of them being different in the one and the other 
regression line. No regression line therefore will be 
a true reflection of an underlying causal (or rather stochastic ) 
relation. We shall have a better chance of understanding the 
meaning of joint size distributions of this type if we regard 
them as residues of a growth process. Set us therefore return 
to the allometric law. As far as its relation to the joint 
distribution wealth-income is concerned we have to make 
two observations: 
1) If the regression line income on wealth could 
be regarded as an expression of the allometric law then, 
as it will be remembered, the regression coefficient 
7 - 70 
is the ratio of the two Pareto,coefficients of the income 
and the wealth distribution. * 
2) Following up the idea that wealth can be 
explained from saving over a certain time and saving cam 
be explained from income, taking saving propensity as given, 
we can darive the distribution of wealth from that of income 
in much the same way .as the other way round: 
We explain'the saving distribution as a convnlution 
of^the income distribution amd of the(distribution of the 
» ( 
propensity to save ( savings ratio ): 
q'(s) - q(y) * g ( iry -is ), \ (9) 
amd the wealth distribution a s a convulution of this and 
the time the saving has accumulated (which will be finite 
in the case of earned income but not necessarily for unearned 
income ): : „ . - 
q''(w) - q'(s)*h(s-w) (lO) 
From this wealth distribution we should by means of the 
original transformation (o) come back to the income 

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