# Full text: The Personal Distribution of Income

```extent an inversion of the other; in addition, each will be
influenced by the dispersion f the values r^und the other
recession line.
Thus ltfiT. each-.*# 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 ither
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. Cet 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 he remembered, the regression coefficient
is the rati ■ of the tw P&ret ja efficients if the inc me
and the wealth distributi n
2) Foil wing up the idea that wealth can be
explained fr m saving ver a certain time and saving can
be explained fr m inc me taking saving r pensity as given,
we can deirive the distributi n f wealth fr m that of income
in much the same way as the ther way r undi
V/e explain the saving distributi n as a c nvnluti n
ofjthe income distribution and >f thesistribution f the
propensity to save ( savings ratio ):
q«(s) - q(y) * g ( Vy - s ), (9)
and the wealth distribution a s a convalution 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 )s
q«»( w ) « ^ q'(s) * h ( s - w ) (10)
From this wealth distribution we should by means f the
original transformati n (6) c me back to the income
distribution
```

### Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.