Full text: Konvolut Wealth and Income Distribution 2

0 / y 
income is unity/(thus Y = 0), and the reciprocal rate of 
’eturn is therefore given by W. Ult shoulcj/be noted that 
a doublepdLded Laplace transform £ould i^dt help us, because 
it codld never converge at the empirical values of ©c /• 
Ttie density of the rate of return^will thus be truncated. 
In~the case of dependence the ./truncation - will be worse, 
if \k<1, because the function f* (W) will be stretched 
by a factor 1/k. 
There is, however,a deeper reason for the restriction: 
The validity of the Pareto law cannot be assumed for low 
values of W (in fact,for negative values, if we put the 
unit of wealth at a level which limits the range of 
linearity of the distribution). Owing to the irregular 
ity of the wealth distribution for low values of wealth 
the possibility of very high rates of return might disturb 
the regularity of the pattern of incojne distribution. We 
mudb, therefore, set a limit to the perkltted rate of 
In reality the return rates which have been truncated in 
our exercise may, however, exist. The point is, th^n, that 
to the extent that they exist - and that will be the x more 
likely the smaller k is - the income distribution will \£e 
less Regular than the wealth distribution. In practice 
this will mean that the range dominated by the Pareto law 
will be narrower for income than for wealth.

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