9 
q (Y) - cdY 
OO 
f* (¥ - Y) e _<7CW dW *» 
= c(f(oC) e -oCY dY 
(w> HO) 
(3) 
where Cf> (oo) is the Laplace transform of i*(x). 
The first result is thus: If the rate of return is inde 
pendent of wealth, the Pareto law will he reproduced in 
the distribution of income, and the coefficient will be 
the same as for wealth. The particular form of the return 
rate distribution is of no account, except for a scale 
»> 
factor. 
This result can be somewhat generalized. If the rate of 
return is not ^dependent of wealth - and indeed it will 
hardly be in reality - then there will be a correlation 
between income and wealth. If this dependence of income 
on wealth is linear in the logs and if the linear re 
gression is also homoscedastic we can virtually re-establish 
the previous case of equation (3) by stretching or con 
tracting the scale of W.(see fig. 1). That is to say, we 
/ 
- k- W ^