Full text: The Personal Distribution of Income

9 
conditional distribution of income,given the wealth. 
Economically speaking this is the probability of a certain 
rate of return to wealth, or profit rate. From this, if we 
know it,we can derive the distribution of income,provided 
we know the distribution of wealth. But the distribution 
of wealth is known: It follows the Pareto law over a 
fairly wide range and its pattern can also be explained 
theoretically (see the preceding paper in this volume ). 
Denoting wealth by W ,let us write for the density of the 
wealth distribution 
p*(W) = c W a-1 dW 
or,putting w = In W 
p(w) = c e“ aw dw for w > 0 
p(w) = 0 for w < 0. (7) 
If Y denotes income and y = In Y ,the conditional density 
function of income can be represented in the form 
f*(y-w),the density of a certain return on wealth. Even 
without knowing this function 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. The method 
will be to "mix" the conditional distribution of income
	        

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