# Full text: The Personal Distribution of Income

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showing disproportionately increasing output with any increase
in input ( cost, or employment ). In fact, however, we often
find that it is not so amd that both regression coefficients
are smaller than one, decreasing cost and decreasing returns
apparently coexisting.
How is this possible? It can only occur with
wide dispersion round the regression line, The exceptionally
efficient plant will tend to be counted as small plant
in the input dimension while the unusually inefficient ones
?;ill be counted as large. In c nsequence there will be
a bias in fav ur of decreasing returns as measured in the
input dimension ( regression of output on cost or employment ),
The inversi n bf the regression corresponds
t the fact that the rati % of the two standard deviations
is recipr cal in the two regress! n c efficients If it
is 9/11 in the regression f input n >utput, it is to/9
in the other re ressi n But unless the correl ti n c efficient
is sufficiently high, the regression coefficients
will both have values be law unity.
The same mechanism must also be at work ir.tfc
the wealth-income distribution: Those with high return for
a given wealth will be classified among large incomes, those
with low returns with the same we 1th among small incomes,
which tends to counteract the natural tendency of wealth to
increase with income. ;'his may have contributed to the
flatness of the wealth-income regression in the lower income
rage, although the chief reason for that is no doubt the
truncation of the wealth distribution.
The preceding example of plant size, in which
only one underlying theoretical relation is presumed to exist,
shows that while it is logical to expect in this case,
if one regression reflects the underlying relation, that the
other should as it were represent the inverse of it, yet in
reality this will not be true because t e sec nd regress! n
will be m re or less distorted by the dispersi n of values
round the first regression line.
If we have two underlying relati-ns then each f
the regress! n lines will be influenced by b th f them,
either directly r indirectly, because each will be t sme
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