Chapter 2income varies greatly with income. In fact the gain in hap-
piness is inversely proportional to income. So when a poor
person gets a dollar from someone who is ten times richer
than him or her, the poor person gains ten times more hap-
piness than the rich person loses. This so- called Diminish-
ing Marginal Utility of Income was an article of faith in
nineteenth- century economics and was a central argument
for the redistribution of income. It is now substantiated
by hard evidence, both across individuals (see below) and
across countries (see Chapter 8).
But how big is the effect? How much of the variation
in happiness is due to income inequality? For this purpose
income is measured in the BCS as household disposable in-
come per adult- equivalent^7 in the household.^8 The distribu-
tion of this income in the BCS is the familiar bell shape—
not perfectly “normal” but fairly symmetrical, as Figure 2.1
shows. The standard deviation of log income is 0.74.^9 (We
use the word log somewhat loosely throughout, to mean
natural logarithm, i.e., log to the base e.)
There is a clear relationship between income and hap-
piness. This can be seen in Figure 2.2, which distributes
the whole adult population according to income and life-
satisfaction. As it shows, of the richest third of the popula-
tion, only 16% have life- satisfaction of 6 or less, while for
the poorest third this figure is 29%. However, the overall
correlation between log income and life- satisfaction is only
0.05— the variance of log income “explains” only 0.25% of
the variance of life- satisfaction.
To evaluate the effect of a policy change it is clearest if
we measure how extra income affects life- satisfaction when
this is measured in absolute units (0– 10). If we regress life-