# University of Virginia Library

1. The notion of utility, under whatever form, could
never have acquired its importance in economics
if it had not been for the law that came to be attached
to it. This law, which is known as the Principle of
Decreasing Marginal Utility, simply states that for any
given individual, each additional unit of a commodity
increases utility by a decreasing magnitude.
Curiously,
it was a mathematician, Daniel Bernoulli, who first
formulated the principle (1738). As he tried to solve
the St. Petersburg paradox (a gambling paradox),
Bernoulli was led to argue that the emolumentum
(Latin for “advantage”) of the ducat a gambler gains
is smaller than the emolumentum of the ducat he loses.
Owing to the lack of mathematical interest of the
traditional economists, Bernoulli's esoteric memoir
remained unknown to them for almost two centuries.
So, as far as social scientists are concerned, Bentham
was the first to formulate the Principle of Decreasing
Marginal Utility for the case of money (Principles of
the Civil Code,
1802), and Lloyd (op. cit., 1833) the
first to formulate it for a commodity.

Behind the apparently simple enunciation of the
principle, there lie some strong assumptions and some
intricate issues. The least vulnerable of these assump-
tions is that every commodity is cardinally measurable,
which in common terms means that every instance of
a commodity is a sum of perfectly identical parts (or
units). Obviously, this is not true for a vacation or a
stamp collection, for instance.

The truly vulnerable assumption, that utility, too,
is cardinally measurable (in some fictitious units that
have come to be called “utils”), goes back to Bernoulli
and to Bentham. But Bentham went further and main-
tained that the utilities of all individuals have a com-
mon measure and hence can be added together to yield
the total pleasure of a community, just as the addition
of all individual farm areas yields the total farm area
of a country. Once, he did admit that “you might as
well pretend to add twenty apples to twenty pears”
and even denounced the measurability of the individ-
ual's utility; but he set a lasting pattern for social
scientists in arguing that without the addibility of
different utilities “all political reasoning is at a stand-
still.” Certainly, without this addibility Bentham's
principle of the greatest happiness of the greatest
number becomes vacuous. He therefore had a reason
for dreaming about a “political thermometer.” Vain
though such a hope is, economists have kept looking
for a “welfare function” by which to measure the
welfare level of any economy. Even Alfred Marshall
(1879), in a controversial argument which was first
advanced by a French engineer, J. Dupuit (1844),
claimed that the total utility of any community is
measured by the amount of money its members would
pay for each commodity rather than go without it.