University of Virginia Library

UTILITY AND VALUE
IN ECONOMIC THOUGHT

I

1. The common word “utility” was introduced into
the special vocabulary of the social scientist only in
the last half of the eighteenth century. By it the initia-
tors understood that inherent property of a thing which
in English is best rendered by “usefulness.” Thus, Abbot
Ferdinando Galiani (Della moneta, 1750) defined utilità
as “the power of a thing to procure us felicity.” Simi-
larly, Jeremy Bentham at first spoke of utility as “that
property in any object, whereby it tends to produce
benefit, advantage, pleasure, good or happiness” (An
Introduction to the Principles of Morals and Legislation,
1780). But the meaning of the term has shifted contin-
uously and even today “utility” circulates with various,
albeit cognate, connotations. By referring to the prin-
ciple of utility as the principle of the greatest happiness
of the greatest number, Bentham himself paved the
way for this terminological license. The ensuing confu-
sion prompted W. Stanley Jevons to insist that “Utility
is not an Intrinsic Quality,” but “the sum of the pleas-
ure created and the pain prevented” (The Theory of
Political Economy, 1871).

In the end, Bentham was disturbed by his license,
but blamed the unfortunate choice of the term for his
confusion, and the French for insisting on that choice.
The choice was indeed unfortunate, especially in the
case of those Romance languages which do not distin-
guish between “utility” and “usefulness.” But even an
English-speaking person needs some mental effort to
relate “utility” to pleasure. Moreover, “utility” can
hardly evoke a relationship between an individual and
the things and services available to him, which is the
core of every modern definition of the concept. Several
other economists have also expressed their dissatisfac-
tion with the term and made various suggestions, not
always well inspired, for a new label. Unfortunately,
even “ophelimity,” the term coined by Vilfredo Pareto
to cleanse the terminology of any vernacular overtones,
did not prevail. The prestige of Jevons added to that
of Bentham sufficed to enthrone “utility” in economics.

A passage from an Oxford lecture delivered in 1833
by W. F. Lloyd admirably illustrates how clear the
whole picture becomes if one is not entrapped by the
ambiguity of Bentham's license:

(pp. 174, 181).

Carl Menger, one of the founders of the modern theory
of utility (“Principles of Economics,” 1950; German
original, 1871), also used “value” for what others called
“utility” and even decried the use of this last term
otherwise than as a synonym of “usefulness.” Jevons
himself began by emphasizing that “value depends
entirely on utility.” And nowadays most economists
would agree with his position. All this shows that the
modern concept of utility is so intimately connected
with that of economic value that it is well-nigh impos-
sible to separate them in thought or analysis.

2. The notion of utility, in fact, goes back under
other names twenty-five centuries to the philosophers
of ancient Greece, who first raised the problem of what
endows certain things with an economic value. The
march of ideas has been unusually slow and exasper-
atingly tortuous, not only because there were numerous
genuine obstacles to circumvent, but also because at
times spurious ones were created. Nevertheless, one
can distinguish four salient landmarks.

The earliest landmark is represented by a thought
of a very modern facture. There are two elements
involved in economic value: an intrinsic property of
the commodity and the user's ability to enjoy it. As
Xenophon observed in his Oeconomicus, even though
a flute has no value for one who cannot play it, it has
a market value because others can. However, the fa-
miliar conviction that science requires a monistic ex-
planation led a long line of students to move away
from this thought in order to look for a single cause
of value.

Clearly, such a cause must be either in us or in
things, but not in both. And since in early times hardly
anyone could think of pleasure as a measurable entity,
the tenet that “the value of a thing lies in the thing
itself”—as J. B. Say was to formulate it not very long
ago—won by default. Other factors, however, account
for the long survival of this commodity fetishism, a
second landmark. There was, first, the authority of
Aristotle, from whom the idea originated (Nicoma-
chean Ethics 1133a 25-26). Secondly, any thought that
there may after all be a subjective element in economic
value was stifled by the so-called paradox of value,
which, according to Plato (Euthydemus 304), was
known even to the poet Pindar. This paradox points
out that some vitally important things (such as water)
have a very low exchange value or none at all, while
others (such as diamonds) have very little importance
and a very high exchange value. Ergo, value cannot
be in man.

Like many other traditional dogmas, commodity
fetishism suffered a setback during the Age of the
Enlightenment. And, as always, the reaction embraced
the diametrically opposite view. This view, the third

landmark, is that “a thing does not have value because,
as is assumed, it has a cost; but it has a cost because
it has value [in use],” as Étienne de Condillac sum-
marized it about 1745 (Oeuvres philosophiques...,
2 vols. [1948], 2, 246).

The fourth landmark is the modern theory which
views utility as being neither in things nor in us, but
in a relation between us and things, and which explains
value as the balance determined by the members of
an economy between utility and disutility.

II

1. In retrospect it may seem curious that the rich
intellectual legacy of ancient Greece included no sys-
tematic economic study apart from a few uninteresting
works on oikonomia, on rules for good housekeeping.
But the attention of an inquisitive mind will never be
arrested by a stationary process. The ancient Greeks
were a nation of busy traders and navigators over many
seas, but their economy was nevertheless stationary,
in the sense that, apart from random fluctuations
caused by natural phenomena, economic life went from
day to day without any perceptible change. What
should surprise us, therefore, is that in spite of this fact
many of their writings are studded with ideas on value
and utility which even nowadays, after the theory of
consumer behavior has become a highly developed
branch of the economic science, retain their full sig-
nificance.

No modern utilitarian has been able to add anything
substantial to Plato's clear formulation of the doctrine.
He tells us repeatedly that life is a “juxtaposition” of
pleasure and pain, and that “each one of us has in his
bosom two counsellors, both foolish and also antago-
nistic; of which we call the one pleasure, and the other
pain” (Protagoras 357; Laws I. 644, V. 733). After more
than two thousand years, Bentham, the modern archi-
tect of utilitarianism, echoed this very thought in the
opening sentence of An Introduction to Principles of
Morals and Legislation: “Nature has placed mankind
under the governance of two sovereign masters, pain
and pleasure.” Hermann H. Gossen, the first author of
a mathematical theory of utility, in 1854 also began
his Entwicklung der Gesetze des menschliches Verkehrs
und der daraus fliessenden Regeln für menschliches
Handeln (1854; “Exposition of the Laws of Human
Relations and the Resulting Principles for Human Ac-
tions”) with it: “Man wants to enjoy life, and on this
he sets his life goal,” because this is the Creator's law.
In a quite modern vein, Plato (Philebus 21, trans. B.
Jowett), further argues that “... and if you had no
power of calculation you would not be able to calculate
on future pleasure, and your life would be the life,
not of a man, but of an oyster or 'pulmo marinus.'”
This time, however, Bentham's echo—that “all men
[even madmen] calculate” pleasure and pain—falls
much short of the convincing power of Plato's original
argument.

Even though Plato's analysis of pleasure and pain,
spread throughout the Dialogues, is not as systematic
as Bentham's, recent trends in utility theory show that
Plato's is superior. Whilst Bentham maintains that
pleasures and pains are “addible” so that in any situa-
tion the net result is a quantum of either pleasure or
pain, Plato argues that although they “both admit of
more and less” neither can be subtracted from the other
because “the negation of pain will not be the same
with pleasure” (Philebus 41, 43). This idea is further
strengthened by several observations in The Republic
on the nature of wants and, especially, on their hierar-
chy. Plato even notes that new wants emerge with the
increase in income and also touches the important idea
that basic wants are irreducible to one another. Else-
where (Euthydemus 299), he adumbrates another vital
principle for the theory of utility, namely, the principle
that every want is satiable.

2. We owe to Aristotle the fundamental distinction
between value in use and value in exchange (Politics
1257a). Less known is the fact that both his Politics
and Topics contain many other first thoughts on utility.
We find, for example, the idea that “the more con-
spicuous good” is the more desirable and also the
concept of complementarity among commodities,
which F. Y. Edgeworth was to introduce in economics
more than two thousand years later. Also, the observa-
tion that wants satisfied by material consumption alone
are subject to satiety was made again in 1855 by
Richard Jennings. On the other hand, Aristotle's analy-
sis becomes cumbersome as he forces upon it his
strongly ethical views. While recognizing that the
number of human wants is normally unlimited, he
contends that a good household should aim at setting
a limit to the satisfaction of these wants (Politics I.
9-10). He also denounces the craving for money on
the part of money-making people as abnormal and the
practice of “money-breeding” (money-lending) as the
most obnoxious of all. So set was Aristotle on this point
that he invoked the legend of King Midas in its support
without realizing that the legend illustrates only the
principle of want irreducibility. Even if everything
Midas touched had turned into bread, he still would
have died—of thirst.

Unfortunately, the most fateful of Aristotle's
thoughts on value are crowded in a few pages of
Nicomachean Ethics (1132a-1133b) and more often
than not are off the mark. His argument that commodi-
ties could not be exchanged with one another if every
commodity did not possess one measurable quality

common to all, is the origin of commodity fetishism.
In a somewhat cryptic sentence Aristotle asserted that
what renders all commodities comparable is χρεία,
which means “need” and may mean also “demand.”
Most likely, all he wanted to say was that exchange
is possible because people, generally, have the same
wants. Aristotle was very clear on the point which
anticipates the teaching of classical economists: the
quality that endows commodities with value is labor,
and the value of a commodity is proportional to the
amount of labor embodied in it. But, like many after
him, he simply begged the question of whether every
kind of labor is reducible to the same unit of measure-
ment.

A logician of Aristotle's stature could not possibly
overlook the logical implication that, if value is in
things (in whatever form), then exchange cannot in-
crease it—an idea that Karl Marx, in particular, was
to defend in modern times. The point that after a just
exchange or a just remuneration everyone must come
out without gain or loss harmonized splendidly with
Aristotle's ethical views. But the fallacy, shielded by
such a high authority, constituted the sturdiest obstacle
for more than two millennia to a clarification of the
problem of utility.

3. With the fate that awaited knowledge after the
Athenian Akademeia came to an end, the rekindled
intellectual activity of the Middle Ages found no other
authoritative guide than Aristotle's integrated philo-
sophical system. So, as the Scholastic doctors turned
their attention during the thirteenth century to man's
secular problems, they found Aristotle's ethical views
of economic life perfectly congenial to the Christian
teachings. Aristotle's thought that the basis of value
is χρεία offered to Saint Thomas Aquinas a splendid
ground for arguing that value represents the need of
the whole society, not the whimsical need of the indi-
vidual. Moreover, this need must reflect social justice,
without which any society is doomed. However, in the
end the Scholastics began to ask what value is, instead
of what it should be. It was Saint Antoninus who, about
the middle of the fifteenth century, reached the highest
point on a trail broken by Duns Scotus. In his explicit
formulation, the value of an object involves (1) its
quality in comparison with other similar objects, (2)
its scarcity, and (3) its complacibilitas—a notion equiv-
alent to that of utility as defined later by Galiani and
Bentham.

4. During the next three hundred years or so—until
the Enlightenment—the problem of value even
suffered a regress. If some histories of economic
thought leave a different impression it is only because
the historian, either through ignorance of the older
writings or through faulty logic, gratuitously credited
some authors with original thoughts. The truth is that
this period contributed an erroneous idea which had
grown out of the fact that throughout Western Europe
the structure of production remained practically con-
stant over the years. The idea, which constituted an
analytical obstacle for a long time, is that demand is
an invariant coordinate for each community. We find
it first stated in an essay, Della moneta: trattato mer-
cantile (1686), by an Italian scholar, Geminiano
Montanari. But its clearest formulation came some
twenty years later from the financier John Law: “If
the Quantity of Wine brought from France be a 100
Tunn, and the Demand be for 500 Tunn, the Demand
is greater than the Vent” (Money and Trade..., p. 4).
Even Galiani spoke of the demand for wheat in the
Kingdom of Naples as a fixed quantity. And, along with
Montanari, he insisted that only fashion, “an affection
of the mind,” may change the demand.

The mercantilist mood induced later writers to rep-
resent demand by an invariant expenditure, instead of
an invariant quantity. According to this view, the price
of a commodity is the quotient between the money
allocated for that purchase and the quantity of the
commodity brought to the market, as Richard Cantillon
neatly explained in a celebrated essay of 1755 (Essai
sur la nature du commerce en général). This fallacy
is stated in equally plain words by Adam Smith (The
Wealth of Nations [1776], Ch. vii) and appears several
times in Karl Marx's circuitous discussion of demand
(Capital, III, Ch. x). J. B. Say derived from it the
theorem that the rise of price is in direct ratio to the
demand, and in inverse ratio to the supply.

One exception strenghens the view that this errone-
ous conception of demand was fostered by the con-
stancy of economic patterns. The great variations
in grain prices caused by climatic fluctuations led
Gregory King to observe as early as 1686 that the
smaller the crop, the greater its cash value. King,
however, remained totally ignored for almost two
centuries. Only much later—with A. A. Cournot (1838)
in France and Fleeming Jenkin (1870) in England, and
independently of King's work—did the notion of de-
mand at a price emerge to clear the way for the mod-
ern theory of utility.

5. The publication of Galiani's Della moneta (1750)
was an important event, not because the treatise
abounded in remarks which redistilled systematically
some thoughts of Plato's and Aristotle's or because it
substituted utilità for Saint Antoninus' complacibilitas,
but because it marked a change of temper. The treatise
contains the first sparks of subjectivist ideas, of the
recognition of man as the center of everything social,
which was in line with the reformist ideas of the Age
of Enlightenment. Galiani thus argues that the only

invariable standard of value is man himself, for while
the value of all things changes, “man has been, is, and
will be everywhere the same self.” And in his analysis
of man's behavior we find the thesis that the desire
for “rank, titles, honor, nobility, authority” is stronger
than that for luxuries, and the desire for luxuries
stronger than the desire of the hungry for food—a
thesis germane to a recent idea that man works harder
for that additional income which elevates him on the
social scale (Milton Friedmann and L. J. Savage,
1948).

Most important of all is the fact that Galiani antici-
pates the highest thought advanced on utility, namely,
the modern theory of choice. Value, he says, is “an
idea of the balance between the possession of one thing
and that of another in the mind of an individual.” No
wonder then, that Galiani himself did not grasp the
full relevance of this thought. Otherwise he would not
have continued to cling to the Aristotelian fallacy that
in a just exchange there can be neither loss nor gain.
The idea of subjective choice is even more sharply
outlined in a little known essay, “Valeurs et monnaies”
by Turgot (1768):

(Oeuvres... [1844], I, 80).

Turgot goes on to explain that choice reflects the hier-
archy that exists among the individual wants. He also
is the first writer to admit that in barter each party
values what it gets more than what it gives. But, symp-
tomatically, Turgot still could not free himself from
the Aristotelian tradition completely, for he goes on
to argue that in free barter the gains of both parties
must be equal.

5. Thoughts such as Turgot's betrayed the increasing
economic awareness brought about by the increased
commercialization of economic life and, especially, by
the ebullient transformation of the Industrial Revolu-
tion. Students of economic affairs not only became
more visibly interested in the problem of value but
also, on the disappearing trails of mercantilism, began
searching for the source of value. An economy, such
as that of France ruined by the wars of Louis XIV
and crippled by a nobility who deserted the country-
side for Versailles, led François Quesnay to see the
source of value in natural resources, particularly in the
agricultural ones. “Rich peasants, rich kingdom,” is the
way he epitomized his doctrine. Equally natural is
the fact that an economy—such as England's during
the same period—which could not find enough hands
to keep pace with a revolutionary increase in the de
mand for manufactured wares, should have inspired
Adam Smith to see in labor alone the source of value.

Unfortunately, the rise to glory of the classical school
also meant a total return to the Aristotelian ideas and
hence a setback for the correct approach to the prob-
lem of utility initiated by Galiani and Turgot. While
classical economists freely admitted that a thing must
have some use value in order to have a market value,
they scorned—as David Ricardo did most clearly in
the essay “Absolute Value and Exchangeable Value”
written shortly before his death in 1823—any thought
that the individual may have something to say about
the value of a commodity. And with his excellent logic
Ricardo could but acknowledge and defend the star-
tling conclusion that the value of the income of a
society does not increase at all if, after any technologi-
cal innovations, the society produces more goods with-
out employing more labor.

There certainly was an anachronism in the re-
enthronement of the notion of an invariant demand,
just as the forces of the Industrial Revolution began
swaying markets and values. The problem of why
people do not spend their income entirely on bread
or entirely on pearls did not exist for the followers of
Adam Smith even after Lord Lauderdale lectured them
on its importance. Small wonder then that a consum-
mate economist and philosopher such as J. S. Mill could
proclaim in 1848 that “happily, there is nothing in the
laws of value which remains for the present or for any
future writer to clear up; the theory of the subject is
complete” (Principles of Political Economy... 7th ed.
[1961], p. 436).

The British as a whole spoke the language of utility,
as the historian Élie Halévy judged. Only the British
economists, who lived under the great shadow cast by
Adam Smith and Ricardo, remained immune to
Bentham's influence. Even in the awakening from their
slumber Bentham's utilitarianism played a very small
role. The event came as economists everywhere were
compelled to pay attention to the increasing impor-
tance of the consumer in an expanding market capable
of satisfying a growing spectrum of wants. It was not
a mere coincidence that, almost at the same time and
independently of each other, four authors came up with
an almost identical theory of utility: H. H. Gossen in
Germany (1854), W. Stanley Jevons in England (1871),
Carl Menger in Austria (1871), and Léon Walras (1874)
in France. Gossen alone poses a problem to the his-
torian because at the time the historical school of
thought ruled supreme in Germany. But this condition
accounts for the injustice done to the author who not
only anticipated the others by many years, but also
excelled them in many respects. Even today his name
is overshadowed by those of the others.

III

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.

2. Benthamism was so much in the air, both in
England and on the Continent, that (with the notable
exception of Carl Menger) the early writers on utility
followed Bentham's hedonism and equated utility with
the pleasure experienced by an individual during the
act of consumption. This is especially true of Gossen
and Edgeworth and, to some extent, of Jevons. It is
from this position that Edgeworth, with whom hedo-
nism reached its apogee in economics, was able to
defend the cardinal measurability of utility by invoking
the law of sensations enunciated by G. T. Fechner and
E. H. Weber in 1860. Utility is measurable, he con-
tended, because an actual pleasure may be measured
in terms of its “atoms,” i.e., in terms of “just percep-
tible increments” (Mathematical Psychics, 1881). And,
even though not quite in the same vein as Bentham,
Edgeworth expressed his belief in the eventual con-
struction of a hedonimeter for measuring actual pleas-
ures.

But economics could not go on indefinitely with a
notion of utility which implies that the consumer de-
cides whether or not to buy more coffee while drinking
coffee. The modern notion of utility embodies an idea
laboriously outlined by Richard Jennings in an essay
that received hardly any attention at the time (1855).
Utility (Jennings used “value”) is the expression of the
expected pleasure at which the individual arrives on
the basis of his past actual pleasures. However, it is
the unique, yet totally ignored, merit of Gossen to have
perceived that one can go deeper than that. Indeed,
Gossen alone saw that actual pleasure is governed by
a second diminishing principle: Any pleasure dimin-
ishes in intensity and duration with its repetition, and
the sooner the repetition, the greater the diminution.

When all is said and done and utility is taken in
Jennings' sense, the fact that milk tastes better if con-
sumed less frequently has more to do with the Principle
of Decreasing Marginal Utility than the fact that the
intensity of the pleasure of drinking milk decreases as
one is drinking milk.

3. Still another idea of how man values things is that
of Carl Menger (1871), who never accepted the view
that value (by which he meant utility) is measurable.
Menger's position was that man's wants are hier-
archized and that the first unit of an individual's re-
sources has a higher importance than the second be-
cause it satisfies a more urgent need. This simple idea
is, in essence, a nonquantitative form of the Principle
of Decreasing Marginal Utility for any commodity that
may satisfy several wants. Perhaps this is why the first
formulations of this principle, by Daniel Bernoulli and
Bentham, pertained to money, not to a commodity.

Menger's nonmathematical approach soon died away
under the mathematical landslide caused in economics
by Jevons and Walras. Yet, every time a justification
of the Principle of Decreasing Marginal Utility is
offered in the current literature, it invokes only
Menger's hierarchy of wants.

IV

1. All founders of the utility theory had some doubts
about the cardinal measurability of utility, but they
took for granted that the utility of each commodity
is independent of other commodities, that the utility
of bacon, for instance, does not depend on how many
eggs one has. This means that, if x1, x2,..., xn denote
the amounts of the various commodities possessed by
an individual, his total utility is the sum of the single
utilities, U1(x1) + U2(x2) + ... + Un(xn). It goes
without saying that the assumption greatly simplifies
the analysis of value. Let John have six bushels of
potatoes which he can trade at the price of four eggs
for a bushel. In Figure 1, let the number of bushels
be measured from O1 to X1 and the number of eggs
from O2 to X2. Let A1C1 represent John's direct mar-
ginal utility of potatoes when consumed as such and
let A2C2 represent his indirect marginal utility of pota-
toes derived from the eggs obtained by trading. If John
wants to maximize his total utility—a basic assumption
of every utility theory—he should, obviously, trade the
sixth and fifth bushels: their indirect utility is greater
than their direct utility. And he should stop trading
at the point M, where the two curves intersect, because
the direct utility of the fourth bushel is greater for him
than its indirect utility. And if John possessed initially
twenty-four eggs instead of six bushels of potatoes, he
should end up with the same distribution of commodi-
ties, four bushels of potatoes and eight eggs. The same
result obtains in the equivalent case in which John has
twelve dollars and the prices are two dollars for a
bushel and fifty cents for an egg. But if, as it may well
happen, the marginal utilities are such that A1C1 and
A2C2 do not meet, then John must choose to have
either only potatoes or only eggs, according to which
commodity has everywhere a greater marginal utility.
In any case, the optimal distribution of the budget is
unique, which is a direct consequence of the Principle
of Decreasing Marginal Utility.

The fact that a glance at Figure 1 suffices to clarify
many issues of value is the reason why economists still
use this highly unrealistic framework. For example, the
diagram (with A1C1 and A2C2 being drawn as they are)
shows that John's dollar buys more utility when spent
on potatoes than on eggs. This simple point explains
away the paradox of value. The same diagram shows
that as a potato seller John gains the amount of utility
represented by the area MA2C1, and as an egg seller
he gains the greater amount MA1C2 (which may be
infinite if the first potato is indispensable to life). There
can be then no just exchange in Aristotle's sense. And
to know whether there are just exchanges in Turgot's
sense we need the interpersonal comparison of utilities
in which Bentham believed.

2. The independence axiom was discarded as Edge-
worth (Mathematical Psychics, 1881) proposed to
represent total utility by a general function
U(x1,x2,..., xn). The diagram supplied by Edgeworth
for the representation of exchange under these general
conditions has become the most popular in economic
analysis. Let potatoes and eggs be measured on OX1
and OX2, respectively (Figure 2). Let C1, C2, C3,...

be John's utility isolines, a utility isoline being the loci
of all combinations of potatoes and eggs that have the
same utility. Naturally, utility increases as we move
from an isoline to a “higher” one, from C2 to C3, for
example. The alternatives open to John, whom we may
now assume to have ten bushels and be able to trade
one bushel for six eggs, are represented by the points
of the budget line B1B2. The budget distribution that
maximizes John's total utility is the point M at which
one isoline is tangent to this budget line. Clearly, with
isolines having the shape shown in Figure 2, all other
possible distributions of John's budget lie on lower
isolines. Therefore, John will trade four bushels of
potatoes for twenty-four eggs and retain six bushels
for his own consumption. The same solution is valid
if John has, say, six dollars and the prices are sixty cents
for one bushel and ten cents for an egg.

3. Obviously, for the optimal budget distribution to
be unique the utility isolines must be convex toward
O (as they have been drawn in Figure 2). A new
difficulty arises now because the Principle of Decreas-
ing Marginal Utility does not suffice to guarantee this
convexity. The shape of the utility isolines depends,
in addition, on the relation between the commodities.
As Edgeworth noted, commodities may be rival—like
margarine and butter—if an increase in one diminishes
the marginal utility of the other. They may be comple-
mentary—like bread and butter—if an increase in one
increases the marginal utility of the other. However,
there is no way to reduce the convexity property to
a property related to this classification. The convexity
of the isolines had to be added as a new axiom for
which no transparent explanation has yet been offered.
The axiom says that along any isoline the marginal
rate of substitution increases in favor of the commodity
that is decreased.

V

1. Before the emergence of the modern school of
utility, thoughts on value, demand, and exchange ordi-
narily reflected the economic conditions prevailing
during each period. A turning point in this respect took
place following the process of mathematization fos-
tered by that school. Utility theory has ever since been
its own source of new ideas, suggested primarily (and,
at times, exclusively) by its mathematical framework.
An excellent illustration is the observation made by
Irving Fisher in his doctoral dissertation (1892). The
pure geometry of Edgeworth's diagram led Fisher to
note that in order to determine the optimal budget
distribution we do not need to know how many utils
each isoline represents: the knowledge of the isolines
as such suffices. This simple geometrical truth caused
the first serious dent in the idea that a cardinally
measurable utility is indispensable for explaining value.

It was, however, Vilfredo Pareto (Manuale di econo-
mia politica, 1905) who first constructed a consumer
theory which does not require the notion of utility at
all. His point of departure is that an individual con-
fronted with two baskets of commodities will always
either prefer one basket or be indifferent as to which
one he gets. Given this faculty of binary choice, Pareto
reasoned that, by asking the individual to choose be-
tween M and every other possible basket, we can
determine an indifference curve, i.e., a curve that rep-
resents the loci of all baskets “indifferent” in relation
to M. The procedure does not refer in any way to
utility. And once the indifference curves are deter-
mined, they help determine the optimal distribution
of any budget in exactly the same manner as the utility
isolines. Furthermore, we can construct a function
V(x1,x2,..., xn) such that its value is constant on each
indifference curve, just as the utility function
U(x1,x2,..., xn) is constant on each isoline. The only
difference is that V is not uniquely determined—any
increasing function of V, say V2, would do.

It is for the function V that Pareto coined the term
“ophelimity.” But, as was argued in subsequent devel-
opments, we may still speak of utility and of V as its
ordinal, instead of cardinal, measure. This means that
the value of V simply orders all baskets according to
the individual's preferences. Today the notion of an
ordinal utility dominates consumer theory, the central
problem of which is how to derive an ophelimity
function from directly observable budget data.

2. In fact, this problem is relatively old. It was first
formulated in a neglected memoir of an Italian engi-
neer, G. Antonelli (1886). And, as happens quite often,
the glory went to the more famous rediscoverer of the
idea, in this case to Pareto (1905). In simple terms,
Pareto's idea was this: if the optimal distribution of
every possible budget has been determined by obser-
vation, every indifference curve can be determined by
the tangential artifice shown in Figure 2 for C3. But
he ignored the fact that this artifice (which in mathe-
matics is called “integration”) is not always available
for more than two commodities. An obvious para-
dox—known as the integrability problem—thus arose
to intrigue many a mathematical economist. Some light
was cast on Pareto's theory of choice and the integra-
bility problem when it was shown (Georgescu-Roegen,
1936) that Pareto's argument failed to include two
axioms (1) that any commodity may be substituted for
another so that the first and the second basket be
completely indifferent, and (2) that the binary choice
is transitive. (Choice is transitive if A being chosen over
B and B over C, A is chosen over C.)

3. In a signal contribution, Paul A. Samuelson (1938)

presented a theory of choice based, not on the com-
parison between two baskets, but on observable budget
data. His point of departure is that John, by choosing
the budget distribution M, reveals that he prefers M
to any other distribution (such as M′) compatible with
his budget. To this transparent definition, Samuelson
added only an equally transparent axiom: If a budget
reveals that the basket A is preferred to B, no budget
can reveal that B is preferred to A. Samuelson claimed
that this axiom alone suffices for deriving by integration
the indifference varieties and hence for constructing
an ophelimity function. In fact, the axiom expresses
only a condition equivalent to the Principle of De-
creasing Marginal Rate of Substitution. And as shown
first by Jean Ville (1946) and later, but independently,
by H. S. Houthakker (1950), Samuelson's idea calls for
a stronger axiom (analogous to the transitivity of binary
choice). But soon thereafter it was proved that even
this stronger axiom does not entail the existence of an
ophelimity function. It still leaves large domains for
which there is no comparability among the commodity
baskets (Georgescu-Roegen, 1954b). The problem of
what set of economically meaningful postulates would
make the Antonelli-Pareto idea work still awaits its
solution. If it is ever solved, it will very probably cause
a greater stir in mathematics than in economics.

VI

1. Developments on an entirely different track sug-
gest that economists have never abandoned the hope
of proving that utility is after all cardinally measurable.
A remarkably elegant scheme for determining a cardi-
nal scale for utility was developed by Frank P. Ramsey
(1926) and, independently, by O. Morgenstern and John
von Neumann (1944). The scheme follows Bernoulli's
idea in reverse. Bernoulli determined the stake of the
gambler from the knowledge of the gambler's utility
function. The authors just mentioned proposed to de-
termine the utility function of an individual with the
aid of the odds which that individual would be just
willing to accept. They reasoned that if an individual
is just willing to pay five dollars for a lottery ticket
that gives him one chance in two of winning twelve
dollars, we can infer that for that individual the utility
of the additional seven dollars is equal to the utility
of the five dollars that he may lose. By experimenting
with various gambling propositions, we may thus de-
termine step by step how great is the utility of the
individual's n-th dollar in comparison with all his other
dollars. This is tantamount to constructing a utility
scale which, like that of temperature, is completely
determined once the origin and the unit of measure-
ment are chosen arbitrarily.

The idea was received with enthusiasm as well as
with strong reservations. Some authorities on the sub-
ject of utility openly doubted their ability to construct
a cardinal scale even for their own utility. Various
suggestions have been made as to what piece of the
theoretical apparatus may be at fault. Most probably,
the culprit is the assumption that an individual may
be perfectly indifferent between a dollar in hand and
the probable prospect of winning ten dollars. Indeed,
this assumption overlooks the fact that risk adds a new
and irreducible dimension to man's choice (Georgescu-
Roegen, 1954a).

Whatever the fault, the operational feasibility of the
project has never moved beyond the paper-and-pencil
stage and Ramsey's new vision of a psychogalvanom-
eter had no better fate than Edgeworth's hedonimeter.

2. The conclusion of a recent approach to the proc-
ess of choice is that utility is not even ordinally meas-
urable (Georgescu-Roegen, 1954a). The point of de-
parture is Menger's framework: man chooses in
response to his varied wants and in accord with the
hierarchy of these wants. But the new approach notes
that at the bottom of the hierarchy are the most urgent
wants, which are grounded in the biological nature of
man and consequently are ordered alike for all human
beings. These are followed by the social wants, which
have the same order for all persons belonging to the
same culture. Lastly, there are the personal wants;
these vary irregularly from one individual to another.
Moreover, only some of the personal wants may possi-
bly compensate for each other. That is, a person might
be just as happy with more records and fewer movies.
But biological and social wants are irreducible. He who
does not have enough to eat cannot satisfy his hunger
by wearing more shirts.

In this framework, choice is determined by the least
important want that can be satisfied in the given situa-
tion. For example, a person who does not have enough
food will prefer the grocery basket with the greatest
food value. But between two baskets with the same
food value, the same person will choose the one with
tastier foods, taste thus becoming the least important
want. Should the baskets differ only with respect to,
say, packaging, the next want will come into play.
Choice, in this case, completely orders all possible
baskets, but there are no completely indifferent baskets.
The result is that choice no longer yields indifference
lines and hence cannot be represented by an ophelimity
index.

Several criticisms may be levelled against this ap-
proach. There is, first, the fact that wants are not
sharply defined notions and hence fit poorly into a
quantitative framework. Blurred as the hierarchy of
wants may be, it offers a legitimate, objective basis for
the interpersonal comparison of welfare—without

which taxation must remain a completely arbitrary
operation. It also justifies, for example, such useful
analytical tools as the distinction between wage goods
and luxury goods.

The preceding picture is foreign to the utility theory
launched by Gossen, Jevons, and Walras. This theory
has instead accumulated an impressive mathematical
arsenal around the idea of the complete reducibility
of wants, which is tantamount to the assumption of
complete substitutability among commodities. The ul-
timate product needs unparsimonious stressing: the
modern utility theory reduces all wants to one general
abstract want called “utility.” In line with this reduc-
tion, one need not say “these people need more shoes”;
instead, “these people need more utility” should suffice.
The reduction is responsible for the fact that the same
theory teaches that there is no objective basis for inter-
personal comparison of utility. All this may again be
due to a particular feature of the economies in which
the builders of the modern theory of utility lived. Those
were not economies in which a low income kept basic
wants in front of everybody's eyes; they were econo-
mies where most people were able to satisfy even many
personal wants. Modern utility theory is a theory of
a consumer who has a relatively ample income and
whose economic choice is guided only by the quantities
of commodities.

BIBLIOGRAPHY

In addition to the classic authors (ancient and modern),
the following special works cited in the text may be con-
sulted for details: Giovanni B. Antonelli, Sulla teoria mate-
matica della economia politica (1866; Milan, 1952); M.
Friedman and L. J. Savage, “The Utility Analysis of Choices
Involving Risk,” Journal of Political Economy, 56 (1948),
279-304; Ferdinando Galiani, Della moneta (1750; Bari,
1915); Nicholas Georgescu-Roegen (1936), “The Pure The-
ory of Consumer's Behavior,” reprinted in Nicholas
Georgescu-Roegen, Analytical Economics: Issues and Prob-
lems (Cambridge, Mass., 1966), pp. 133-70; idem, “Choice,
Expectations, and Measurability” (1954a), reprinted ibid.,
pp. 184-215, from the Quarterly Journal of Economics, 68
(1954), 503-34; idem, “Choice and Revealed Preference”
(1954b), reprinted ibid., pp. 216-27, from Southern Eco-
nomic Journal, 21 (1954), 119-30; Hendrik S. Houthakker,
“Revealed Preference and the Utility Function,” Eco-
nomica, N.S., 17 (1950), 159-74; John Law, Money and Trade
Considered with a Proposal for Supplying the Nation with
Money (1705), reprinted in Oeuvres complètes, 3 vols. (Paris,
1934) I, 4; William F. Lloyd, “A Lecture on the Notion
of Value as Distinguishable Not Only From Utility But Also
From Value in Exchange” (1833), Economic History, 1
(1927), 170-83; Alfred Marshall, The Pure Theory of Domes-
tic Value (1879), Reprints of Scarce Tracts in Economics
and Political Science, No. 1 (London, 1930); Oskar
Morgenstern and John von Neumann, Theory of Games and
Economic Behavior (New York, 1944); Vilfredo Pareto,
Manuel d'économie politique (Paris, 1909), an expanded
version of his Manuale di economia politica (Milan), pub-
lished in 1905 but dated 1906; Frank P. Ramsey, The Foun-
dations of Mathematics and Other Logical Essays (1926; New
York, 1950); Paul A. Samuelson, “A Note on Pure Theory
of Consumer's Behavior,” Economica, N.S., 5 (1938), 61-71
and 353-54; Jean Ville, “The Existence-conditions of a Total
Utility Function” (1946), Review of Economic Studies, 19
(1951-52), 123-28.

General surveys of the technical aspects of the problem
of utility are: Kenneth J. Arrow, “Utilities, Attitudes,
Choices: A Review Article,” Econometrica, 26 (1958), 1-23;
John S. Chipman, “The Foundations of Utility,” Economet-
rica, 28 (1960), 193-224; Nicholas Georgescu-Roegen,
“Utility,” International Encyclopedia of the Social Sciences,
17 vols. (New York, 1968), 16, 236-67 (it includes a substan-
tial bibliography); George J. Stigler, “The Development of
Utility Theory” (1950), reprinted in J. J. Spengler and
W. R. Allen, eds., Essays in Economic Thought: Aristotle to
Marshall (Chicago, 1960), 606-55, from Journal of Political
Economy, 18 (1950), 307-27, 373-96.

NICHOLAS GEORGESCU-ROEGEN

[See also Economic History; Economic Theory of Natural
Liberty; Happiness and Pleasure; Social Welfare; Util-
itarianism.]