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is to be noted that when two physically dissimilar commodities are perfect
substitutes for one another”where, that is, there is no purpose served by
a given quantity of the one that cannot be served equally well by a given
quantity of the other”then, from an economic point of view, they are not
"different" goods at all. If, for example, there were no purpose for which
a blue pencil is used that is not perfectly served by a red pencil, and vice
versa, then it would not be expedient to distinguish economically between
red and blue pencils at all; they would be used interchangeably. If two
nickels could perform all the uses required of a dime, and vice versa, then
UTILITY THEORY 53


the two coins would make up an economically homogeneous kind of good.
Within this economically homogeneous group there would be, it is true,
physical differences”some members of the group being made up of two
nickels, the other being each one dime. But this would be as irrelevant
as, say, the different registration numbers on two identical automobiles
where the difference in number is the only physical means of distinction
between them.
Most substitute goods are, however, only imperfect substitutes for one
another. A characteristic of goods that a consumer considers as substi-
tutes for one another is that the marginal utility to him of any such good
declines, other things being the same, as the quantity possessed of the
substitute goods increases. The more rapidly the marginal utility declines
in this manner, the more perfect is the substitute relationship between
the goods. The special case, as we have seen, of perfect substitutes is one
where the marginal utility of the one good declines, with increased pos-
session of the other, exactly as rapidly as it would decline were the
quantities possessed of this good itself to be increased in the same pro-
portions.

MARGINAL UTILITY”SOME FURTHER REMARKS
It is worthwhile at this point to emphasize a number of points con-
cerning the marginal utility concept as we have used it thus far. These
points will serve to clarify the content of our utility analysis and, at the
same time, point to the way our analysis is related to the very earliest at-
tempts to use the tool of marginal utility.
The Paradox of Value Modern utility theory emerged in the 1870's
at the hands of Jevons, Menger, and Walras. One of the earliest uses of
the theory was to sweep away a misunderstanding that had prevented the
earlier classical economists from using the utility concept to explain prices.
The earlier writers found themselves unable to explain the prices of
goods by reference to the use-value or utility of these goods. To be sure,
the prices of many goods seem to reflect their relative degrees of usefulness
to men; the classical economists would have welcomed such a theory. But
they were troubled by the many goods whose prices seemed to defy any
such explanation. Diamonds, for example, are clearly much less impor-
tant for human life than water, yet the price of water is quite negligible
compared with that of diamonds. This paradox had forced the classical
economists to seek an entirely different method of explaining prices.
Marginal utility theory is able to dispose of the problem quite simply.
The basis for the paradox was the premise that water is more significant
for man than are diamonds. This premise is no doubt correct, but not in
a way that can support the classical conclusions. Water, in the abstract,
54 MARKET THEORY AND THE PRICE SYSTEM


is no doubt more important than diamonds in the abstract. But for human
action the greater importance of water over diamonds must be demon-
strated through choice among alternatives. For an analysis of human
action no other meaning can be attached to the term "more important."
From this point of view the greater importance of water must mean that
we assume if a man has to choose between water and diamonds, he will
choose water. But for the statement of alternatives a man must choose
among, it is clearly insufficient to specify only that these are water and
diamonds. One must specify the terms and conditions on which he is
to choose. And here the irrelevance of the "greater importance of water
over diamonds" for understanding their relative prices becomes immediately
clear.
Water is more important than diamonds only where a man must choose
between renouncing all water or renouncing all diamonds. Faced with
such a choice it is indeed likely that a man will place diamonds distinctly
in second place. But this kind of choice is one that the market does not
confront the consumer with and therefore cannot have bearing on the
determination of market prices. In the market a man buying or refrain-
ing from buying water is choosing not merely whether to have water or
not to have water, but whether to have some additional quantity of water
or not; and similarly, of course, for diamonds. Thus, the law of diminish-
ing marginal utility provides the key.
The marginal utility of water cannot be said to be either higher or
lower than that of diamonds until there are first specified (a) the size of the
marginal unit and (b) the margin at which marginal quantities of water
and diamonds are being compared. The marginal utility of water is
indeed lower than that of diamonds”when a small quantity of water is
compared with a similar weight of diamonds and when the loss of this
small quantity of water would still leave the consumer with ample water.
These are, in fact, the conditions under which consumers choose whether
to buy water or diamonds. The quantity of water usually available is
ample; thus, the margin at which an additional quantity of water is
valued is such as to make its marginal utility low, according to the law
of diminishing marginal utility. On the other hand, diamonds are usu-
ally possessed in sufficiently small amounts to ensure that the typically
sized marginal unit still possesses high marginal utility.
If conditions were otherwise, prices would indeed reflect the altered
conditions. If, for example, a thirsty owner of diamonds were to bargain
in a desert with the owner of a quantity of water, we would indeed expect
to find the price of water far from negligible. Clearly, in these circum-
stances, the marginal utility of water must be immensely higher than under
normal conditions. Here, indeed, water would show itself as "more
important for man than diamonds."
UTILITY THEORY 55


The Subjective Character of Utility The concept o£ utility as we have
developed it thus far in this chapter, and as we shall use it to analyze the
demand side of the market, is essentially a subjective concept. We must
not consider utility as in anyway intrinsic to an object or service. A good
is not to be thought of as bearing a tag inscribed with some degree of
utility. We do not require any philosophical sophistication to distinguish
sharply between the utility relevant to the analysis of human actions and
such qualities as the mass, extension, and even color or beauty of an object.
For the analysis of demand this distinction is of the greatest importance.
For the economist, what is relevant is merely that a consumer prefers
some specific quantity of a good or service to some specific quantity of
the same or another good or service. One alternative is considered to
satisfy a want that is more urgent than that which could be satisfied by
the rejected alternative. The relatively greater want-satisfying power of
the first good or service is called its greater utility. Of course, "want-satis-
fying power" springs from some quality, real or imagined, associated with
the use or enjoyment of the good or service. The utility of coal springs
from its heating powers, that of a painting from its artistic merits; the
utility of a shoeshine is associated with an appropriate glossiness, the utility
of a textbook with the knowledge it confers. But all these are the specific
qualities that characterize goods or services on the basis of which one good
is preferred over another. Acting man considers these "objective" qualities
of the goods among which he chooses; he weighs, with more or less expert
knowledge, the relative objective merits of the goods and then arranges
them on one scale”the scale of preference.
Man cannot "objectively" compare the glossiness of a newly shined
pair of shoes with the thermal capacity of a quantity of fuel, but he must
sometimes choose between them. When he chooses he is arranging them
in order of "importance." There is a homogeneous common denominator
that makes it possible to compare them: that of their relative positions on
the utility scale. The one is more urgent, significant, and important than
the other. The economist, concerned exclusively with the logic of choice,
needs only to be indirectly conscious of the "objective" qualities of goods.
It is not the intensity of these qualities, but the degree of subjectively
felt significance with which the law of diminishing marginal utility is con-
cerned, and from which demand analysis takes its start.
Several corollaries follow immediately from the establishment of the
subjective character of utility. Most important is the implication that
the utilities of the same good for two different people cannot be compared.
This, it is noted, is saying considerably more than that it is possible for
the same good to have different utilities to two different people. It is even
saying more than that there is no conceivable way of discovering for which
of two people a given good has more utility. The impossibility of inter-
56 MARKET THEORY AND THE PRICE SYSTEM


personal utility comparisons implies that no meaning at all can be at-
tached to a statement comparing the utilities of the same (or different) goods
to two people.
Utility refers to relative position on a value scale. A good of greater
utility is higher on the scale and thereby preferred over a good of lower
utility. There is no single value scale on which a specific "good-for-/4"
can take up a position relative to a "good-for-ZT'; there is no conceivable
act of "choice" that should "prefer" a good for A rather than for B.
The impossibility of comparing the utility of a good for two people
does not affect, of course, the fact that each of us frequently engages in
comparisons concerning the relative "usefulness" of a good to different
people. We say that a hungry man "needs" food more than one who has
just dined. We try to give charity "where it will do most good"; we
distribute gifts among our friends or children where we think they will
be the most useful or pleasurable. All this is quite in order, but it does
not involve any comparisons of that utility demand analysis depends upon.
An outsider C is entitled to his opinion, however irrational, as to how a
quantity of a good "ought" to be shared out between two other people, A
and B. Frequently he does so by placing himself mentally in the positions
of both these people simultaneously. But it is always his choice, always
his assessment of relative "urgency," which operates in such decisions.
Another, and a related, implication of the subjective character of
utility is that utility must be clearly distinguished from both ethical values
and psychological pleasure-pain sensations. As far as ethics is concerned,
the matter is straightforward. In studying demand, we are interested in
the patterns of action that follow from given tastes, no matter what these
tastes may be. Utility refers to the importance attached by man to pos-
session of goods. What degrees of importance a man attaches to different
goods is indeed a matter determined in part by his ethical values. But
just as the economist analyzes the demand for coal not by reference to its
technological thermal capacity but to the subjective significance that men
attach to coal (of course chiefly on technical, objective grounds), quite
similarly the economist analyzes the demand for goods (flowers or bullets,
knowledge, or liquor) by starting out in a quite "positive" way, and with-
out the need for any moral evaluation, from men's demonstrated preferences.
The distinction between the utility used in demand theory and
pleasure-pain sensations should be equally clear cut. The distinction must
be especially stressed because many of the earliest expositions of utility
analysis did fail, in fact, to recognize such a distinction or were phrased
as if they failed to do so. This failure was both unfortunate and un-
necessary. The utility of a loaf of bread, insofar as demand theory is
concerned, is not to be identified either with the hunger pangs suffered
for lack of the bread or with the sensation of satiety experienced upon its
UTILITY THEORY 57


consumption. These sensations may be "real" and important enough,
but like ethical values, underlie the preferences that men reveal in their
actions. A man's value scale and the utility to him of given commodities
are doubtless dependent on the intensity of these sensations. But the
economist must be satisfied to commence from the colorless fact of prefer-
ence.
Utility as a Relative Concept We conceive of utility as a purely relative
notion. In saying that a good has utility to a man, we mean that it pos-
sesses importance, or significance, to him because of its power to remove
uneasiness. As we have seen, "importance" and "significance" take on
meaning only in the context of a comparison with other goods. Utility
reveals itself only in acts of choice when two or more goods are being
compared. Thus, it is quite meaningless to conceive of the utility of a
loaf of bread, as it were, in a vacuum. All we can say is that a loaf of bread
may have either more or less utility than a glass of beer, a news magazine, or
twenty cents.
If utility could be identified with some "objective" property of a good,
say its mass, calorific value, or even moral worth, then the concept would not
depend on the relationship between one good and another. But the utility
of demand analysis refers to none of these objective qualities and does, there-
fore, by its very definition, imply a comparison with other goods or services.
Utility refers to position on a scale of values. Without other goods or serv-
ices, there is no scale of values and hence no utility concept at all.
The relative character of utility means that men's preferences can be
the subject of interpersonal comparisons. There is, as we have seen, no
value scale upon which the relative positions of a loaf-of-bread-for-v4 and
a loaf-of-bread-for-jß can be observed. But it may be possible for an
observer to discover whether a loaf of bread bears the same relationship
to twenty cents on A's scale of values as it does on B's; and it may be
possible to assert that a loaf of bread has greater utility to A than twenty
cents, but that for B the situation is reversed. In fact, this kind of as-
sertion is, as we shall discover, the foundation of market theory.
The Ordinal Character of Utility Two conflicting approaches to utility
theory are met in the literature. The older (but by no means extinct)
approach was to treat the utility of a good for an individual as a magnitude
to which, in principle, a cardinal number could be assigned. An apple
has, let us say, 10 units of utility; a shirt, 50 units; and so on. Such an
approach involves the postulation of a numerical scale of utility against
which the utilities of goods might”again only in principle”be measured
with precision.- The theoretical concept of numerical quantities ol
2 As can be imagined, cardinal utility theorists encountered serious difficulties in at-
tempts to devise methods of measuring this utility. The earliest notions of cardinal
58 MARKET THEORY AND THE PRICE SYSTEM


utility involves, again, the notion that a larger "quantity of utility" (one,
that is, comprising a larger number o£ "units" of utility) is built up
through the addition of smaller quantities of utility or of units of utility.
A good with utility of 10 possesses 10 times the utility of a good with unit
utility; and so on. The cardinal utility approach would consider a man
enlarging his stock of a good as, at the same time, increasing his store of
utility afforded by possession of the good. The total store of utility af-
forded by the entire stock would be the sum of the successive increments
of utility obtained as the stock successively expanded from the acquisition
of the first unit up to the addition of the last acquired unit. The rate at
which the addition of successive physical units of the good increases the
total utility of a stock of the good is termed (in the cardinal terminology) the
"marginal utility" of the good.3
The ideas, however, underlying the cardinal approach present con-
siderable conceptual difficulty. Without attempting to enlarge on this
difficulty, we can contrast this approach with the currently more accepted
ordinal approach. This view denies the very notion of cardinal quantities
of utility. The only numbers that can be assigned to utilities are ordinal
numbers. Utilities can be arranged in order; for example, first, second,
and so on. They cannot however be assigned numerical magnitude. A
shirt may be said to have greater utility than an apple; one may not
say how many times the utility of the shirt is greater. A "unit" of utility
has no meaning for the ordinal approach. When men value goods, they
arrange them in order of value; they do not attach cardinal numbers to
them.
The discussion we have presented in this chapter follows the ordinal
approach to utility. For us, the utility of a good corresponds to a ranking
on the scale of values; to speak of the utility of a good is to involve only
the comparison of its significance with that of some other good. An im-
portant consequence of our adopting this ordinal viewpoint is that the
term "marginal utility" is used in this book in a somewhat different sense
from its use in a "cardinal" approach. This matter of terminology needs
a brief explanation.

utility arose out of the vain attempts to build an economic theory of consumer choice
based on the psychological content of the feelings of satisfaction (associated with differ-
ent acts of consumption) that account for a man's preference of one good over another.
On the other hand, ordinal utility, as we have seen, is quite distinct from such psycho-
logical magnitudes.
3 The statement that a man acts so as to achieve his goals in order of their impor-
tance to him is translated directly, in cardinal-utility terminology, into the statement that
he acts so as to maximize his total utility. In this context marginal utility is employed
most conveniently as a mathematical tool simplifying the analytical task of finding the
maximum position.
UTILITY THEORY 59


Total Utility and Marginal Utility For a cardinal utility theorist, we
have seen, the term "marginal utility" is used in contradistinction to "total
utility." Total utility refers to the quantity of (cardinal) utility afforded
by a stock of a commodity. Marginal utility refers to the rate at which
total utility changes as the size of the stock of the commodity changes. An
approximation to this rate of change of total utility is given by the amount
of change in that utility resulting from a one-unit increase in the stock of
the commodity. (Sometimes cardinal utility theorists loosely refer to this
approximation as "marginal utility.") 4
For ordinal utility theory, such a distinction between total and mar-
ginal utility is not called for. Since there is no cardinal quantity of utility
that increases, there can be no such concept as a rate of change of such a
quantity. For an ordinal theory, marginal utility means the significance
attached to the addition to (or decrease of) the quantity possessed of a good
by the marginal unit. It does not, it must be noticed, refer to a change
in the significance of the stock of the good, but to the significance of a change
in the size of the stock. But total utility, too, for the ordinal theorist
means the significance attached to the acquisition or loss of a given stock
of the commodity. Both the utility of a stock of a good and the marginal
utility of a marginal unit being added (or subtracted) from the stock "are
total utilities" (in that they do not refer to "rates of change"); but, and
more important, at the same time they are both "marginal utilities" in
the sense that the utility of any quantity of a good, large or small, implies
that this quantity is being considered "marginally"”that is, that somebody
is contemplating the acquisition or loss of this quantity.
The "marginal unit," in fact, is never anything else than the unit
that happens to be under consideration. It is the unit relevant to the
act of choice confronting a man. The size of this unit depends only on
the circumstances of the situation where a choice has become necessary. A
man may be contemplating the purchase of several shirts. For certain
sums of money, he can buy one, two, or several shirts. In choosing among
the alternatives open to him, the man will be comparing the marginal
utilities of the appropriate number of shirts”that is, the smallest number
of shirts separating one possible decision from another. If any number
of shirts can be bought, then a single shirt is the marginal unit; if shirts
can be bought only in packages of three, then three shirts make up the
marginal unit”and the decision whether or not to buy additional shirts
will involve the difference that three more shirts will make to the pur-
chaser's sense of well-being. Suppose a situation where a man is forced to
choose between purchasing all of a supply of shirts or of obtaining none at
all; then the entire supply would be the relevant "unit." The man must
4 The total utility of a stock of a commodity is thus the sum of the marginal utilities
of the units making up the stock, taken successively.
60 MARKET THEORY AND THE PRICE SYSTEM


assess the difference that the entire supply would mean to him in con-
sidering the attractiveness of the price it can be had at. In such a situation
the marginal unit is the entire supply, and the man is in a position where
the "marginal utility of shirts" means nothing else than the significance
to him of this entire shirt supply.

MARGINAL UTILITY AND THE CONDITIONS FOR EXCHANGE
The utility analysis discussed in this chapter provides a framework
within which to understand the emergence of exchange between individuals.
Interpersonal exchange is the essence of the market process, and market
theory is devoted to the explanation of the way objects will be produced
for exchange, the quantities that will be offered for exchange, and the rates
at which different exchanges will take place. Here we analyze the basic
conditions that exist when two individuals exchange goods. This analysis
will be fundamental to much of the subsequent material in this book.
The conditions for exchange exist between two individuals A, B, when-
ever a specific quantity of a good possessed by A is ranked lower on his
value scale than a specific quantity of a good possessed by B, while the
ordering is the reverse on B's value scale. That is, wherever the marginal
utility of a quantity of one good possessed by A is lower for A than that of
a quantity of another good possessed by B, while for B the marginal utility
of the latter quantity is the lower, then each of the two gain by giving up
what is less important to him in exchange for what is more important.
If these conditions are absent, no exchange can take place. It is not
sufficient that A ranks B's brand new automobile higher than his own
ancient jalopy; if B concurs in A's relative valuation, both vehicles will
remain where they are. No exchange will take place freely unless each
party believes that he will be better off having made the exchange. This
fundamental and self-evident truth is the central theme of the market
process and of its theory.
The implications of these conclusions are far reaching. Where two
men each possess both of two goods, then, as we have seen, any difference
in the rankings that specific quantities of the two goods occupy on the
value scales of the two men will result in exchange if the two men are "in
the same market" (that is, if they are each in contact with the other and
aware of the other's relative ranking). This is so because it will benefit
each man to give some of the good he values less for some of the good he
values more. A state of rest, where both men, although in the same market,
do not barter, can exist therefore only when both men rank both goods in
the same order on their individual scales of value. But if this is so for two
goods, it is so for any two goods. Thus, for two men to be in a state of
rest with respect to each other, each must rank the marginal quantities of
UTILITY THEORY 61


all the goods, which both possess, in exactly the same order as does the
other.
Moreover, if this is the condition for absence of exchange between two
men, it must be so also for any two men. Thus, for a market to be at
rest, each participant in a market must rank each one of the goods he
possesses in exactly the same order of significance, at the margin, as does
every other participant in the market.
To put the same proposition in a different and more useful form, in
any market a tendency will exist for each participant to barter in the
market place so long as the relative marginal utilities to him of all the goods
he possesses is in anyway different from those of any other participant with
respect to those that he possesses. As each participant exchanges, the
marginal utility of given quantities of the goods that he sacrifices rises (in
accordance with the law of diminishing utility), while that of given quanti-
ties of the goods that he acquires correspondingly falls. The process of ex-
change thus raises those marginal utilities that had been relatively low (that
is, of the goods that the owners for this reason wished to sell) and lowers
those marginal utilities that had been relatively higher (that is, of the goods
that the owner for this reason wished to buy). Hence, as the exchange
process continues, the value scale of each member of the market tends
toward consistency with that of every other member, with respect to the
goods possessed by each member.
As men's tastes change, as for various reasons the quantities and kinds
of the commodities and services each man possesses changes, the relative
marginal utilities of the goods he possesses alter for each participant in the
market and thus, again and again, diverge from the rankings of other
participants. There is thus constant recurrence of opportunities for each
participant to exchange profitably.
The rates exchanges will take place at, of course, are closely bound up
with the degree of divergence between the value scales of different partici-
pants. These are matters that will concern us in later chapters. Our dis-
cussion has been carried on in barter terms consistent with our assumption

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