Chapter 4—Prices and Consumption (continued_
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Chapter 4—Prices and
Consumption (continued)
9.
Some Fallacies Relating to Utility
A doctrine commonly held by writers on utility is that the consumer
acts so as to bring the marginal utility that any good has for him into
equality with the price of that good. To understand this
thesis, let us examine the preference scale of Mr. Jones in
contemplating the purchase of one or more suits (and we shall assume
that each suit is of the same quality—the same
“good”). Suppose his value scale is as follows:
And
suppose also that the market price is 2.9 grains per suit. Jones will
buy not one or three, but two, suits. He will buy up to the
last unit at which the diminishing marginal utility that the suit has
for him exceeds the increasing marginal utility of money.
This is obvious. Now, if a
writer couches the exposition in terms of highly divisible goods, such
as butter, and in terms of small units of money, such as pennies, it is
easy to leap unthinkingly to the conclusion that the consumer
for each good will act in such a way as to equalize, at the market
price, the marginal utility of the sum of money and the marginal
utility of the good. It should be clear, however, that there is never
any such “equalization.” In the case of
the suit, the rank of the second suit is still considerably above the
rank of the 2.9 grains. So there is no equalization. Even in the case
of the most divisible of goods, there will still be a difference
in rank, not an equalization, between the two utilities. A
man may buy 11 ounces of butter at 10 cents an ounce, until there is
nothing ranking between the 11th ounce and the 10cents on his utility
scale; yet there is still no equality, but a
difference in rank, with the last ounce bought ranking higher than the
last sum of money spent. Of course, the consumer tries to spend his
money so as to bring the two as close as possible, but they can never
be equal.
Furthermore,
the marginal utility of each particular good, after the purchases are
made, differs in rank from that of every other. Thus, let us take one
grain of gold as the monetary unit under consideration. Let us say that
the given market-prices of various goods are as follows:
Now each individual will purchase each commodity until the last point
at which the marginal utility of the unit exceeds the marginal utility
of a grain of gold. For one man, this might mean the purchase of five
pounds of butter, three loaves of bread, two bars of candy, etc. This
would mean that either a sixth pound of butter or a fourth loaf of
bread would have a lower marginal utility than a grain of gold forgone.
However, the marginal utility of each good will still differ in rank
from that of every other and will not be equal to that of any other.
Another, even more curious doctrine holds that in equilibrium the ratio
of the marginal utilities of the various goods equals the ratio of
their prices. Without entering in detail into the manner by which these
writers arrive at this conclusion, we can see its absurdity clearly,
since utilities are not quantities and therefore cannot be divided.
These fallacies stem from a related one: the idea that an
individual will act so as to equalize the
marginal utility that any good will have in each of its uses. Applied
to money, this would imply that the marginal utility of a unit of money
is equal for each field of expenditure for each person. This is
incorrect, as we have just seen that the marginal utilities of the
various goods are not equalized. Successive units of a good are
allocated to the most desired end, then to the next most desired
satisfaction, etc. If there are several uses for the good, each one
involving many possible units, the marginal utility of a unit in each
use continues to decline as the supply increases. As goods are
purchased, the marginal utility of each good purchased diminishes, and
a man may allocate his money first to one use, then to another, and
then to the first use again. However, in no case is there any
equalization of marginal utilities.
The dogma of the equalization of marginal utilities may best be
illustrated in the following passage from perhaps the originator of
this line of argument:
Let
s be the whole stock of some commodity, and let it
be capable of two distinct uses. Then we may represent the two
quantities appropriated to these uses by xl
and y1, it being a
condition that xl
plus y1 equal s.
The person may be conceived as successively expending small quantities
of the commodity; now it is the inevitable tendency of human nature to
choose that course which appears to offer the greatest advantage at the
moment. Hence, when the person remains satisfied with the distribution
he has made, it follows that no alteration would yield him
more pleasure; which amounts to saying that an increment of commodity
would yield exactly as much utility in one use as in another. Let Du1,
Du2,
be the increments of utility, which might arise respectively from
consuming an increment of commodity in the two different ways. When the
distribution is completed, we ought to have Du1 =
Du2 .
. . The same reasoning . . . will evidently apply to any two
uses, and hence to all uses simultaneously, so that we obtain a series
of equations less numerous by a unit than the number of ways of using
the commodity. The general result is that the commodity, if consumed by
a perfectly wise being, must be consumed with a maximum production of
utility.
The chief errors here consist in conceiving utility as a certain
quantity, a definite function of an increment in the commodity, and in
treating the problem in terms of infinitely small steps. Both
procedures are fallacious. Utilities are not quantities, but ranks, and
the successive amounts of a commodity that are used are always discrete
units, not infinitely small ones. If the units are discrete, then the
rank of each unit differs from that of every other, and there can be no
equalization.
Many errors in discussions of utility stem from an assumption that it
is some sort of quantity, measurable at least in principle. When we
refer to a consumer’s “maximization” of
utility, for example, we are not referring to a
definite stock or quantity of something to be maximized. We refer to
the highest-ranking position on the
individual’s value scale. Similarly, it is the assumption of
the infinitely small, added to the belief in utility as a quantity,
that leads to the error of treating marginal utility as the
mathematical derivative of the integral “total
utility” of several units of a good. Actually, there is no
such relation, and there is no such thing as “total
utility,” only the marginal utility of a larger-sized
unit. The size of the unit depends on its relevance to the particular
action.
This illustrates one of the grave dangers of the mathematical method in
economics, since this method carries with it the bias of the assumption
of continuity, or the infinitely small step. Most writers on economics
consider this assumption a harmless, but potentially very useful,
fiction, and point to its great success in the field of physics. They
overlook the enormous differences between the world of physics
and the world of human action. The problem is not simply one of
acquiring the microscopic measuring tools that physics has
developed. The crucial difference is that physics deals with inanimate
objects that move but do not act.
The movements of these objects can be investigated as being governed by
precise, quantitatively determinate laws, well expressed in
terms of mathematical functions. Since these laws precisely
describe definite paths of movement, there is no harm at all in
introducing simplified assumptions of continuity and
infinitely small steps.
Human
beings, however, do not move in such fashion, but act purposefully,
applying means to the attainment of ends. Investigating causes
of human action, then, is radically different from investigating the
laws of motion of physical objects. In particular, human
beings act on the basis of things that are relevant
to their action. The human being cannot see the infinitely small step;
it therefore has no meaning to him and no relevance to his action.
Thus, if one ounce of a good is the smallest unit that human beings
will bother distinguishing, then the ounce is the basic unit, and we
cannot simply assume infinite continuity in terms of small fractions of
an ounce.
The key problem in utility theory, neglected by the
mathematical writers, has been the size of the unit.
Under the assumption of mathematical continuity, this is not a
problem at all; it could hardly be when the mathematically conceived
unit is infinitely small and therefore literally sizeless.
In a praxeological analysis of human action, however, this becomes a
basic question. The relevant size of the unit varies according to the
particular situation, and in each of these situations this relevant
unit becomes the marginal unit. There is
none but a simple ordinal relation among the utilities of the
variously sized units.
The
tendency to treat problems of human action in terms of equality of
utility and of infinitely small steps is also apparent in recent
writings on “indifference maps.” Almost the entire
edifice of contemporary mathematical economics in consumption
theory has been built on the “indifference”
assumption. Its basis is the treatment of large-sized classes of
combinations of two goods, between which the individual is indifferent
in his valuations. Furthermore, the differences between them
are infinitely small, so that smooth lines and tangents can be drawn.
The crucial fallacy is that
“indifference” cannot be a basis for action.
If a man were really indifferent between two alternatives, he could not
make any choice between them, and therefore the choice could not be
revealed in action. We are interested in analyzing human action. Any
action demonstrates choice based on preference: preference for
one alternative over others. There is therefore no role for
the concept of indifference in economics or in any other praxeological
science. If it is a matter of indifference for a man whether he uses
5.1 or 5.2 ounces of butter for example, because the unit is too small
for him to take into consideration, then there will be no
occasion for him to act on this alternative. He will use butter in
ounce units, instead of tenths of an ounce. For the same reason, there
are no infinitely small steps in human action. Steps are only those
that are significant to human beings; hence, they will always be finite
and discrete.
The error in reasoning on the basis of
“indifference” is the failure to appreciate the
fact that a problem important in the field of psychology
may have no significance in the realm of praxeology, to which economics
belongs. Psychology deals with the problem of how
or why the individual forms value scales, and for this question it is
relevant to consider whether the individual is decisive or inclined to
be “indifferent” between various
alternatives. Praxeology, however, is a logical science based
on the existence of action per se; it is interested
in explaining and interpreting real action in its universal
sense rather than in its concrete content. Its discussion of
value scales is therefore a deduction from the nature of human
action and not a speculative essay on the internal workings of the
mind. It is consequently irrelevant for praxeology whether a man, in
having to decide between alternatives A and B,
makes a choice firmly and decisively, or whether he decides by tossing
a coin. This is a problem for psychology; praxeology is
concerned only with the fact that he chooses, for example, A
rather than B, and that therefore A
ranked higher in his preference scale than B.
Utility theory is not concerned with psychology or the internal
operations of the mind, but is part of a separate science based on the
logical consequences of the simple existence of action.
Neither is praxeology based on behaviorist psychology. In fact, in so
far as praxeology touches on psychology, its principles are the reverse
of those of behaviorism. As we have seen, far from simply observing
action in the same way as we observe and record the movements of
stones, praxeology is based on a fundamental distinction between human
action and the motion of inorganic matter, namely, that human action is
motivated toward the achievement of certain ends.
Means and resources are used for the achievement of these ends. Far
from leaving mind out of the picture, praxeology rests fundamentally on
the basic axiom of action, action caused and put into effect by human
minds. However, praxeology is not concerned with the content
of these ends, the manner of arriving at them, or their order; it is
concerned with analysis of the logical implications of the existence of
these ends.
Some writers, in their artificial separation of value scales from real
action, have actually gone to the length of attempting to discover
people’s indifference maps by means of questionnaires. These
attempts, besides being open to the stricture that
indifference is not praxeologically valid, fail to realize
that value scales can and do change continually and that therefore such
questionnaires have no relevance to the business of economics.
Economics is interested not in value scales professed in response to
questionnaires, but in the values implied by real action. As
Ludwig von Mises states, with regard to all attempts to separate value
scales from action:
.
. . the scale of value is nothing but a constructed tool of thought.
The scale of value manifests itself only in real acting; it can be
discerned only from the observation of real acting. It is
therefore impermissible to contrast it with real acting and to
use it as a yardstick for the appraisal of real actions.
Since indifference is not relevant to human action, it follows that two
alternatives for choice cannot be ranked equally on an
individual’s value scale. If they are really ranked equally,
then they cannot be alternatives for choice, and are therefore not
relevant to action. Hence, not only are alternatives ranked
ordinally on every man’s value scale, but they are
ranked without ties; i.e., every alternative has a
different rank.
The famous illustration used by the indifference theorists to
demonstrate the relevance of indifference to human action is the case
of Buridan’s ass. This is the fable of the ass who stands,
hungry, equidistant from two equally attractive bales of hay, or,
thirsty, equidistant from two water holes. Since the two bales or water
holes are equally attractive in every way, the ass can choose neither
one and must therefore starve. This example is supposed to prove the
great relevance of indifference to action and to be an indication of
the way that indifference is revealed in action.
Compounding confusion, Schumpeter refers to this ass as
“perfectly rational.”
In the first place, it is of course difficult to conceive of an ass or
a person that could be less rational. He is
confronted not with two choices, but with three,
the third being to starve where he is. Even on the
indifferentists’ own grounds, this third choice will be
ranked lower than the other two on the actor’s value scale.
He will not choose starvation.
If both the left and right water holes are equally attractive, and he
can find no reason for preferring one or the other, the ass or the man
will allow pure chance, such as a flip of a coin, to decide on either
one. But on one he must and will decide. Again, we are interested in
preference as revealed through choice
and not in the psychology of preferences. If the
flipped coin indicated the left water hole, then the left water hole
was finally placed higher on the actor’s value scale, as was
revealed when he went toward it. Far from being a proof of the
importance of indifference, the case of Buridan’s ass is an
excellent demonstration of the fact that indifference can play no part
whatever in an analysis of human action.
Another way of attempting a justification of the indifference analysis
is to suppose that a man, Jones, chooses each of two alternatives A
and B about 50 percent of the time, upon
repeated opportunities. This shifting is alleged to be a
demonstration that Jones is really indifferent as between the
two alternatives. Yet what is the reasonable inference?
Clearly, that in some cases, A was preferred
to B on Jones’ value scale, and that in
the others, the positions were shifted so that B
was preferred to A. In
no case was there indifference between the two alternatives.
The shift of choice indicates a shift in the preference scale, and not
indifference on a constant value scale. Of course, if we were dealing
with psychology, we could enter into a discussion of
intensities of preferences and opine that the man, with
respect to his underlying personality, was relatively indifferent
rather than intensely biased, as between the two alternatives. But in
praxeology we are not interested in the concrete content of
his value scales nor in his underlying personality. We are interested
in value scales as revealed through choice.
APPENDIX A
THE DIMINISHING MARGINAL UTILITY
OF MONEY
Some writers, while admitting the validity of the law of
diminishing marginal utility for all other goods, deny its
application to money. Thus, for example, a man may allocate each ounce
of money to his most preferred uses. However, suppose that it takes 60
ounces of gold to buy an automobile. Then the acquisition of the 60th
ounce, which will enable him to buy an automobile, will have
considerably more value than the acquisition of the 58th or of the 59th
ounce, which will not enable him to do so.
This
argument involves a misconception identical with that of the argument
about the “increasing marginal utility of eggs”
discussed in chapter 1, above.
There we saw that it is
erroneous to argue that because a fourth egg might enable a man to bake
a cake, which he could not do with the first three, the marginal
utility of the eggs has increased. We saw that a
“good” and, consequently, the
“unit” of a good are defined in terms of whatever
quantity of which the units give an equally serviceable supply.
This last phrase is the key concept. The fourth egg was not equally
serviceable as, and therefore not interchangeable with, the first egg,
and therefore a single egg could not be
taken as the unit. The units of a good must be
homogeneous in their serviceability, and it is only to such units that
the law of utility applies.
The
situation is similar in the case of money. The serviceability of the
money commodity lies in its use in exchange rather than in its direct
use. Here, therefore, a “unit” of money, in its
relevance to individual value scales, must be such as to be homogeneous
with every other unit in exchange-value. If another ounce permits a
purchase of an automobile, and the issue is relevant to the case in
question, then the “unit” of the money commodity
must be taken not as one ounce, but as 60 ounces.
All that needs to be done, then, to account for and explain
“discontinuities” because of possible
large purchases is to vary the size of the monetary unit
to which the law of utility and the preferences and choices apply.
This is what each man
actually does in practice. Thus, suppose that a man is considering what
to do with 60 ounces of gold. Let us assume, for the sake of
simplicity, that he has a choice of parceling out the 60
ounces into five-ounce units. This, we will say, is
alternative A. In that case, he decides
that he will parcel out each five ounces in accordance with the highest
rankings on his utility scale. The first five ounces will be allocated
to, or spent on, the most highly valued use that can be
served by five ounces; the next five ounces to the next most
highly valued use, and so on. Finally, his 12th five ounces he will
allocate to his 12th most highly valued use. Now, however, he is also
confronted with alternative B. This alternative is
to spend the entire 60 ounces on whatever single use will be most
valuable on his value scale. This will be the single highest-ranked use
for a unit of 60 ounces of money. Now, to
decide which alternative course he will take, the man compares the
utility of the highest-ranked single use of a lump sum of 60 ounces
(say, the purchase of a car) with the utility of the
“package”—the expenditure of five ounces
on a, five ounces on b, etc.
Since the man knows his own preference scale—otherwise he
could never choose any action—it is no more difficult to
assume that he can rank the utility of the whole package with the
utility of purchasing a car than to assume that he can rank
the uses of each five ounces. In other words, he posits a unit of 60
ounces and determines which alternative ranks higher on his value
scale: purchase of the car or a certain package distribution by
five-ounce (or other-sized) units. At any rate, the 60 ounces are
distributed to what each man believes will be its highest-ranking use,
and the same can be said for each of his monetary exchange decisions.
Here we must stress the fact that there is no numerical
relation—aside from pure ordinal rank—between the
marginal utilities of the various five-ounce units and the utilities of
the 60-ounce units, and this is true even of the package combination of
distribution that we have considered. All that we can say is that the
utility of 60 ounces will clearly be higher than any one
of the utilities of five ounces. But there is no way of determining the
numerical difference. Whether or not the rank of the utility of this package
is higher or lower than the utility of the car purchase, moreover, can
be determined only by the individual himself.
We have reiterated several times that utility is only ranked, and never
measurable. There is no numerical relationship whatever
between the utility of large-sized and smaller-sized units of
a good. Also, there is no numerical relationship between the utilities
of one unit and several units of the same size. Therefore, there is no
possible way of adding or combining marginal utilities to form some
sort of “total utility”; the latter can only be a marginal
utility of a large-sized unit, and there is no numerical
relationship between that and the utilities of small units.
As Ludwig von Mises states:
Value
can rightly be spoken of only with regard to specific acts of
appraisal. . . . Total value can be spoken of only with reference to a
particular instance of an individual . . . having to choose between the
total available quantities of certain economic goods. Like every other
act of valuation, this is complete in itself. . . . When a stock is
valued as a whole, its marginal utility, that is to say, the utility of
the last available unit of it, coincides with its total utility, since
the total supply is one indivisible quantity.
There are, then, two laws of utility, both following from the apodictic
conditions of human action: first, that given the size of a
unit of a good, the (marginal) utility of each unit decreases as the
supply of units increases; second, that the (marginal) utility of a
larger-sized unit is greater than the (marginal) utility of a
smaller-sized unit. The first is the law of diminishing
marginal utility. The second has been called the law of increasing
total utility. The relationship between the two laws and
between the items considered in both is purely one of rank, i.e.,
ordinal. Thus, four eggs (or pounds of butter, or ounces of gold) are
worth more on a value scale than three eggs, which in turn are worth
more than two eggs, two eggs more than one egg, etc. This
illustrates the second law. One egg will be worth more than a
second egg, which will be worth more than a third egg, etc. This
illustrates the first law. But there is no arithmetical relationship
between the items apart from these rankings.
The fact that the units of a good must be homogeneous in
serviceability means, in the case of money, that the given
array of money prices remains constant. The serviceability of a unit of
money consists in its direct use-value and especially in its
exchange-value, which rests on its power to purchase a myriad of
different goods. We have seen in our study of the money regression and
the marginal utility of money that the evaluation and the marginal
utility of the money commodity rests on an already given structure of
money prices for the various goods. It is clear that, in any given
application of the foregoing law, the money prices cannot change in the
meantime. If they do, and for example, the fifth unit of money is
valued more highly than the fourth unit because of an intervening
change in money prices, then the “units” are no
longer equally serviceable and therefore cannot be considered as
homogeneous.
As we have seen above, this power of the monetary unit to purchase
quantities of various goods is called the purchasing power of
the monetary unit. This purchasing power of money consists of
the array of all the given money prices on the
market at any particular time, considered in terms of the prices of
goods per unit of money. As we saw in the regression theorem above,
today’s purchasing power of the monetary unit is determined
by today’s marginal utilities of money and of goods,
expressed in demand schedules, while today’s marginal utility
of money is directly dependent on yesterday’s purchasing
power of money.
APPENDIX B
ON VALUE
Economics has made such extensive use of the term
“value” that it would be inexpedient to abandon it
now. However, there is undoubtedly confusion because the term
is used in a variety of different ways. It is more important to keep
distinct the subjective use of the term in the sense of
valuation and preference, as against the
“objective” use in the sense of purchasing
power or price on the market. Up to this chapter,
“value” in this book has meant the subjective
individual “valuing” process of ranking
goods on individual “value scales.”
In this chapter, the term “value of capital”
signifies the purchasing power of a durable good in terms of money on
the market. If a house can be sold on the market for 250 ounces of
gold, then its “capital value” is 250 ounces. The
difference between this and the subjective type of value is apparent.
When a good is being subjectively valued, it is ranked by someone in
relation to other goods on his value scale. When a good is being
“evaluated” in the sense of finding out its capital
value, the evaluator estimates how much the good
could be sold for in terms of money. This sort of activity is known as appraisement
and is to be distinguished from subjective evaluation. If Jones says:
“I shall be able to sell this house next week for 250
ounces,” he is “appraising” its
purchasing power, or “objective exchange-value,” at
250 ounces of gold. He is not thereby ranking the house and gold on his
own value scale, but is estimating the money price of the house at some
point in the future. We shall see below that appraisement is
fundamental to the entire economic system in an economy of
indirect exchange. Not only do the renting and selling of
consumers’ goods rest on appraisement and on hope of monetary
profits, but so does the activity of all the investing producers, the
keystone of the entire productive system. We shall see that the term
“capital value” applies, not only to durable
consumers’ goods, but to all nonhuman factors of production
as well—i.e., land and capital goods, singly and in various
aggregates. The use and purchase of these factors rest on appraisement
by entrepreneurs of their eventual yield in terms of monetary income on
the market, and it will be seen that their capital value on the market
will also tend to be equal to the discounted sum of their future yields
of money income.
We are omitting possible shifts in
rank resulting from the increasing utility of money, which would only
complicate matters unduly.
W. Stanley Jevons, The
Theory of Political Economy (3rd ed.; London: Macmillan
& Co., 1888), pp. 59–60.
See Appendix A below,
“The Diminishing Marginal Utility of Money,” and
Rothbard, “Toward a Reconstruction of Utility and Welfare
Economics.”
Mises, Human Action,
p. 102. Dr. Bernardelli justly says:
If
someone asks me in abstracto whether my love for my
country is greater than my desire for freedom, I am somewhat at a loss
how to answer, but actually having to make a choice between a trip in
my country and the danger of losing my freedom, the order of
intensities of my desire becomes only too determinate. (Harro
F. Bernardelli, “What has Philosophy to Contribute
to the Social Sciences, and to Economics in
Particular?” Economica,
November, 1936, p. 451)
Also
see our discussion of “consumer surplus” in section
4 above.
Schumpeter, History of
Economic Analysis, pp. 94 n. and 1064.
See chapter 1, pp. 73–74.
Cf. the excellent discussion of
the sizes of units in Wicksteed, Common Sense of Political
Economy, I, 96–101 and 84.
Mises, Theory of Money
and Credit, pp. 46–47. Also see
Harro F. Bernardelli, “The End of the Marginal
Utility Theory,” Economica, May, 1938,
pp. 205–07; and Bernardelli, “A Reply to Mr.
Samuelson’s Note,” Economica,
February, 1939, pp. 88–89.
It must always be kept in mind
that “total” and “marginal” do
not have the same meaning, or mutual relation, as they do in the
calculus. “Total” is here another form of
“marginal.” Failure to realize this has plagued
economics since the days of Jevons and Walras.
For further analysis of the
determination of the purchasing power of money and of the demand for
and the supply of money, see chapter 11 below on
“Money and Its Purchasing Power.”
On appraisement and valuation, cf.
Mises, Human Action, pp. 328–30.
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