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that exchange is carried on with the assistance of a medium of exchange
that only facilitates, and in no way distorts, the expression by men of their
relative valuations of real goods and services.

SUMMARY
Acting men, in choosing between available alternatives, arrange them
in order of preference. The scale of values made up in this way indicates
the relative marginal utilities of different specific quantities of different
goods and services. Men act so as to replace a good of lower marginal
utility by one of higher marginal utility.
62 MARKET THEORY AND THE PRICE SYSTEM


The marginal utility of successively available additional units to a
stock of a commodity steadily diminishes, other things being equal. This
is the law of diminishing marginal utility.
Goods are either related or unrelated. Related goods may be either
complementary to one another or substitutes (rivals) for one another. Com-
plements are goods whose marginal utility rises, other things being the same,
as the quantity possessed of the others increases. Substitutes are goods
whose marginal utility falls, other things being the same, as the quantity of
the others increases. Unrelated goods are those whose marginal utilities
are unaffected by the quantities possessed of the other.
The marginal utility view is able to resolve the classical paradox con-
cerning the relative values of diamonds and water. The utility concept
is subjective and relative in character. The utility of a good refers to
nothing inherent in the good itself and is meaningless unless it refers to a
comparison with the utility of something else. Utility is an ordinal con-
cept. No cardinal "units" of utility are implied in utility theory. "Mar-
ginal utility" is therefore to be interpreted not as the "rate of change of
total utility," but as the (total) utility afforded by an increment of a good
or service.
The utility theory provides the framework to understand exchange
between market participants. Exchange will take place wherever the value
scale rankings of two goods possessed by one man are different for him than
the corresponding ranking for another man. In a market there is therefore
a constant tendency for participants to exchange so that the value scale of
each represents rankings identical with that of every other participant, for
goods possessed by each of them.

Suggested Readings
Wicksteed, P. H., The Common Sense of Political Economy, Routledge and Kegan
Paul Ltd., London, 1933, pp. 1-125.
Mises, L. v., Human Action, Yale University Press, New Haven, Connecticut, 1949,
p. 119-127.
Rothbard, M., "Toward a Reconstruction of Utility and Welfare Economics" in
On Freedom and Free Enterprise, D. Van Nostrand Co., Inc., Princeton, New
Jersey, 1956, pp. 232-243.
Consumer Income Allocation



VVE HAVE developed
thus far the tool of
marginal utility. We must now put this tool to use in analyzing the
pattern of consumer behavior in spending his income in the market
place on the goods and services he desires. Such an analysis (a) will
enable us to understand the forces of demand as they are felt in the
market, and (b) will help explain the ways demand may be expected
to adjust to changes in relevant market facts. The analysis will thus
give us perhaps the most important link in the chain of causation
through which the market mechanism works.

MARGINAL UTILITY AND THE ALLOCATION OF INCOME
The consumer decides at any given time on what goods to buy,
and in what quantities to buy them, on the basis of three sets of
factors. First, the consumer consults his own scale of values, built
upon his personal tastes, and the requirements of his own particular situa-
tion. Second, the consumer at any given time finds himself with a limited
amount of money with which to buy (or, considering purchases over time,
finds himself with limited money income per unit of time).1 Third, the
1
A consumer finds himself with given money income only after he has made his de-
cisions concerning the quantity of his labor services, for example, that he will offer to
the market at going wage rates. Taking a broader perspective, it should be clear that
the terms on which a resource owner will make offers to sell resource services to the
market depend on the direct satisfaction that he might himself derive, as consumer, by
not selling them (for example, the utility to him of leisure), as compared with the con-
sumer satisfaction that he can secure from their proceeds in the market. The analysis
of consumer decisions can be extended to take explicit notice of all this. In such an
analysis money income would not be one of the ultimate determinants of consumption
expenditures; its place would be taken by the "income" the consumer is endowed with
in his capacity of resource owner; that is, the flow of resource services he is naturally
endowed with and free to sell in the market if he wishes. See p. 226.
63
64 MARKET THEORY AND THE PRICE SYSTEM


consumer faces a market where each good he is interested in is obtainable
only at a definite price. The consumer finds, that is, that the expenditure
of all his income on a particular good will provide him with a definite and
limited quantity of the good; but, more important, that the expenditure of
this amount might also provide a large number of alternative combinations
of purchases, the contents of each combination being, with given expendi-
ture, rigidly determined by the prices of the goods entering into the com-
bination, and the proportion of expenditure allocated to each of the goods
in the combination.
The essence of the problem facing the consumer thus consists in choos-
ing one out of an immense number of alternative assortments of goods. A
man may spend all his income per unit of time on good A, or all of it on
good B, or good C, and so on. But he may spend all his income on some
combination of the goods A, B, C. He must decide on which goods to
include in his combination of purchases.2 Confining our attention to the
man's consumption expenditures, it is clear that with his own given value
scale of the moment, he will act to secure, so far as is possible, as many of the
goods and services he desires in their order of importance to him. In
other words, he will act to make sure that no one item of the available
goods, which he does not buy, is of greater significance to him (that is, is of
higher utility) than any item, obtainable for the same expenditure, which
he does buy. Let us ponder the implications of this proposition.
Our consumer, with, let us say, $100 to spend on consumption, may
if he desires spend everything on shirts at, say, $4 per shirt. But if he
spends $4 on a shirt, this is because he can find no article, available for $4,
of greater utility. If he can buy a steak dinner for $4, and a steak dinner
has greater utility than a shirt, he will buy the dinner, not the shirt. If
he spends all his $100 on shirts, this can only mean that having even a
twenty-fifth new shirt is more important than a single meal. Now several
new shirts may have greater utility than eating, but the law of diminish-
ing utility tells us that, relative to a first steak dinner, each additional shirt
will have lower and lower utility. At some point, it is likely, the consumer
will feel that another shirt has less utility than a first dinner, and expendi-
ture will have somehow to be divided between dinners and shirts.
In fact, consumers usually buy a host of different kinds of goods: shirts,
meals, haircuts, TV sets, college tuition, theatre tickets, and cigarettes. The
important point to observe is that the movement from selecting one possible
combination of goods to the selection of a differently proportioned combina-

2 He must further decide, of course, what portion of his income to allocate to saving.
Although the analysis of this chapter can be applied to deal explicitly with this question,
our discussion will apply most simply to the situation where the consumer does not wish
to save anything. For further analysis of consumer decisions that have, like decisions
to save, a bearing on the future, see beloAv in the Appendix on multi-period planning,
pp. 311-320.
CONSUMER INCOME ALLOCATION 65


tion involves shifting dollars between different goods at the margin. The
one combination calls for fewer dollars spent on the theatre, but more
dollars spent on food; a little leaner budget for clothing, a little more
liberality for books. Any selected combination of goods could be discarded
in favor of some other combination simply by drawing back the margin of
expenditures on one or more items and correspondingly advancing the
margin of spending in other branches of consumption. The conditions
for such a movement on the part of a consumer are simply that the marginal
utility of the additional units in the new combination be greater than the
discarded units in the old. The condition for consumer equilibrium (that
is, the position where the consumer takes no action to improve his position)
is that the marginal utility to be gained by adding any amount of money
to any branch of consumption be offset by the marginal utility sacrificed by
subtracting this sum of money from any of the already adopted branches of
consumption.
The law of diminishing utility explains how consumers approach their
equilibrium positions. Suppose a consumer has provisionally allocated his
income so that he is spending "more than he needs" on food and "less than
he needs" on clothing. Then he is in a position where several dollars
taken from the food budget could be more advantageously put to use added
to the clothing allocation. The marginal utility of several dollars' worth
of clothing is greater than that of the same number of dollars' worth of
food. The consumer's actions will remove this discrepancy. As he with-
draws dollars from food, the marginal utility of a dollar's worth of food
rises; as he adds dollars to clothing, the marginal utility of a dollar's worth
of clothing falls. This narrows the gap between the marginal utilities of
food and clothing, until it no longer pays to transfer expenditure from one
to the other. By his actions the consumer has improved his position and
thus at the same time reached a position where further improvement
cannot be achieved.

THE POSITION OF CONSUMER'S EQUILIBRIUM
The degree of precision to which a consumer may be able to carry
the allocation of his income will depend on the sizes of the marginal units
of the goods available to him. If these goods are each divisible into very
small physical units and can be purchased in any desired number of these
small units, then income allocation can be made as precise as the consumer
wishes; that is, as precise as the consumer feels worthwhile in view of the
difficulty of choosing carefully between a number of closely similar alterna-
tives. Disregarding the disutility of deliberation, it may be possible for the
consumer to allocate his income so carefully that the further shift of even
one penny of expenditure from any one good to any other must result in a
66 MARKET THEORY AND THE PRICE SYSTEM


gain from the new purchase that is more than offset by the sacrifice of
the old.3
It is very possible, however, that the goods obtainable in the market
are available only in units of considerable size. In such a situation, the
consumer contemplating shifts in expenditure at the margins of different
goods can consider only the possibility of reallocating sums of money that
are of some size. The decision whether or not to purchase a second car
may involve comparing the marginal utility of a car on the one hand, and
several thousand dollars' worth of other commodities on the other hand.
There can be no question here of shifting about pennies, dimes, or even
dollars at the different margins of expenditure. Nevertheless, it can be
said, here too, that the consumer will act to secure that assortment of goods
so that no opportunity still remains to reduce the expenditure on any items,
by any amount, in favor of other items, without the marginal utility of the
additional purchases being lower than the marginal utility of the eliminated
purchases.
At the position of equilibrium for a consumer, the following condi-
tions hold with respect to any two kinds of goods available to him. Con-
sider the higher priced of the two goods (that is, the one whose marginal
unit is of such a size that it sells at the higher price). Consider the marginal
utility of one unit (to be lost by restricting expenditure on this good by the
price of one unit); denote this by a. (That is, a is an ordinal number
denoting the relative position of this unit on the consumer's utility scale.)
Consider the marginal utility of the unit to be gained by expanding expendi-
ture on this good by the price of one unit; denote this by b. (Of course, b
will denote a position lower than a.) Consider now the number of units
of the lower-priced good that can be purchased for the price of a unit of
the higher-priced good. Denote by c the (ordinal) marginal utility of this
number of units (of the lower-priced good) to be lost should expenditure
on this lower-priced good be contracted (in favor of a unit of the higher-
priced good); denote by d the marginal utility of the same number of units
of the lower-priced good to be gained at the expense of a unit of the higher-
priced good. (Again, of course, d will denote a position lower than c.)

3 Cardinal utility theorists translated this condition directly into "the equi-marginal
principle." Denoting the cardinal marginal utility of a unit of commodity a by the
symbol Ma (in utility units), and its price by the symbol Pa (in money units), it follows
that the cardinal quantity of utility that can be bought with a unit of money is (ap-
proximately) MJPa. The equi-marginal principle requires that, for utility maximiza-
tion, income be distributed among any two commodities a and b in such a way that
Ma/Pa ” Mh/Pb (approximately). In the absence of such an income distribution, a net
gain in utility could be obtained by transferring expenditure from one commodity to the
ojther. The discussion in the text presents the logic of the corresponding ordinal utility
''conditions; in addition, the discussion in the text makes allowance for marginal units of
various sizes.
61
CONSUMER INCOME ALLOCATION

At equilibrium, for any two goods, a will be higher on the ordinal utility
scale than d (so that the consumer will not give up a unit of the higher-
priced good in favor of a number of units of the lower-priced good), and c
will rank higher on the ordinal scale than b (so that the consumer will not
buy an additional unit of the higher-priced good at the expense of a number
of units of the lower-priced good).4

A GEOMETRICAL ILLUSTRATION
The allocation of income by a consumer can be illustrated graphically.
We consider, in the diagram (Figure 5-1), the allocation of expenditure be-




Figure 5-1

tween two goods X and Y (assuming the total expenditure on both goods to
be fixed). Any point (such as Fj) in the diagram represents a "bundle" made
up of a quantity of X, represented by the abscissa of the point (such as OS
for the point Pj) and a quantity of Y, represented by the ordinate of the
point (such as OR for the point Pj). With given expenditure allotted to be
spent wholly on X and Y a consumer faced with given market prices for
X and Y finds that he can acquire only a limited number of "bundles"; only
a limited number of points in the X”Y field in the diagram are actually
open to him.
It is fairly easy to describe a line (AB) drawn so that it passes through
all points open to the consumer. The consumer, we suppose, can buy any
amount of the good X at the price px per unit; and he can buy any amount
of good Y at the price py per unit. Then if we denote the allotted amount
to be spent on X and Y by M, it is clear that if all of M is spent on X, the
4 The consumer must of course compare the marginal utility a, not only with d, but
also with the possibilities available for using the income (required to purchase a) to
purchase, instead, a package made up of additional quantities of several alternative com-
modities.
68 MARKET THEORY AND THE PRICE SYSTEM


number of units of X that can be bought is M/px. Similarly, if all of M be
spent on Y, the number of units of Y that can be bought is M/py. Marking
off the distance OB along the X-axis, where OB represents the quantity
M/px; and marking off the distance OA along the Y-axis, so that OA rep-
resents the quantity M/py; it is clear that B and A are two of the points on
the X-Y field that are open to the consumer. If he spends all on X, he
can place himself at B; if he spends all on Y, he can place himself at A.
If, however, he desires to purchase a bundle that contains not Y alone but
some quantity of X together with the quantity OR of Y, then the quantity
of X that will be included in the bundle must be determined. Instead of
spending all of M (that is, OA X py) on Y, the consumer wishes to spend
only the amount OR X py on Y. This leaves him with M ” (OR — py)
to spend on X. Now M=OA X py so that the consumer has, to spend on
X, the amount (OA ” OR)py or AR — py. At a price, per unit of X, of px,
this amount will therefore yield AR X py/p¦ units of X. Denoting this
quantity of X by the distance OS (= i?Pi), we have discovered that the
point Pi is a point open to the consumer. It represents a bundle of OR
of Y and OS of X.
It is easy and of some importance to show that the point Px must lie
(on our assumption) on the straight line AB. The straight line AB has
the downward slope OA/OB. But OA = M/py and OB = M/px so that
OA/OB = px/py· Consider the line joining APX\ it has the downward slope
AR/RPV But RPX = AR— py/pw (by definition) so that AR/RPX = p¦/py.
The slope of APX is thus the same as that of AB; Px (and thus in general any
point representing a bundle of goods that can be purchased with the allotted
expenditure) must lie along AB. AB joins all the "bundles" that are avail-
able to the consumer with his allotted expenditure; it is frequently called
the opportunity line.
The consumer must thus select a point on AB representing the allo-
cation of this expenditure most satisfactory to him. Suppose the con-
sumer is at point Pj_; then he will act to improve his position by moving
along AB either toward A or B, until he reaches the point of consumer
equilibrium. A movement, for example, from Pl· to P2 implies that P2
is an alternative that is preferred over Pv The point P2 represents a
bundle that contains a little more of X (CP2 of X) and a little less of Y
(CP1 of Y) than the bundle at Pv If movement occurs from Px to P2 this
means that the consumer has compared the marginal utility of CP2 of X
with that of CP± of Y and considers the former to be higher than the latter.
He considers the gain of CP2 additional X, more than sufficient to outweigh
the sacrifice of CP1 of Y. The market enables the consumer to translate
his preferences into action. He is able to sell GP± of Y and buy CP2 more
of X; in the diagram he has moved from Px to P 2 .
If P2 is a point preferred over all other points on the opportunity line,
CONSUMER INCOME ALLOCATION 69


the consumer acts to attain P2, thereby rejecting all the other alternatives
open to him (that is, refraining from selecting any other point on the line).
At P2 the consumer is at equilibrium. The diagram shows how this
equilibrium position differs from other positions, say P 3 or Plt on the
line. The size of the increments of Y and X, respectively, PXC and CP2
between Px and P2, or P2D and DP3 between P2 and P3, are, let us suppose,
the smallest that can be exchanged for one another. At P3 the consumer
is not at equilibrium, because he prefers the additional quantity of Y, P2D
to the marginal quantity DPS of X. He will therefore shift DP3 — px
{=P2D — py) of expenditure from X to Y. Similarly, as we saw, at point
Px the consumer shifted P ^ — py (= CP2 — px) of expenditure from Y to
X. Only at P2 will the consumer not act to alter his position, because, on
the one hand, the marginal utility of P2D of Y is higher than that of an
additional DP3 of X, while on the other hand the marginal utility of CP2
of X is higher than that of PXC of Y.


THE EFFECTS OF CHANGES
We have been describing the pattern of consumer action in the market
place. We have seen that a given income enables the consumer to take
advantage of goods available in the market so as to place himself in the
most advantageous position that the relative prices of these goods permit.
The consumer achieves this by adjusting the proportions of his income
spent on different kinds of goods so that a transfer of money from the
margin of spending on one good to that spent on another is not profitable.
The conditions for equilibrium thus involved (a) his own relative
preferences and tastes, (b) his income, and (c) the prices of the different
goods available. We now turn to examine the effect on consumer allo-
cation of income brought about by changes in each of these three groups
of factors.

1. Change of Tastes Consumer equilibrium was determined in part by
tastes, because it was the consumer's relative eagerness to obtain different
goods that determined the marginal utilities of the goods at various margins
of expenditures. If, after reaching equilibrium, the consumer's tastes
change or his circumstances change, then it is likely that he will no longer
be in equilibrium. A man who has achieved equilibrium in the summer
may soon be impelled to action by the imminent threat of a severe winter.
A change of tastes means simply a reordering of the relative positions
of items on the consumer's scale of values. One good, or a number of
units of the good at the margin, will now occupy a higher position in
the utility scale. Necessarily this means that some other good or goods,
or units of them, now occupy relatively lower positions.
70 MARKET THEORY AND THE PRICE SYSTEM

This will affect equilibrium by altering the marginal utilities of the
several kinds of goods so that the marginal utilities of the units of some
kinds of goods (which would have to be given up should expenditure upon
them be curtailed) are now relatively lower, while the marginal utilities
of additional units of the goods (to be gained should expenditure on them
be expanded) are now relatively higher. It may well be wise to switch
some expenditure from the former goods to the latter.




B x

Figure 5-2

In the diagram (Figure 5-2) a consumer was initially in equilibrium
at the point P2· This means that a movement from P2 to P 3 (which was
possible since it is along the opportunity line AB) was not taken because
the marginal utility of DP2 of Y was higher to the consumer than that of
DP3 of X. Suppose however that the consumer's tastes change, shifting
somewhat away from Y toward X. Then it may well be that the relation
between the marginal utility of DP3 of X to that of DP2 of Y is reversed.
If so, P2 is no longer an equilibrium position, and the consumer acts to
achieve the situation P3.
2. Change of Income A consumer attains equilibrium with expendi-
ture upon different goods and services. If the total amount available
for spending, let us say, had been considerably larger, the consumer's
equilibrium pattern of expenditure allocation would probably be rather
different. How would the consumer's allocation of income be altered
if his income were larger (everything else, tastes as well as prices, remaining
unchanged)?
A larger total expenditure must mean, of course, that a larger quantity
of some goods will be bought, but it is unlikely indeed that the increased
expenditure will be spread proportionally among all the goods that the
consumer buys. Some goods will be bought in much larger quantities,
some goods will be bought in only slightly larger quantities, and some
71
CONSUMER INCOME ALLOCATION

goods may be bought in exactly the same quantities as with lower total
expenditure, while it is quite possible for the amount bought of some
goods to be actually lower with the higher total expenditure. When the
larger total expenditure now available makes it possible to acquire (superior
quality) goods that are close substitutes for a good of lower quality that
was bought with lower income, then it is likely that the amount bought
of this "inferior good" will decrease as total expenditures increase.

Y


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