<<

. 3
( 10)



>>

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


6

E

C

A


BDF H BDF H B DF H
(a) (b) (C)
Figure 5-3

In general, the proportion of increased available expenditure allocated
to any one good will express a number of factors. Where the marginal
utility of a good diminishes, with its increased consumption, relatively
rapidly as compared with other goods so that the utility of the marginal
dollar becomes higher when spent on other goods, a shift of income al-
location toward other goods will occur. Again, as noted before, the effect
of increased income on the consumption of a good will depend on the
relationship between the marginal utility of this good, and the advancing
margin of consumption of other goods, which is made possible by an in-
creased income.
The possibilities thus outlined can be illustrated with the type of
diagram used in the previous section. In the diagram [Figure 5`3 (a)], the
line AB is the opportunity line, and Plt the consumer's equilibrium po-
sition, for a consumer with a given expenditure (OA — py = Mx) that is
to be spent wholly on the goods X, Y, these goods being available in
unlimited amounts at given constant prices p¦, py, respectively. The line
CD represents an opportunity line (with P2 the equilibrium position) for
the consumer where the available expenditure is no longer M1 (= OA — py)
but some larger sum M2 = OC — py. The prices of X, Y have not been
changed so that the line CD is parallel to AB (with its slope px/py)- The
new opportunity line clearly enables the consumer to purchase bundles
72 MARKET THEORY AND THE PRICE SYSTEM

containing larger quantities of both X and Y. The new equilibrium
position P2 is clearly more satisfactory than the position P± to which the
consumer would be limited by the smaller budget allocation Mx. It is
possible to draw any number of lines parallel to AB, such as EF`, OH, and
so on, each of which represents the opportunity lines for the consumer
if his budget allocation of X and Y were progressively increased. And
on each of these opportunity lines we may denote the corresponding
bundle that the consumer would select (that is, the respective positions
of consumer equilibrium) by the points Ps, P4, and so on. Thus, the
line joining these equilibrium points Plf P2, F3, . . . denotes the different
bundles that the consumer would select at different budget levels. This
line is frequently called the income-consumption line.
The three diagrams describe the possible effects that a rise in avail-
able expenditure may have on the consumption of the good X. In Figure
5-3 (a), the income-consumption line shows a continual increase in the
quantity of X that would be bought with increasing total expenditure.
Figure 5-3(b) describes a good whose consumption increases with increases
in total expenditures, until a point is reached where further increases
in "income" are channeled entirely into other goods, no further quantities
of X being bought. Figure 5-3(c) describes the situation with respect to
an "inferior" good whose consumption actually declines after "income"
rises beyond a certain point.
Generalizing from the two-goods situation where we examined the
effects upon consumption of different budget allocations for total ex-
penditure on the two goods, we can easily understand the differences in
income allocation at different income levels. It is impossible to say any-
thing about the income-consumption line for any one particular good.
The proportion allocated for given goods will probably alter with changes
in income. Which goods will get a relatively larger share of lower in-
comes and which a larger share of higher incomes, will depend, once again,
on the particular tastes of the consumer under consideration, on what
he considers an "inferior" good, and on the availability and prices of
other goods upon which he can spend the increases in income. These
effects upon income allocation of changes in income have an important
bearing, as we shall see, on the effects upon income allocation of price
changes for particular goods.
3. Change of Prices The most important kind of change theory at-
tempts to grapple with is that of prices. Supposing that a consumer's
preferences, tastes, and income are given; what can be said about the
different ways he would allocate income with different prevailing sets of
prices? And, in particular, can any definite statement be made concerning
CONSUMER INCOME ALLOCATION 73


the relationship between consumption of a particular good and its price,
other things being assumed to remain unchanged?
Now we have seen that relative prices play a key role in determining
the allocation of income by a consumer in a given situation. T h e con-
sumer acts to reach a position where a shift of expenditure from any one
kind of good to any other would mean substituting a less preferred for a
more preferred situation. The selection of such a position involves valu-
ation of the quantity of each good that must be relinquished or gained,
consequent on such a contemplated shift in any given amount of expendi-
ture. These quantities in turn depend, for any given expenditure, upon
the prices of each good.
A consumer who has planned the allocation of his budget in the light
of a definite set of prices, but who later discovers that the actual prices
are different from what he has previously believed, will find it necessary
to make adjustments in his purchasing plans. He will find that it is no
longer the case that a shift of expenditure at the margin from one good to
another cannot improve his position. He will find, say, that whereas with
the erroneously assumed prices, a dollar withdrawn from the planned meat
allocation and added on for bread meant the sacrifice of a quantity of meat
that has higher utility than that of the additional bread, under the new
prices this may not be so at all. He will find, perhaps, that with the price
of meat higher than was originally believed, the quantity of meat that is
sacrificed in contracting the margin of expenditure upon it by a dollar
is so reduced that its marginal utility is now lower than that of the
additional quantity of bread this dollar can buy. He will buy less meat
and more bread.
In order to analyze the effects of price changes upon a consumer's allo-
cation of income, we can perform a mental experiment. We can imagine
a given set of prices for the available goods, and we can imagine a consumer
spending his income on these goods according to his tastes and preferences.
His allocation, as we have seen, would be such that the shift of any amount
of expenditure from any one good to any other would mean replacing
one quantity having higher marginal utility, with another quantity having
lower marginal utility. Now we imagine sudden drastic changes in the
prices of many goods, while the consumer's money income and his tastes
are assumed not to have changed. The prices of some goods have risen,
some more than others; the prices of some goods have fallen, some more
than others; the prices of other goods, perhaps, have not changed at all.
We can now classify the possible consequences of this change in prices
in three possible ways. First, it is possible that since prices have altered so
drastically, the consumer finds that the purchasing power of his income
lias increased in the sense that he finds it possible to spend his income on
exactly the same goods, in the same quantities, as before, and yet have
74 MARKET THEORY AND THE PRICE SYSTEM


some income left over unspent.5 Second, it is possible that the change
in prices has been such as to reduce the purchasing power of the consumer's
income in the sense that he finds it impossible to purchase, even if he would
wish to do so, the same bundle of goods previously bought. And third,
it is just possible that price increases and decreases so offset one another
that the consumer's income is exactly sufficient to buy the bundle of goods
previously bought.
Let us take up this last case. Although the consumer's income and
tastes are assumed to be unchanged, it is clear that the previous bundle,
although still within his reach, is no longer necessarily the most preferred
among the alternatives open to him. The alterations in the relative prices
of goods make it possible for the consumer to translate his income into
bundles made up of quantities and proportions of goods different from
those making up the bundles among which he chose previously. The new
bundles may well include one or several that are preferable to the alterna-
tives previously available and even preferable to the bundle previously
selected. In fact this is likely to be the case.
As we have seen, the consequence of the change in prices is to alter
the relative marginal utilities of those quantities of different goods that it
is contemplated to add or subtract at the respective margins by shifting
expenditure among goods. A "dollar's worth" of the goods that have risen
in price will now tend to have lower marginal utilities, since a dollar now
buys only a reduced quantity, while, on the other hand, a "dollar's worth"
of the goods whose price has fallen will correspondingly tend to have higher
marginal utilities. This will express itself in the actions of the consumer
by his shifting expenditure away from the former goods toward goods either
of the latter group or of those whose prices have not changed, while, in
addition, he will tend to shift expenditure at the margin away from goods
whose prices have not changed toward those that have fallen in price. The
proportions in which expenditure will shift away from the different goods
whose prices had risen will depend on the rapidity with which the respec-
tive marginal utilities rise as the margin of consumption is drawn back.
As expenditure is shifted away from any one good, the marginal utility of
a "dollar's worth" of that good rises (while at the same time the marginal
utility of a dollar's worth of the other goods whose margin of consumption
is being advanced, falls), until the consumer no longer wishes to transfer
5 This is only one of the possible senses intended to be conveyed by the phrase "an
increase in purchasing power." Where a sum of money may be spent on a number of
different goods that undergo various independent price changes, it is not possible to as-
sert unambiguously whether the sum of money can purchase more or less than before,
unless it is specified how the sum is to be allocated among the various goods. Any index
of purchasing power must correspond to some such (arbitary) specification. The Las-
peyres method of price-index construction is based on the interpretation of "increases in
purchasing power" employed in the text.
CONSUMER INCOME ALLOCATION 75


expenditure. The goods whose marginal utility rises most rapidly with
decreasing consumption will be those from which the least expenditure
will be shifted. On the other hand, among those goods toward which ex-
penditure is being shifted, the consumer will shift expenditure least toward
the goods whose marginal utility falls most rapidly with an advancing
margin of consumption.
The net result of this readjustment would thus be a tendency for the
consumer to increase the purchase of goods whose prices have fallen and
curtail the purchases of goods whose prices have risen, in accordance with
the sets of factors discussed above. However, there are additional compli-
cations that have to be borne in mind in connection with the purchase of
related goods. As seen earlier, the marginal utility of a good falls, other
things remaining the same, with increased possession of substitute goods;
and, on the other hand, rises, other things remaining the same, with in-
creased possession of goods complementary to it. It has already been noted
that an increase in income, by bringing within reach goods of a superior
quality and so reducing the marginal utility of inferior goods for which
the superior product is a substitute, may actually bring about the curtail-
ment of purchases of the inferior good. In the case of price changes, simi-
lar effects may occur. A fall in the price of a given good, leading to a shift
of expenditure toward it, may so increase the marginal utility of a second
good complementary to it that expenditure on the second may be increased
although its price has not fallen or even risen. Similarly, it may happen
that consequent on a changing pattern of prices, the expenditure on a cer-
tain good may rise (thereby reducing the marginal utility of a second good
for which the first is a substitute) to a degree sufficient to cause a shift of
expenditure away from the second, even though its price may actually have
fallen.
Where the prices of the various goods have changed, increasing the
purchasing power of the consumer's income, in the sense that this is more
than sufficient to purchase the previously purchased bundle of goods, these
complications assume added importance. Where price changes of this kind
have occurred, the consumer will desire to alter the make-up of his pur-
chases, not only because relative prices have changed (altering the utility of
a dollar's worth of expenditure at the margins of the various goods as dis-
cussed in the previous paragraphs). He will wish to do so for an important
additional reason. The purchase of the original bundle would, at the new
prices, leave unspent income to be spent in the present period. This addi-
tional expenditure would be distributed by the consumer, among the various
goods, as if an increase in his income had occured. In such a situation the
effect of the changed prices upon income allocation is as if compounded
of two distinct kinds of change. First, the alteration in prices includes
the pure change in relative prices dealt with in the preceding paragraphs;
16 MARKET THEORY AND THE PRICE SYSTEM

second, it includes the equivalent of an increase in income, and we must
expect the same kind of effects on income allocation that we discovered
to occur in that situation.
In the same way, where the change in prices diminishes the purchasing
power of a man's income so that he can no longer buy the previously pur-
chased bundle of goods, we must expect the consumer to act in a way reflect-
ing two kinds of change. First, his actions will reflect the change in the
utility of a dollar's expenditure at the margin for each good that has been
caused by the change in relative prices. Second, his actions will reflect a re-
duction in his income and a consequent necessity to draw back the margin
of expenditure on the various goods, consistent with the normal analysis of
such an income change.
Price Change For a Single Good The special case of a price change of a
single good will enable us to grasp more clearly the argument of the previous
section and will at the same time focus attention directly on the factors
underlying the usual analysis of the market demand for an individual com-
modity.




Bz X




For this purpose we return to the two-commodity world employed in
the earlier diagrams of this chapter. AB1 is the opportunity line of a con-
sumer with income M1 faced with prices pWl and pVl for X and Y, respec-
tively; Px denotes the position of consumer equilibrium. A change in the
price of X now occurs, lowering it to pXo\ the price of Y has not changed.
The change in market data has altered the opportunity line from AB± to
AB2 in the following manner. Since the price of Y and the consumer's in-
come have not changed from pVl and Mlf respectively, A is still a point on
the opportunity line, since expenditure of Mx entirely on Y would still yield
OA (= M1//?1/1) of Y. However, since the price of X has fallen from pXl to
pX2, the amount of X that could be bought by spending all of Mx on X will
CONSUMER INCOME ALLOCATION 77


have increased from OB± (= MJp^ to OB2 (= M^p^). The slope of the
opportunity line has fallen from pxJPVx to pX2/pvv
The altered price of X has thus brought within the consumer's reach a
whole new series of alternatives to choose from (many of them containing
more of both X and Y than was included in the bundle at P^. Let us ana-
lyze three different possible positions of consumer equilibrium on the new
opportunity line; namely, the points P2, P¦i, and P4. Points P2 and F 3 imply
that as a result of the fall in the price of X, the consumer will tend to buy a
larger quantity of X (since P2 and P 3 are to the right of Px); while F4 implies
a curtailment of the quantity purchased of X as a result of its fall in price.
To assist in this analysis we draw, through the point Plf the line CD,
parallel to the new opportunity line AB2. This line represents the oppor-
tunities available at the new set of prices (pVl, px<>)> f° r * ne consumer whose
income is just sufficient at these prices, to purchase the bundle P^ The
three lines ABlt AB2, and CD express the situation of the consumer in the
face of the fall in the price of X. ABX sets forth the alternatives open to
him, with income M l · at the old prices; AB2 sets forth the alternatives open
to him, when, with his income and the price of Y unchanged, the price of
X falls. Clearly, this situation means that his income M1 has risen in pur-
chasing power, in the sense that, if he were to buy the bundle Plf some
unspent income would still be left. This is shown in the diagram by Px
being below the new opportunity line AB2. The line CD sets forth the
alternatives open to the consumer if he was in someway prevented from
enjoying this rise in the purchasing power of his income. That is to say
we put the consumer in a position where, acting in a market with the new
prices, he is permitted to spend only that amount of money now needed to
buy the previously purchased bundle Pv The relation CD to ABlf shows
the new alternatives opened to the consumer by a pure change in relative
prices, without any alteration in the purchasing power of his income (in the
above defined sense).0 The relation of AB2 to CD shows the new alterna-
tives opened by the consumer by a pure rise in income (from OC — pVl to
OA X pVí [= MJ,with the price of X and Y unchanged at pX2 and pVl,
respectively). The relation of AB2 to ABlf then, shows in combination the
new alternatives opened to the consumer who has experienced a change in
relative prices as well as a rise in the purchasing power of his income.
Considering the opportunity line CD (and comparing it with ABx)t it is
clear that the consumer would tend to select a bundle on CD that lies to the

6 Corresponding to other possible senses of the term "purchasing power of income,"
other CD lines may be drawn. For each such possible construction, a "substitution ef-
fect" will result (and therefore also an "income effect") somewhat different from that
described in the text. For a survey of the possibilities in this regard, see Machlup, F.,
"Professor Hicks' 'Revision of Demand Theory,'" American Economic Review, March,
1957 p. 125.
78 MARKET THEORY AND THE PRICE SYSTEM


right of Pv Since the price of X has fallen relative to that of Y, the con-
sumer will find that a dollar's worth of X at the margin has increased in
quantity, while that of Y has decreased. This will tend, as we have seen,
to make the marginal utility of a dollar's worth of X higher than that of Y
(at Pi), leading the consumer to shift some of his expenditure from Y to X.
It is clear, then, that insofar as the fall in the price of X has merely changed
the relative prices of X and Y (that is, abstracting from the rise in the pur-
chasing power of the consumer's income), the consumer will tend to substi-
tute X for Y, as compared with his previous purchase of Px. This shift
toward X, from P1 to (say) P\, is known as the substitution effect.
Because the change in the price of X, besides altering the relative
prices of X and Y, has actually increased the purchasing power of the con-
sumer's income, we should look to the concept of the income-consumption
line discussed earlier in this chapter. The income-consumption line,
we saw, passes through the different positions of consumer equilibrium
that would be taken up as his income increased, while prices of goods re-
mained unchanged. The problem in our own case is to understand the
way a consumer with opportunity line CD, and equilibrium position P\,
will allocate his income when his opportunity line rises to AB2. This in-
volves the shape of the income-consumption line passing through P/1. As
we saw, the slope of such a line may be either positive or negative.
In the diagram the dotted line P\P2 shows a positively inclined income-
consumption line. This line depicts a situation for a consumer who, having
chosen the bundle P\ out of the series of alternatives open to him shown by
CD, would buy more of X if his income were increased. For such a con-
sumer, a change in opportunity line from AB1 to AB2 will result in a change
in equilibrium position from P1 to P2. The fall in the price of X will move
the consumer to increase the quantity of X that he buys; first, as a result of
the substitution effect (from Px to P'j), and second, as a result of the income
effect from P\ to P2. The effect of a fall in the price of X represents the
combined effects of a pure change in relative price (which by itself would
move the consumer to buy bundle P'i); and, in addition, of a rise in the
consumer's purchasing power (which at the new prices would move the con-
sumer to replace bundle P\ by P2). For the positively inclined income-
consumption line P\P2, the income effect, like the substitution effect, shows
that the fall in the price of X results in an increased demand for X by the
consumer.
Where, on the other hand, the income-consumption line passing
through P\ has a negative slope, the results of a fall in the price of X are
somewhat less definite. Such a slope represents the actions of a consumer
to whom X is an "inferior" good; thus, a rise in his income moves him to
replace it by additional purchases of Y. The fall in the price of X, besides
altering the purely relative prices of X and Y in the favor of X, has also
CONSUMER INCOME ALLOCATION 79


increased the consumer's real income. The change in relative prices, as
before, will yield a positive substitution effect; the consumer would (ab-
stracting from the change in purchasing power) move from Px to the right,
to P\. But the income effect in this case is negative. The increase in real
income will tend to reduce the quantity of X that the consumer will pur-
chase. Two possibilities exist; either the negative income effect is, or is
not, greater than the substitution effect. The first possibility is shown in
the diagram by the dotted line P\P½; its slope is so steeply negative that P4
is to the left of Pv This depicts the extremely rare case where a fall in the
price of a good actually decreases the quantity that a consumer will purchase.
(Such goods are called "Giffen-goods.") The second possibility, where the
negative income effect is not greater than the positive substitution effect, is
shown by the line P\PS. Although, in this case, the fall in the price of X
results in an increase in the quantity purchased, as shown by P?> being to the
right of Pt; nevertheless, the increase is not as great as it would have been
if the price fall had not involved a rise in the consumer's real income.

THE INDIVIDUAL DEMAND CURVE
The analysis of the allocation by the consumer of his consumption ex-
penditure, which has occupied much of this chapter thus far, provides us
with the background necessary for the understanding of the consumer's de-
mand curve for specific goods. This traditional tool of price theory relies
heavily upon the analysis of the effect of price changes upon income alloca-
tion discussed in preceding pages.
The demand curve is the graphic representation of a very important
conceptual tool. The analysis of consumer income allocation has taught
us that the manner in which a consumer will divide his expenditure between
various available goods depends on a host of factors: the kinds of goods avail-
able, the preferences of the consumer himself, the size of his income, and the
prices the various goods can be bought for. Focusing attention on any one
commodity, and inquiring into the quantity of it that a consumer will tend
to buy, we face a highly complex problem because of the many factors that
have a share in determining this quantity. The economic theorist attempts
to introduce a measure of conceptual order into this problem by concen-
trating on what is, from his point of view, the key factor”namely, the price
of the good itself. He asks himself, what effect a given change in its price
will have upon the quantity of a commodity demanded by a consumer, as-
suming the other determining factors to be given and, for the purposes of
this mental experiment, unchanging. By abstracting in this way from the
effects of other factors, the economist is able to extract a simple relationship
between its market price and the quantity of a good that a consumer will
buy. The demand curve depicts this relationship graphically.
80 MARKET THEORY AND THE PRICE SYSTEM

In the diagram (Figure 5-5), the horizontal axis, as in the previous
diagrams, represents the quantity of the good X that a consumer may buy.
The vertical axis, unlike those in the earlier diagrams, represents here the

Price




D'




price of X. A point in the price-quantity field associates a given quantity
with a given price for the good. The point R, for example, associates the
quantity OQ of X with a price of OP dollars per unit for X. For a con-
sumer the point R is a relevant point if, at the price of $OP per unit of X,
he actually buys the quantity OQ (during a given period of time). The
curve DD' joins all those points that are relevant for the consumer. The
abscissa of the curve, for any given price ordinate, indicates the quantity
that the consumer will take at the price.7 The curve abstracts from all the
many other kinds of change that might alter the quantity taken by a con-
sumer, and concentrates on the consumer's response to price changes, other
things being left unchanged.
Although the demand curve, both as a diagrammatic aid and as a con-
ceptual tool, depends on "other things remaining equal," it cannot of course
exist in a vacuum. The demand curve associates with each price of a good
the quantity that a consumer will buy under a given set of conditions with
respect to those "other things." A demand curve is drawn for a consumer
with a definite income, facing a definite subjective value scale of his own.
A change in any of these other things will cause the entire demand curve
to change: the set of quantities of a good that a consumer will buy at differ-
ent prices, under one set of these "other" conditions, being quite different
7 The individual demand curve may be looked at from another, no less important
angle. A point on the demand curve represents the highest price per unit that the
consumer will be prepared to pay (if forced to do so) for a given quantity of the com-
modity.
CONSUMER INCOME ALLOCATION 81


from those relevant to different conditions. A rise in income, for example,
may shift a demand curve to the right (or, for an inferior good, to the left)
and, besides changing its position, will probably also change its shape.
The demand curve of the individual consumer for a single commodity
is thus just one piece in the complex jig-saw puzzle that is made up by the
understanding of the different ways the consumer would allocate his income
in response to different sets of conditions. Its usefulness in analysis, we will
discover, is not so much in explaining the actions of the consumer himself;
these are best understood by attacking the problem of income allocation on
marginal utility lines. The demand curve becomes of value in helping
explain the forces that, in the market, are being exerted by individuals
upon the price of particular goods. And for this reason it becomes fruitful
to concentrate attention on the (admittedly partial) relationship existing
between price and quantity alone.
The shape of the demand curve of the individual is of considerable
theoretical importance. This is especially so when we consider, in the next
chapter, the shape of market demand curves derived from the individual
curves. The question we are faced with is whether any generalizations can
be made concerning the relationship between the quantity a consumer will
buy of a good and its price, which should be valid under all possible assump-
tions regarding relevant "other things." Can we say, for example, that a
lower price for a good will invariably be accompanied by a larger purchase
of it on the part of a consumer”no matter what the particular good may be,
no matter what the income of the consumer may be (that is assumed to be
constant), and no matter what the (constant) prices of other goods are
assumed to be? Or can we at least make some such generalization that
should be valid under a limited but specified range of conditions?
Our marginal utility analysis of consumer income allocation enables
us to provide answers to these questions. We saw that a fall (rise) in the
price of one good, other things being equal, affects a consumer's action in
two ways. First, it alters the relative prices of goods in favor (at the expense)
of this good so that the marginal utility of an additional dollar's worth of
this good is now higher (lower) than that of a dollar's worth of other goods,
at the margin. This moves the consumer to replace expenditure at the
margin on other goods by additional expenditure on a good that has become
cheaper, and vice versa for a good that has become more expensive. This
substitution effect will tend to make a negatively sloping demand curve,
showing that a consumer will buy more of a good as its price falls. This
effect is perfectly general. The second way a fall (rise) in the price of a good
affects the consumer's actions (and thus the shape of his demand curve) re-
sults, as we have seen, from the fact that a change in one price alone, which
leaves all other things "the same," is by that very token the change in price
that at the same time changes the real income of the consumer. A fall (rise)
82 MARKET THEORY AND THE PRICE SYSTEM


in one price can only leave the consumer with more (less) than sufficient
money income than is required, at the new price, to buy the old bundle of
purchases. This income effect, of course, is likely to be extremely small
in the case of a moderate price change for a commodity that occupies a
relatively minor place in the budget. Moreover, the income effect of a fall
in price of a good that is not "inferior" tends, we have seen, to increase the
quantity purchased. The negative slope of the demand curve that we
found to be associated with the substitution effect is thus reinforced by the
income effect.
Even for inferior goods the negative income effect may still leave the
demand curve sloping downward to the right. Since this effect may in the
real world be expected to be very small, where it exists it is likely that a fall
in price of even an inferior good will increase the quantity that a consumer
will buy. The theoretical possibility does exist, of course, that a fall in
price of a good may have so strong a negative income effect as to make a
demand curve with a positive slope, representing the case where a man will
buy more of a good when its price is higher. This constitutes the so-called
"Giffen-paradox."

SOME REMARKS ON EXPECTATIONS
The analysis of this chapter has been almost purely formal in character,
and this has enabled us to group together under "tastes and preferences," a
host of factors that have a bearing on the way a consumer will allocate his
income, and on the shape of his demand curve for a particular commodity
or service. Several further remarks are necessary in this regard, in order to
prevent possible misunderstanding of the scope of the tools of demand
analysis, due to the simplicity of the framework that we have been using.
Demand analysis is concerned with the way the consumer acts in spend-
ing his income. Our analysis has been static in the sense that we have
assumed a given scale of values and worked out the consequences for con-
sumer behavior of changes in income and prices in the light of the given
scale of preferences. We discussed the consequences upon consumer actions
of a formal change in his relative preferences, from one value scale to a
different one. This procedure, valid in itself, must not lead us to believe
that we have not taken into account the fact that acting human beings are
forward looking; that they act on the basis of expectations, anticipations,
and uncertainty; and, of course that, in consequence, they frequently make
"mistakes." In the course of time, human beings "learn by their mistakes"
and constantly revise their assessment of future requirements and their
interpretations of current market events. All this must certainly be kept
in mind and lies very close indeed to the core of the possibility of a science
of human action.
CONSUMER INCOME ALLOCATION 83


For the purposes of demand analysis, these aspects of action are under-
stood as reflected in the tastes and preferences of the moment under con-
sideration; they are implicit in the marginal utilities associated by consum-
ers with given quantities of specified goods and services. The marginal
utility of an air conditioner depends, for a consumer at the start of summer,
on his guess of the heat expected in the coming months. The demand curve
for air conditioners for this consumer will reflect all his guesses in this re-
spect. It will reflect, perhaps, his guess as to the degree of discomfort to be
expected in the various rooms of his home; it will reflect, perhaps, his guess
how an air conditioner in one room will help to lessen or increase the dis-
comfort in adjoining rooms.8 No matter what uncertainties enter into his
choice, his scale of values will still reflect the law of diminishing utility-
utility, of course, itself reflecting the expectations and estimates of the con-
sumer. The psychology of choice in the face of risk and uncertainty would
certainly help in making concrete statements about the actual choices made.
For the formal analysis of "static" demand this is unnecessary.
These considerations must be kept in mind when the tools of demand
analysis are applied to the real (dynamic) world. A rise in price for a
particular commodity, for example, may bring about a revision by a con-
sumer of his estimates of future prices, and therefore of the significance of
additional current purchases of the good. This must be interpreted as a
shift in consumer "tastes." It would be inadvisable to apply a demand
curve that has reference to one set of expectations, to a different set. The
recognition of the limitations of the demand curve is of importance in ex-
ploiting its appropriate usefulness and in pointing to the directions where
more refined analysis is called for.

SUMMARY
Marginal utility analysis enables us to explain the way a consumer will
allocate his income. He will act to share expenditure between different
commodities and services so that (having regard to the disutility of careful
deliberation) no further opportunity exists to shift any amount of money
from the margin of expenditure on one good to that of another, without
sacrificing a quantity with higher marginal utility for one of lower marginal
utility. A consumer will act, "exchanging" marginal quantities of one good
for another, so tending towards such an "equilibrium" position.
The content of the "bundle" purchased at this position depends on (a)
the consumer's tastes and preferences, (b) his income, and (c) the market
prices of the various goods. Alteration in any of these sets of data will lead

8 See the Appendix on multi-period planning for an outline of the way current
market decisions depend upon expectations concerning future market conditions.
84 MARKET THEORY AND THE PRICE SYSTEM


the consumer to alter the allocation of his income toward a position in
equilibrium with respect to the new sets of data.
The analysis focuses particular attention on the effects of price changes.
In general, a fall in the price of a (non-inferior) commodity, other things
being equal, results (a) in a tendency for the consumer to purchase more of
the good, as a consequence of the substitution effect of the change in purely
relative prices; and (b) in a tendency for more of the good to be bought as
a consequence of the income effect of the rise in the consumer's purchasing
power (brought about by the fall in the one price). For inferior goods, the
substitution effect is not different, but this may be partly offset (or in excep-
tional cases be more than completely offset) by the negative character of
the income effect.
The demand curve for any good of an individual consumer presents the
relationship between the possible prices of the good and the quantities of it
that he will buy. It assumes given conditions with respect to tastes (includ-
ing expectations), income, and prices of other goods. Insofar as a change
in price can itself affect these other conditions, the demand curve cannot be
used without further refinement.

Suggested Readings
Böhm-Bawerk, E. v., Capital and Interest, Vol. 2, Positive Theory of Capital,
Libertarian Press, South Holland, Illinois, 1959, Bk. 3, Part A.
Marshall, A., Principles of Economics, The Macmillan Co., London, 1936, Bk. 3,
Chs. 1, 2, 3.
Knight, F. H., Risk, Uncertainty and Profit, Reprint, University of London, Lon-
don, 1957, Ch. 3.
Hicks, J. R., Value and Capital, Oxford University Press, New York, 1946, Part I.
Machlup, F., "Professor Hicks' 'Revision of Demand Theory,' " American Economic
Review, March, 1957.
Market Demand



i chapter we will carry forward
N THIS
the analysis of consumer demand from the individual to the market. Each
individual, we found, attempts to allocate his consumption expenditures
among various available goods according to fairly well-defined principles.
There will therefore be in the market, at any one time, a demand for par-
ticular goods and services made up of demands of individuals as determined
by their allocation of expenditures. Analysis of market demand carries us
a significant step nearer a complete understanding of the way prices for
particular goods emerge, and of why prices for particular goods change
relatively to the prices of other goods in the way they do. At the same time
market demand analysis is solidly founded on the theory of individual de-
mand explored in the preceding chapters. It serves, therefore, as one of the
most important links relating market phenomena back to the actions of the
individual participant in the market process.

MARKET DEMAND
In a market, at any one time, a set of prices prevails for the various
goods and services available. In addition, consumers have limited sums of
money available for current expenditure. Each consumer acts to allocate
his current expenditure so as to improve his position as far as possible. The
data of the market, at the same time, describe the opportunities open to
each consumer and outline the limitations of these opportunities. Each
consumer consults his own tastes and preferences in deciding which oppor-
tunities he should grasp. For him, his available expenditure and the prices
of the market place determine his actions according to his own scale of
values.
Looking at the market as a whole, therefore, we see a mass of individ-
85
S6> MARKET THEORY AND THE PRICE SYSTEM


uals each attempting to secure definite quantities of different goods and
services according to the market data of the moment and their own individ-
ual scales of value. The result is that for each particular commodity or
service, the market as a whole is bidding definite sums of money for definite
quantities of the good. The determinants of the particular bids made by
the market as a whole for particular goods are of course the very same as
those that guide individuals in their demand for goods, since it is the
aggregate of these actions that constitutes market demand.
As we shall discover in later chapters, the bids made by the market
as a whole play a decisive role in the determination of subsequent market
events. It is the peculiarity of market prices that they emerge as a result
of actions taken at the beckoning of other prices. Analysis of market
demand therefore is directed to help us in understanding its influence on
the emergence of subsequent prices. Considerable assistance in this regard
is afforded by the analysis of the market demand for particular commodities
taken independently, and it is therefore with this aspect of the subject that
this chapter principally deals.
The quantity of any one commodity for which the market as a whole
bids depends, then, on the tastes of the individuals for this and other
commodities, on the incomes of the individuals, and of the prices of this
and other commodities that the individuals believe are the relevant market
prices they are free to bid at. In analyzing the quantities of the specific
good that the market will seek to buy during a given period of time, we
once again focus attention on price as a key determinant. We assume
that consumers' individual incomes are given, that prices of other goods
are given, and that each individual is endowed with a given scale of values
”and we ask how much (per unit of time) the market would seek to buy
of the commodity under consideration at various different prices. This
question can be answered by our analysis of the individual demand for the
particular commodity. At a given price for the commodity, each individual
would seek to buy a particular quantity of it. Summing these quantities
for all individuals gives the quantity that the market as a whole would
seek to buy at this price. Repeating this operation for a series of possible
prices yields the market demand schedule”the list of quantities of the good
that the market will seek to buy at the series of prices. If the individual
demand schedules for participants in the market indicate that each such
participant would seek to purchase a larger quantity of the commodity at
lower than at higher prices, then the market schedule will express this in
the very same way. The market demand schedule is only the aggregate
expression of a series of alternative potential actions of individuals.1
1 There may of course be goods for which a relevant market demand schedule exists
but for which no individual demand schedules are relevant. Stock examples are goods
that are typically consumed in common by a large number of people, such as major-
87
MARKET DEMAND

As we have seen, the analysis of demand for a particular commodity
at different possible prices, but with nothing else permitted to change, means
the analysis of individual behavior when subject to (a) pure changes in
relative prices, together with (b) changes in the purchasing power of in-
come. While the effects of the latter changes, we saw, do not always run
the same way, the effects of pure changes in relative price are, in fact,
invariably to increase the quantity of a commodity that individuals seek
to buy as the price falls. The demand of the market as a whole will there-
fore faithfully reflect these tendencies.

THE MARKET DEMAND CURVE
The graphic representation of the market demand schedule yields the
market demand curve. The curve represents the "lateral summation" of
all the individual demand curves for the commodity under consideration.
Any point on the market demand curve shows by its abscissa the quantity
that the market will seek to buy (during a given period of time) at the
price represented by the ordinate of the point. The length of this abscissa
is found by adding together the abscissae of those points on all the indi-
vidual demand curves with the same price ordinates as the point on the
market demand curve. Suppose, for example, that Figures 6-1 (a), (b), (c)

Price
Price Price

Ap




(a) (b)

Figure 6-1

league baseball, concerts, and so on. For such goods it is hardly useful to talk of in-
dividual consumer demand schedules; the prospective consumers must somehow band
together to buy them”whence the market demand schedule. Tn a market economy
entrepreneurial activity frequently serves prospective consumers of such goods by un-
dertaking the task of organizing production and then selling "tickets of admission." In
any event, the price that the market as a whole is prepared to pay for a given quantity
of such goods is made up of the shares of the total cost various individuals are prepared
to pay for the privilege of admission.
88 MARKET THEORY AND THE PRICE SYSTEM

represent the individual demand curves of a number of market participants
for a commodity. Then points Pa, Ph> Pc indicate that at a given price
OA for the commodity, these participants will seek to buy quantities OBa,
OBh, OBC, respectively. The quantity that will be sought for the market
as a whole at price OA is indicated in Figure 6-2 by the point Pq. This




Figure 6-2

quantity OQ is made up by adding together OBa> OBh, OBC, and so on for
all the market participants. Thus, the market curve DDq can be thought
of as obtained by "adding together sideways" the individual demand curves
DDa, DDl·, DDC, and so on. (It will be noticed that the quantity axis for
the market demand curve represents a far greater order of magnitude than
the corresponding axes in the individual curves.) It is clear that the shape
of the market demand curve DDq depends completely on the shapes of the
individual curves DDa, DDh, DDC, and so on. The reaction of the market
as a whole to a particular change in price is made up entirely of the
individual reactions.
The market demand curve is a graphic device for presenting compactly
a series of postulated relationships. It can, of course, only tell us what
we have already put into it, but it is nevertheless a highly useful aid in
organizing our thinking about both the determination and effects of price
changes. Two kinds of questions can be answered, at least in principle,
by the organization of our information into the framework of the demand
curve. First, the curve lists the quantities that the market as a whole will
bid for at different given prices. Here price is the independent variable,
with quantity the variable that is made to depend on the prevailing price.
(From this point of view, the demand curve would ordinarily be expected
to have its axes transposed, with quantity measured along the vertical axis.
The prevailing practice however, is the one sanctioned by long economic
usage and is thus well-entrenched.) Second, the curve lists the prices that
MARKET DEMAND 89


given quantities of the commodity can bring if placed on the market.2
Here it is price that we seek to make dependent on the quantity.
It should be emphasized that the demand curve relates quantity to
price in the two ways mentioned, corresponding to two different ways the
term "price" is used in analysis. When we ask what quantity the market
will demand at a given price, we are speaking about a hypothetical or pro-
visional price. As we shall see, the fact that a given quantity will be asked
may in fact be the reason why the provisional price may rise or fall, or why
the hypothetical price cannot in fact become actual. On the other hand,
when we ask what price a given supply will bring on the market, we are
asking about the price that will in fact be realized in the market under
the postulated circumstances.
The use of the demand curve must never mislead us into treating
"price" and "quantity" as being somehow mechanically related, apart from
the actions of individual market participants. Any statement making
quantity bought depend on price asked, or making price determined depend
on quantity offered, must be interpreted as summing up the purposeful
actions of individual human beings in response to definite alternatives
being offered to them or in response to a change in the terms of the available
alternatives.
DEMAND ELASTICITY
The mental tool that is represented by the demand curve attacks the
problem, we have seen, by focusing attention on the influence exerted by
price upon the quantities that will be bought by individuals and by the
market as a whole. This involves the process of mentally "freezing" all the
other factors that have any bearing on the quantity purchased and allowing
the price to vary. Using marginal utility analysis, we were able to make
the generalization that (with the possible exception of certain "inferior"
goods) a fall in price, other things remaining unchanged, is associated with
a greater quantity of goods desired to be purchased. In graphic terms,
this meant that the demand curve slopes downward to the right. It is
useful to further classify demand curves, within the sweep of this gener-
alization, on the basis of their elasticities.
The concept of elasticity, as applied to demand, refers to the degree
of sensitivity to the influence exerted by price that individuals show with
respect to the quantity of a good they seek to buy. A lower price, we
2
This second view of the market demand curve corresponds to the alternative view
of the individual demand curve to which reference was made on p. 80, ftnt. 7. A point
on the market demand curve thus denotes the highest uniform price a given quantity of
the commodity can be sold at in the market without any remainder being left unsold. In
Ch. 7 we will see that this implies that when the quantity has been sold at this price,
all consumers who have failed to buy (even the most eager among them) are not pre-
pared to pay any higher price for additional units.
90 MARKET THEORY AND THE PRICE SYSTEM

found, generally means a larger quantity being purchased. But "larger
quantity" can mean "slightly larger quantity," or "much larger quantity,"
depending on the responsiveness o£ the individuals or group of individuals
to price changes. Demand curves can be ranked in this way as either more
elastic or less elastic. One demand curve is more elastic than a second
if a given change in price exerts a more powerful influence on quantity
purchased in the first than in the second situation. In the diagram, a
decrease in price from p to p' means an increase in quantity purchased

Price


P




Figure 6-3

from q to qa for the demand situation shown by the curve DDa, but an
increase only of from q to qb for the demand situation shown by DDh.
DDa is more elastic than DDb. The concept of elasticity refers both to
demand curves of individuals and of markets. The demand curve of one
individual for sugar may be more or less elastic than his own demand
curve for meat; it may be more or less elastic than his neighbor's demand
for sugar.
MEASURES OF ELASTICITY
In order to rank different demand situations in order of their elastici-
ties, the elasticity concept must be defined with more precision than we
have thus far attempted. Specifically, we must spell out what is meant
by the statement that a given change in price "exerts a more powerful
influence on quantity purchased" in one situation than in another. The
diagram used in the previous section suggests that one curve is more elastic
than another, if its slope is less steep than that of the other. In this case
we found a given fall in price resulted in a larger quantity being bought
where the curve fell less steeply.
This, however, is unambiguously true only in the special case of that
diagram where both curves referred to the same quantity axes, and the
MARKET DEMAND 91


initial position was common to both curves. In general, slope is a mis-
leading indicator of relative elasticity. Where the elasticities of demand
for two commodities are being compared, there is no obvious equivalence
in their units of quantity that should make it possible to compare the
effects of given price changes. A drop in price of say $10, increases the
demand for suits by 2 per year and increases the demand for steel by 5
tons. How does one compare 5 tons with 2 suits? Moreover, the slope
of any demand curve depends entirely on the scale used for both quantity
and price.
The standard measure of elasticity makes the concept independent of
the size of the units the quantities or the prices happen to be expressed in.
Elasticity is measured by the proportional change in quantity purchased,
that is associated with a given proportional change in price. If a 10%
drop in the price of one good is accompanied by a 50% increase in quantity
demanded, while a similar drop in the price of a second good brings about
only a 5% increase, then the first demand situation is more elastic over the
specified price range than the second.
More specifically, absolute measures of elasticity are assigned to demand
situations in the following way. A fall in price, which results in an increase
in the quantity purchased, may or may not increase the money value of
the purchases. On the one hand, a bigger quantity is being purchased;
but on the other hand, a lower price per unit is being charged. Where
the fall in price causes the quantity of purchases to increase in an amount
more than sufficient to offset the lower price per unit so that total money
value of the volume of sales increases, then the demand is said to be elastic
or to have an elasticity of more than one. Where a price fall increases
quantity demanded just sufficiently to offset the lower price per unit so
that the money value of total sales is unchanged, then the demand is said
to be of unitary elasticity or to have an elasticity of one. Where a price
fall causes quantity demanded to increase so little as to be insufficient to
maintain the original value of the volume of sales in the face of the lower
price per unit, then the demand curve is said to be inelastic or to have an
elasticity of less than one. The extreme cases are those of perfectly elastic
demand and perfectly inelastic demand.
In Figure 6-4(a), De is a perfectly elastic demand curve. No matter
whether the supply is q1 or q2, the same price can be obtained. Total
money value of sales can be increased to any desired amount without low-
ering prices even slightly; the volume of sales can be increased without
limit, even without lower prices per unit.
In Figure 6-4 (b), Dt is a perfectly inelastic demand curve. It reflects
a situation where there is no response to a price change. Lowering the
price here simply diminishes the value of total sales by reducing the
revenue per unit without in any way increasing the number of units sold.
92 MARKET THEORY AND THE PRICE SYSTEM

Price Price




A "¯*




Figure 6-4

It should be clear from this discussion that, in general, it is meaning-
less to speak about the elasticity of "a demand curve." Elasticity, as a
concept that is measurable, at least in principle, relates to a response to
a given price change. In speaking of the elasticity of a demand curve, one
must specify the particular range of prices over which the response of
quantity taken to price changes is being measured.3 This can be illus-
trated by means of Figure 6-5.

Price




Figure 6-5
3 The term "elasticity of demand" is frequently reserved for the elasticity concept as
measured over an infinitesimally small portion of the demand curve. Where p, q, re-
spectively represent the price and quantity at a point on the demand curve, and ¿±p,
¿±q represent infinitesimally small changes in price or in quantity, the elasticity of de-
mand at that point is calculated as ¿±q/q ¯¯ AP/P· (It: w i l 1 b e observed that for a
·
downward-sloping demand curve this formula will result in a negative number, since
¿±q and ¿±p are of opposite sign to one another.) Where the range over which demand
elasticity is to be measured is of finite size, the point elasticity formula will yield various
values depending on the particular values of p, q, inserted in the formula. A number
of "arc elasticity" formulas have been devised to yield unique elasticity values for such
cases. (For further discussion of this point see e.g. Weintraub, S., Price Theory, Pitman
Publishing Corp., New York, 1949, pp. 46-48.)
MARKET DEMAND 93

In the diagram AB is a straight line representing a demand curve.
With any point R on the demand curve, is associated the amount of sales
revenue it yields. This sales revenue is, of course, the product (pq) of
(a) the price per unit (p), and (b) the number of units sold at that price
(q). The elasticity of the demand curve in the region of any such point
R depends, we have seen, on whether the value of pq rises with a fall in
price (elastic demand) or falls (inelastic). With a straight line demand
curve such as AB, starting at A and going down to B, the value of p—q
rises from zero, reaches a maximum, and declines once again, at B to zero.
It is clearly impossible to call the demand either elastic or inelastic. At
high prices demand is elastic (lowering the prices increases total revenue);
in the neighborhood of the price at which revenue is a maximum, elasticity
is approximately unitary (because a fairly small price change in that neigh-
borhood leaves total revenue about the same); while at the lower prices
(where a further fall in price would reduce total revenue) demand is dis-
tinctly inelastic.
Elasticity measures apply, of course, both to individual and market
demand. In all cases an inelastic demand over a given price range means
that individuals are only slightly responsive to the price changes. Only
a significant price fall is sufficient to attract any increase in the quantity
that market participants will buy; only a significant price rise is sufficient
to force a cutback in quantity purchased. In marginal utility terms, an
individual whose demand for a good is inelastic ranks a unit of the good
on his value scale very much higher than those units of other goods that
are lower on the scale; and, on the other hand, he ranks the unit of this
good very much lower than those units of other goods that are higher on
the scale. Evidence of this is the fact that a moderate change in price
is unable to alter the relative position on the value scale, with respect to
fixed quantities of other goods, occupied by a "dollar's-worth" of this good
”even though the size of a "dollar's-worth" is now larger or smaller than
before the price change.
On the other hand, an individual whose demand for a good is elastic
ranks a unit of this good with respect to given sized units of other goods
in such a way that even a small change in relative price makes it attractive
for him to shift expenditure at the margin between this good and the
other alternatives available. In the market as a whole the elasticities of
demand curves manifest themselves, as we have seen, in the change in the
amount of total sales revenue which is expected to follow a fall or rise in
price.
94 MARKET THEORY AND THE PRICE SYSTEM



MARKET DEMAND AS SEEN
BY THE INDIVIDUAL ENTREPRENEUR
Thus far we have discussed market demand as a whole. We have
seen that this concept focuses on the quantities the market will ask at
different market prices. These quantities, we found, reflect the quantities
that the individual market participants separately ask at these prices. We
must now put ourselves in the position of the individual firm producing
goods for sale and ask how market demand appears from this position.
The perspective on market demand, which we have already gained, to-
gether with that on market demand as seen by the firm, which we now
consider, will enable us at a subsequent stage to understand how the inter-
locking chains of decisions of buyers and producers determine market prices
and the output of both individual firms and entire industries.
To the individual entrepreneur operating a firm in an industry, the
relevance of market demand does not hinge directly on the relation be-
tween market price and the quantity that the market as a whole will seek
to buy. For him market demand is relevant only as it relates to the quanti-
ties that the market will buy of his product, and to the prices that he may
charge, other factors remaining unchanged. He is interested, in other
words, in the different alternatives the market as a whole might present
to him as a result of alterations by him in the alternatives that he presents
to the market.
It is clear that the alternatives the market as a whole presents to any
one entrepreneur, in response to a given price posted by him, depend on
a number of factors besides the shape of the market demand curve, or its
elasticity in the neighborhood of this price. The quantities of a com-
modity that the market will seek to buy altogether at a given market price
depend, we have seen, on a number of factors, including the prices and
availability of other goods. The quantities of a good the market seeks
to buy from any one entrepreneur, at a given price charged by him, will
depend, in addition to all the factors that we found operative upon market
demand”upon the prices and availability elsewhere of the same good.
This plays an important role in explaining the different ways prices and
output are determined in monopolized and competitive markets.
If we place ourselves in the position of a firm that monopolizes the
particular commodity, then the relevant demand curve is identical with the
demand curve of the market as a whole. In such a situation the only
alternatives (with respect, it must be emphasized, to purchase of the mo-
nopolized product) available to market participants are those offered by
the monopolist. The only competition he faces is that of other goods and
services; thus, the quantities of this good that the market will seek to buy
from the monopolist are identical, for each price, with the quantities that
MARKET DEMAND 95


the market as a whole would seek to buy altogether, at the same market
prices, from a market of competing producers.
The elasticity of the demand curve facing a monopolist, over any
price range, is thus the same as that of the market demand curve. The
decisions of the monopolist concerning what price to ask will therefore
hinge, partly, on his estimation of the elasticity of demand of the market,
since it is this factor that reflects the alternative amounts of revenue the
market permits him to choose from.
The situation is quite different when viewed by an entrepreneur whose
product is made available to the market by other producers as well. The
competitive entrepreneur realizes that there is a going market price at
which the market can buy elsewhere. If he himself asks a higher price
than that asked elsewhere in the market, it is plain that everybody will go
elsewhere when the same good is available more cheaply. On the other
hand, it is equally plain to the competitive entrepreneur that even a
moderate reduction of his price below that asked elsewhere in the market
will attract a large number of buyers to him. In other words, if he offers
the market alternatives less favorable to consumers than those offered
by his competitors, the quantity of his products the market will ask for
will be very slight; if he offers alternatives more attractive to the consumers
than those offered elsewhere, the quantity asked of his product will be
very large. The elasticity of the demand of the market for his output is
thus very high”much higher than that of the market demand curve as a
whole. The individual entrepreneur in a competitive market knows that
the consumers will be highly responsive to any price change on his part.
Whether or not the elasticity of demand faced by a competitive firm
will be infinitely high (that is, whether the demand curve facing it will be
a horizontal straight line) depends largely on the degree of similarity be-
tween the products offered by the competing firms. If these products are
exactly the same in all respects, from the point of view of consumers, then
indeed any one entrepreneur will find that a very small reduction in price
(from slightly above the market price to slightly below the market price)
will increase his sales revenue from zero to very large amounts indeed.
If the similarity between the products, as seen by the consumers, is
not quite perfect, however, then the elasticity of demand faced by any one
competing firm, while probably very high, will be something less than in-
finite. Thus, a slight reduction by one corner drugstore on the retail
prices charged for a branded commodity, say toothpaste, will not attract
all the customers for toothpaste away from other drugstores that have not
made the price cut. This is because "toothpaste available at one drug-
store" may not be perfectly similar to "toothpaste available at another
drugstore," from the consumers' point of view. The physical identity of
the branded merchandise is not necessarily the relevant criterion here; to
96 MARKET THEORY AND THE PRICE SYSTEM

some consumers one drugstore may be a few steps further away than an-
other, one drugstore may be more pleasant to do business in than another,
and so on. Where there is some (real or imagined) physical difference be-
tween two closely similar products, such as two different kinds of tooth-
paste, or an identical toothpaste marketed under two different brand names,
then of course we can similarly expect the demand curve facing any one
seller to be highly, but still less than infinitely, elastic.
These considerations need to be borne in mind when we come to
analyze the market forces determining prices in various types of markets.

DEMAND AND REVENUE
Our discussion of the demand curve and its elasticity faced by the firm
suffices to make clear the relationship between demand and revenue. The
entrepreneur is interested in knowing all the alternatives open to him.
Among the key alternatives concerning which he desires information are
the various amounts of sales revenue that may be expected to be forthcom-
ing under specific circumstances of price and output. Here the demand
curve facing the firm plays the decisive role.
Let us suppose that a firm believes itself to be confronted with a de-
mand curve DDX. This means that he can sell a particular quantity, OB,

Price




of the good at a price OA per unit. There are a number of revenue con-
cepts implicit in this price-quantity relationship, and the entrepreneur may
be interested in each of them for particular purposes. The most obvious
revenue concept is that of total revenue. If he is able to sell the quantity
OB at a price of $OA per unit, then he receives the quantity OB—OA dol-
lars in total sales revenue. This figure is clearly important to the entre-
preneur, because by subtracting the total costs of its production from the
MARKET DEMAND 97


total revenue of a given quantity of output, he can immediately calculate
the profit associated with a given level of output. In graphic terms, the
total revenue for any output OB is represented by the area of the rectangle
OBRA (that is, quantity, OB, multiplied by price, OA).
A second and related concept is that of average revenue per unit of
output. Since the total revenue from the sale of the quantity OB is OBX
OA, it follows that the revenue per unit is OB—OA; that is, $OA per
OB
unit. OA was the price each unit of the quantity OB can be sold at and
is thus, of course, the average revenue for this number of units received by
the entrepreneur. It is noted that as the quantity of output increases (in
the situation shown in Figure 6-6), the revenue obtained per unit of output
declines. Larger quantities of output can only be sold by the firm at pro-
gressively lower prices since the demand curve facing it slopes downward
to the right. It can be seen, in fact, that the curve of demand facing the
firm is identical with a curve relating the firm's average revenue from out-
put to the size of the output. Any point on the demand curve facing the
firm, showing the quantity that the market will buy of the firm's products at
a given price, shows at the same time the price per unit this quantity of
output can be sold at”which, from the point of view of the firm's books,
means the revenue, per unit of output, obtained from this level of output.
The coincidence of the demand curve facing a firm, with the firm's curve
of average revenue for output, holds true, in this way, regardless of the
slope of the demand curve. If a firm is in a highly competitive market so
that the elasticity of the demand it faces is very high, then it will find that
it is able to expand output with hardly any drop in the revenue obtained
per unit. The average revenue curve in this case, like the demand curve,
is very nearly a horizontal straight line.
Another related concept is marginal revenue. Marginal revenue is
the amount of revenue at stake in any decision whether or not to produce
a given marginal unit. Suppose a firm could obtain $1,000 total revenue
by producing and selling 100 units of a commodity, and an increase of out-
put by 1 unit would raise total revenue to $1,005; the marginal revenue of
a 101st unit would be $5. The addition to output and sales of a 101st
unit means an additional $5 in total revenue. Any decision as to expan-
sion or contraction of output by any given number of units must hinge
partly on the difference to total revenue made by the number of units under
consideration.4
4 The reader will observe the parallel between the notion of marginal utility (dealt
with in the preceding chapter) and that of marginal revenue treated here. Both no-
tions (like other marginal concepts we will be dealing with) focus attention on the
difference that a proposed additional unit of something (such as "quantity sold") makes
in some calculation (such as an estimate of revenue) made by an interested individual.
98 MARKET THEORY AND THE PRICE SYSTEM

It is worthwhile to notice some straightforward arithmetical relation-
ships between total, average, and marginal revenue.5 (1) The average rev-
enue of any output, as we have seen, is simply the total revenue obtained
from that output divided by the number of units of the output. (2) The
marginal revenue of any marginal unit, we saw, is the difference between
the total revenue of output including this unit and the total revenue of
output excluding this unit. The marginal revenue of the 101st unit is
thus the difference between the total revenue from 101 units and the rev-
enue from 100 units. (3) It follows directly that the total revenue of, say,
101 units is equal to the sum of the marginal revenues of the 1st, 2nd, 3rd,
. . . and 101st units (since the marginal revenue of each unit of output is
the amount added on to total revenue by the decision to step up output
to include this unit).6 (4) If revenue per unit of output (average revenue)
were the same for all levels of output, this must mean that the marginal
revenue of any one unit is the same as that of any other unit, and that the
value of this marginal revenue is the same as the average revenue. If a firm
can sell any amount it pleases at a constant price, then this price is by
definition both average revenue and marginal revenue. Thus, where a firm
faces a perfectly elastic (horizontal) demand curve, this curve, beside being
coincident with the average revenue curve, coincides also with the marginal
revenue curve. (5) Where average revenue falls with increasing output,
then marginal revenue must be less than average revenue. If the additional
revenue obtained by adding a marginal unit to a given level of output were
more than the revenue per unit of this level of output, then the revenue per
unit of the expanded level of output would be increased. If marginal
revenue were the same as the previous revenue per unit, then the revenue
per unit would not change with the expanded output. Falling average
revenue thus signifies a marginal revenue less than the average. It is pos-
sible for average revenue to fall so low that marginal revenue is negative.
Such a situation exists when increased output can be sold only at so low
a price that total revenue declines with the expanded output.
The marginal revenue of any particular unit of output thus clearly
depends on the slope of the demand curve facing the firm at this level of
output”that is on the elasticity of the demand curve in the neighborhood of
this output.7 For a demand curve of less than perfect elasticity, increased

An important respect in which marginal revenue differs from (ordinal) marginal utility
is that the former notion (unlike the latter) refers to a cardinal number (a specific sum
of money).
5 Analogous relationships exist between the total, average, and marginal values for all
cardinal magnitudes (such as cost, output, and so on).
6 Graphically, therefore, the area below the marginal revenue curve up to a given sales
quantity may represent the total revenue for that quantity.
7 Mathematically the relationship between price (p), marginal revenue (MR), and
elasticity of demand (e) is represented by the formula MR = p + p/e· For a down-
MARKET DEMAND 99


output requires a lower price. Whether this increase in output raises total
revenue, lowers it, or leaves it unchanged, depends, we found, on demand
elasticity over the relevant range. With elastic demand, total revenue
increased; with inelastic demand, total revenue declined; with unitary elas-
ticity, total revenue remained unchanged. Therefore, with a downward-
sloping demand curve, we can generalize by saying that (a) positive marginal
revenue (that is, rising total revenue) is associated with elastic demand;
(b) negative marginal revenue (that is, falling total revenue) is associated
with inelastic demand, and (c) zero marginal revenue (that is, total revenue
unchanged with increased output) is associated with demand of unitary
elasticity.8

DEMAND AND THE PRICES OF OTHER GOODS
Throughout the discussions of individual and market demand, it has
been emphasized that the quantity of any one commodity that will be asked
for in the market at any given price depends in large part on the prices and
availability of other goods and services. The number of air reservations to
Florida beach resorts at a given price depends in part on the price of train
tickets over the same distance, on the availability and price tag of alterna-
tive resorts, and may even depend partly on the prices of quite different
kinds of goods. Each consumer, we found, allocates his income among an
immense variety of goods according to their relative marginal utilities.
The amount of income he will seek to spend on any one good depends not
only on the marginal utility of a "dollar's worth" of this good, but also on
the marginal utility of a dollar's worth of all other goods. This dependency

<<

. 3
( 10)



>>