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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,

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