6.1 Rationality
A critical behavioural assumption in economics is that agents operate in a
way that is oriented towards achieving a goal. This can be interpreted to
mean that individuals and firms maximize their personal well-being and/or
their profits. These players may have other goals in addition: Philanthropy
and the well-being of others are consistent with individual optimization.
If individuals are to achieve their goals then they must act in a manner
that will get them to their objective; broadly, they must act in a rational
manner. The theory of individual maximization that we will develop in this
chapter is based on that premise or assumption. In assuming individuals are
rational we need not assume that they have every piece of information
available to them that might be relevant for a specific decision or choice.
Nor need we assume that they have super computers in their brain when they
evaluate alternative possible strategies.
What we do need to assume, however, is that individuals act in a manner that
is consistent with obtaining a given objective. The modern theory of
behavioural economics and behavioural psychology examines decision making in
a wide range of circumstances and has uncovered many fascinating behaviours
– some of which are developed in Application Box 6.1
below.
We indicated in Chapter 1 that as social scientists, we
require a reliable model of behaviour, that is, a way of
describing the essentials of choice that is consistent with everyday
observations on individual behaviour patterns. In this chapter, our aim is
to understand more fully the behavioural forces that drive the demand side
of the economy.
Economists analyze individual decision making using two different, yet
complementary, approaches – utility analysis and indifference analysis. We
begin by portraying individuals as maximizing their measurable
utility (sometimes called cardinal utility); then progress to
indifference analysis, where a weaker assumption is made on the ability of
individuals to measure their satisfaction. In this second instance we do not
assume that individuals can measure their utility numerically, only that
they can say if one collection of goods and services yields them greater
satisfaction than another group. This ranking of choices corresponds to what
is sometimes called ordinal utility – because individuals can
order groups of goods and services in ascending order of
satisfaction. In each case individuals are perceived as rational maximizers
or optimizers: They allocate their income so as to choose the outcome that
will make them as well off as possible.
The second approach to consumer behaviour is frequently omitted in
introductory texts. It can be omitted here without interpreting the flow of
ideas, although it does yield additional insights into consumer choice and
government policy. As in preceding chapters, we begin the analysis with
a motivating numerical example.
Application Box 6.1 Rationality and impulse
A number of informative and popular books on decision making have appeared recently. Their central theme is that our decision processes should not be viewed solely as a rational computer – operating in one single mode only, and unmoved by our emotions or history. Psychologists now know that our brains have at least two decision modes, and these are developed by economics Nobel Prize winner Daniel Kahneman in his book "Thinking, Fast and Slow". One part of our brain operates in a rational goal-oriented forward-looking manner (the 'slow' part), another is motivated by immediate gratification (the 'fast' part). Decisions that we observe in the world about us reflect these different mechanisms.
Richard Thaler, a Chicago economist and his law professor colleague Cass Sunstein, have developed a role for public policy in their book entitled "Nudge". They too argue that individuals do not inevitably operate in their own best long-term interests, and as a consequence individuals frequently require a nudge by government to make the long-term choice rather than the short-term choice. For example, when individuals begin a new job, they might be automatically enrolled in the company pension plan and be given the freedom to opt out, rather than not be enrolled and given the choice to opt in. Such policies are deemed to be 'soft paternalism'. They are paternalistic for the obvious reason – another organism is directing, but they are also soft in that they are not binding.
6.2 Choice with measurable utility
Neal loves to pump his way through the high-altitude powder at the Whistler
ski and snowboard resort. His student-rate lift-ticket cost is $30 per
visit. He also loves to frequent the jazz bars in downtown Vancouver, and
each such visit costs him $20. With expensive passions, Neal must allocate
his monthly entertainment budget carefully. He has evaluated how much
satisfaction, measured in utils, he obtains from each snowboard outing and
each jazz club visit. We assume that these utils are measurable, and use the
term cardinal utility to denote this. These measurable utility
values are listed in columns 2 and 3 of Table 6.1. They
define the total utility he gets from various amounts of the
two activities.
Table 6.1 Utils from snowboarding and jazz
1 | 2 | 3 | 4 | 5 | 6 | 7 |
Visit | Total | Total | Marginal | Marginal | Marginal | Marginal |
# | snowboard | jazz | snowboard | jazz utils | snowboard | jazz utils |
| utils | utils | utils | | utils per $ | per $ |
1 | 72 | 52 | 72 | 52 | 2.4 | 2.6 |
2 | 132 | 94 | 60 | 42 | 2.0 | 2.1 |
3 | 182 | 128 | 50 | 34 | 1.67 | 1.7 |
4 | 224 | 156 | 42 | 28 | 1.4 | 1.4 |
5 | 260 | 180 | 36 | 24 | 1.2 | 1.2 |
6 | 292 | 201 | 32 | 21 | 1.07 | 1.05 |
7 | 321 | 220 | 29 | 19 | 0.97 | 0.95 |
Price of snowboard visit=$30. Price of jazz club visit=$20.
Cardinal utility is a measurable concept of satisfaction.
Total utility is a measure of the total satisfaction derived from consuming a given amount of goods and services.
Neal's total utility from each activity in this example is independent of
the amount of the other activity he engages in. These total utilities are
plotted in Figures 6.1 and 6.2.
Clearly, more of each activity yields more utility, so the additional or
marginal utility (MU) of each activity is positive. This
positive marginal utility for any amount of the good consumed, no matter how
much, reflects the assumption of non-satiation—more is always
better. Note, however, that the decreasing slopes of the total utility
curves show that total utility is increasing at a diminishing rate.
While more is certainly better, each additional visit to Whistler or a jazz
club augments Neal's utility by a smaller amount. At the margin, his
additional utility declines: He has diminishing marginal utility.
The marginal utilities associated with snowboarding and jazz are
entered in columns 4 and 5 of Table 6.1. They are the
differences in total utility values when consumption increases by one unit.
For example, when Neal makes a sixth visit to Whistler his total utility
increases from 260 utils to 292 utils. His marginal utility for the sixth
unit is therefore 32 utils, as defined in column 4. In light of this
example, it should be clear that we can define marginal utility as:
 | (6.1) |
where
denotes the change in the quantity consumed of the good or
service in question.
Marginal utility is the addition to total utility created when one more unit of a good or service is consumed.
Diminishing marginal utility implies that the addition to total utility from each extra unit of a good or service consumed is declining.
The marginal utilities associated with consuming different amounts of the
two goods are plotted in Figures 6.3 and 6.4,
using the data from columns 4 and 5 in Table 6.1.
These functions are declining, as indicated by their
negative slope. It should also be clear that the MU curves can be derived
from the TU curves. For example, in figure 6.2, when going
from 2 units to 3 units of Jazz, TU increases by 34 units. But 34/1 is
the slope of the TU function in this range of consumption – the vertical
distance divided by the horizontal distance. Similarly, if jazz consumption
increases from 4 units to 5 units the corresponding change in TU is 24
units, again the vertical distance divided by the horizontal distance, and
so the slope of the function. In short, the MU is the slope of the TU
function.
Now that Neal has defined his utility schedules, he must consider the price
of each activity. Ultimately, when deciding how to allocate his monthly
entertainment budget, he must evaluate how much utility he gets from each
dollar spent on snowboarding and jazz: What "bang for his buck" does he
get? Let us see how he might go about allocating his budget. When he
has fully spent his budget in the manner that will yield him greatest
utility, we say that he has attained equilibrium, because he will have no
incentive to change his expenditure patterns.
If he boards once, at a cost of $30, he gets 72 utils of satisfaction,
which is 2.4 utils per dollar spent (=72/30). One visit to a jazz club
would yield him 2.6 utils per dollar (=52/20). Initially, therefore, his
dollars give him more utility per dollar when spent on jazz. His
MU per dollar spent on each activity is given in the final two columns of
the table. These values are obtained by dividing the MU associated with
each additional unit by the good's price.
We will assume that Neal has a budget of $200. He realizes that his initial
expenditure should be on a jazz club visit, because he gets more utility per
dollar spent there. Having made one such expenditure, he sees that a second jazz
outing would yield him 2.1 utils per dollar expended, while a first visit to
Whistler would yield him 2.4 utils per dollar. Accordingly, his second
activity is a snowboard outing.
Having made one jazz and one snowboarding visit, he then decides upon a
second jazz club visit for the same reason as before—utility value for his
money. He continues to allocate his budget in this way until his budget is
exhausted. In our example, this occurs when he spends $120 on four
snowboarding outings and $80 on four jazz club visits. At this consumer equilibrium, he gets the same utility value per
dollar for the last unit of each activity consumed. This is a necessary
condition for him to be maximizing his utility, that is, to be in
equilibrium.
Consumer equilibrium occurs when marginal utility per dollar spent on the last unit of each good is equal.
To be absolutely convinced of this, imagine that Neal had chosen instead to
board twice and to visit the jazz clubs seven times; this combination would
also exhaust his $200 budget exactly. With such an allocation, he would get
2.0 utils per dollar spent on his marginal (second) snowboard outing, but
just 0.95 utils per dollar spent on his marginal (seventh) jazz club visit. If, instead, he were to
reallocate his budget in favour of snowboarding, he would get 1.67 utils per
dollar spent on a third visit to the hills. By reducing the number of jazz
visits by one, he would lose 0.95 utils per dollar reallocated.
Consequently, the utility gain from a reallocation of his budget towards
snowboarding would outweigh the utility loss from allocating fewer dollars
to jazz. His initial allocation, therefore, was not an optimum, or
equilibrium.
Only when the utility per dollar expended on each activity is equal at the
margin will Neal be optimizing. When that condition holds, a reallocation
would be of no benefit to him, because the gains from one more dollar on
boarding would be exactly offset by the loss from one dollar less spent on
jazz. Therefore, we can write the equilibrium condition as
 | (6.2) |
While this example has just two goods, in the more general case of many
goods, this same condition must hold for all pairs of goods on
which the consumer allocates his or her budget.
From utility to demand
Utility theory is a useful way of analyzing how a consumer makes choices.
But in the real world we do not observe a consumer's utility, either total
or marginal. Instead, his or her behaviour in the marketplace is observed
through the demand curve. How are utility and demand related?
Demand functions relate the quantity of a good consumed to the price of that
good, other things being equal. So let us trace out the effects of a price
change on demand, with the help of this utility framework. We will introduce
a simplification here: Goods are divisible, or that they come in small
packages relative to income. Think, for example, of kilometres driven per
year, or liters of gasoline purchased. Conceptualizing things in this way
enables us to imagine more easily experiments in which small amounts of a
budget are allocated one dollar at a time. In contrast, in the
snowboard/jazz example, we had to reallocate the budget in lumps of $30 or
$20 at a time because we could not "fractionalize" these goods.
The effects of a price change on a consumer's demand can be seen through the
condition that describes his or her equilibrium. If income is allocated to,
say, three goods
, such that MUa/Pa=MUb/Pb=MUc/Pc, and
the price of, say, good b falls, the consumer must reallocate the budget so
that once again the MUs per dollar spent are all equated. How does he do
this? Clearly, if he purchases more or less of any one good, the MU
changes. If the price of good b falls, then the consumer initially gets more
utility from good b for the last dollar he spends on it (the
denominator in the expression MUb/Pb falls, and consequently the value
of the ratio rises to a value greater than the values for goods a and c).
The consumer responds to this, in the first instance, by buying more of the
cheaper good. He obtains more total utility as a consequence, and in the
process will get less utility at the margin from that
good. In essence, the numerator in the expression then falls, in order to
realign it with the lower price. This equality also provides an underpinning
for what is called the law of demand: More of a good is
demanded at a lower price. If the price of any good falls, then, in order
for the equilibrium condition to be re-established, the MU of that good
must be driven down also. Since MU declines when more is purchased, this
establishes that demand curves must slope downwards.
The law of demand states that, other things being equal, more of a good is demanded the lower is its price.
However, the effects of a price decline are normally more widespread than
this, because the quantities of other goods consumed may also change. As
explained in earlier chapters, the decline in the price of good b will lead
the consumer to purchase more units of complementary goods and
fewer units of goods that are substitutes. So the whole budget
allocation process must be redetermined in response to any price change. But
at the end of the day, a new equilibrium must be one where the marginal
utility per dollar spent on each good is equal.
Applying the theory
The demand curves developed in Chapter 3 can be related
to the foregoing utility analysis. In our example, Neal purchased four lift
tickets at Whistler when the price was $30. We can think of this
combination as one point on his demand curve, where the "other things kept
constant" are the price of jazz, his income, his tastes, etc.
Suppose now that the price of a lift ticket increased to $40. How could we
find another point on his demand curve corresponding to this price, using
the information in Table 6.1? The marginal utility per
dollar associated with each visit to Whistler could be recomputed by
dividing the values in column 4 by 40 rather than 30, yielding a new column
6. We would then determine a new allocation of his budget between the two
goods that would maximize utility. After such a calculation we would find
that he makes three visits to Whistler and four jazz-club visits. Thus, the
combination
is another point on his demand curve. Note
that this allocation exactly exhausts his $200 budget.
By setting the price equal to $20, this exercise could be performed again,
and the outcome will be a quantity demanded of lift tickets equal to seven
(plus three jazz club visits). Thus, the combination
is
another point on his demand curve. Figure 6.5 plots a
demand curve going through these three points.
By repeating this exercise for many different prices, the demand curve is
established. We have now linked the demand curve to utility theory.
Application Box 6.2 Individual and Collective Utility
The example developed in the text is not far removed from what economists do
in practice. From a philosophical standpoint, economists are supposed to be
interested in the well-being of the citizens who make up an economy or a
country. To determine how 'well-off' citizens may be, social scientists
frequently carry out surveys on how 'content' or 'happy' people are in
their every-day lives. For example, the Earth Institute at Columbia
University regularly produces a 'World Happiness Report'. The report is
based upon responses to survey questions in numerous economies. One of the
measures it uses to compare utility levels is the Cantril ladder. This is an
11-point scale running from 0 to 10, with the lowest value signifying the
worst possible life, and 10 the highest possible quality of life. In
reporting their findings, the researchers are essentially claiming that some
economies have, on average, more contented or happier, people than others.
Utility can be considered in exactly this way: A higher reported value on
the Cantril ladder suggests higher utility.
A slightly different measure of well-being across economies is given by the
United Nations Human Development Index. In this case, countries score high
by having a high level of income, good health (as measured by life
expectancy), and high levels of education, as measured by the number of
years of education completed or envisaged.
In practice, social scientists are very comfortable using utility-based
concepts to describe the economic circumstances of individuals in different
economies.
6.3 Choice with ordinal utility
The budget constraint
In the preceding section, we assumed that utility is measurable in order to
better understand how consumers allocate their budgets, and how this process
is reflected in the market demands that are observed. The belief that
utility might be measurable is not too extreme in the modern era.
Neuroscientists are mapping more and more of the human brain and
understanding how it responds to positive and negative stimuli. At the same
time, numerous sociological surveys throughout the world ask individuals to
rank their happiness on a scale of one to ten, or something similar, with a
view to making comparisons between individual-level and group-level
happiness – see Application Box 6.2.
Nonetheless, not every scientist may be convinced that we should
formulate behavioural rules on this basis. Accordingly we now examine the
economics of consumer behaviour without this strong assumption. We assume
instead that individuals are able to identify (a) different combinations of
goods and services that yield equal satisfaction, and (b) combinations of
goods and services that yield more satisfaction than other combinations. In
contrast to measurable (or cardinal) utility, this concept is called ordinal
utility, because it assumes only that consumers can order utility
bundles rather than quantify the utility.
Ordinal utility assumes that individuals can rank commodity bundles in accordance with the level of satisfaction associated with each bundle.
The budget constraint
Neal's monthly expenditure limit, or budget constraint, is
$200. In addition, he faces a price of $30 for lift tickets and $20 per
visit to jazz clubs. Therefore, using S to denote the number of snowboard
outings and J the number of jazz club visits, if he spends his entire
budget it must be true that the sum of expenditures on each activity
exhausts his budget or income (I):
Since many different combinations of the two goods are affordable, it
follows that the budget constraint defines all bundles of goods that the
consumer can afford with a given budget.
The budget constraint defines all bundles of goods that the consumer can afford with a given budget.
The budget constraint, then, is just what it claims to be—a limit on
behaviour. Neal's budget constraint is illustrated in Figure 6.6,
where the amount of each good consumed is given on the
axes. If he spends all of his $200 income on jazz, he can make exactly ten
jazz club visits
. The calculation also applies to visits
to Whistler. The intercept value is always obtained by dividing income by
the price of the good or activity in question.
In addition to these affordable extremes, Neal can also afford many other
bundles, e.g., (S=2,J=7), or (S=4,J=4), or (S=6,J=1). The set of
feasible, or affordable, combinations is bounded by the budget
line, and this is illustrated in Figure 6.6.
The affordable set of goods and services for the consumer is bounded by the budget line from above; the non-affordable set lies strictly above the budget line.
The slope of the budget line is informative. As illustrated in Chapter 1, it
indicates how many snowboard visits must be sacrificed for one additional
jazz visit; it defines the consumer's trade-offs. To illustrate:
Suppose Neal is initially at point A (J=4,S=4), and moves to point K
(J=7,S=2). Clearly, both points are affordable. In making the move, he
trades two snowboard outings in order to get three additional jazz club
visits, a trade-off of 2/3. This trade-off is the slope of the budget line,
which, in Figure 6.6, is AB/BK=–2/3, where the negative
sign reflects the downward slope.
Could it be that this ratio reflects the two prices ($20/$30)? The answer
is yes: The slope of the budget line is given by the vertical
distance divided by the horizontal distance, OF/OC. The points F and C were
obtained by dividing income by the respective price—remember that the jazz
intercept is
. Formally, that is I/PJ. The intercept on
the snowboard axis is likewise I/PS. Accordingly, the slope of the budget
constraint is:
Since the budget line has a negative slope, it is technically correct to
define it with a negative sign. But, as with elasticities, the sign is
frequently omitted.
Tastes and indifference
We now consider how to represent a consumer's tastes in two dimensions,
given that he can order, or rank, different consumption bundles, and that he
can define a series of different bundles that all yield the same
satisfaction. We limit ourselves initially to considering just "goods,"
and not "bads" such as pollution.
Figure 6.7 examines the implications of these
assumptions about tastes. Each point shows a consumption bundle of
snowboarding and jazz. Let us begin at bundle R. Since more of a good is
preferred to less, any point such as L, which lies to the northeast of R, is
preferred to R, since L offers more of both goods than R. Conversely, points
to the southwest of R offer less of each good than R, and therefore
R is preferred to a point such as V.
Without knowing the consumer's tastes, we cannot be sure at this stage how
points in the northwest and southeast regions compare with R. At W or T, the
consumer has more of one good and less of the other than at R. Someone who
really likes snowboarding might prefer W to R, but a jazz buff might prefer
T to R.
Let us now ask Neal to disclose his tastes, by asking him to define several
combinations of snowboarding and jazz that yield him exactly the
same degree of satisfaction as the combination at R. Suppose further, for
reasons we shall understand shortly, that his answers define a series of
points that lie on the beautifully smooth contour UR in Figure 6.8.
Since he is indifferent between all points on UR by
construction, this contour is an indifference curve.
An indifference curve defines combinations of goods and services that yield the same level of satisfaction to the consumer.
Pursuing this experiment, we could take other points in Figure 6.8,
such as L and V, and ask the consumer to define bundles
that would yield the same level of satisfaction, or indifference. These
combinations would yield additional contours, such as UL and UV in
Figure 6.8. This process yields a series of indifference
curves that together form an indifference map.
An indifference map is a set of indifference curves, where curves further from the origin denote a higher level of satisfaction.
Let us now explore the properties of this map, and thereby understand why
the contours have their smooth convex shape. They have four properties. The
first three follow from our preceding discussion, and the fourth requires
investigation.
Indifference curves further from the origin reflect higher
levels of satisfaction.
Indifference curves are negatively sloped. This reflects the
fact that if a consumer gets more of one good she should have less of the
other in order to remain indifferent between the two combinations.
Indifference curves cannot intersect. If two curves were to
intersect at a given point, then we would have two different levels of
satisfaction being associated with the same commodity bundle—an
impossibility.
Indifference curves are convex when viewed from the origin, reflecting
a diminishing marginal rate of substitution.
The convex shape reflects an important characteristic of preferences: When
consumers have a lot of some good, they value a marginal unit of it less
than when they have a small amount of that good. More formally, they have a
higher marginal valuation at low consumption levels—that first
cup of coffee in the morning provides greater satisfaction than the second
or third cup.
Consider the various points on UR, starting at M in Figure 6.8.
At M Neal snowboards a lot; at N he boards much less.
The convex shape of his indifference map shows that he values a marginal
snowboard trip more at N than at M. To see this, consider what happens as he
moves along his indifference curve, starting at M. We have chosen the
coordinates on UR so that, in moving from M to R, and again from N to H,
the additional amount of jazz is the same: CR=FH. From M, if Neal moves to
R, he consumes an additional amount of jazz, CR. By definition of the
indifference curve, he is willing to give up MC snowboard outings. The ratio
MC/CR defines his willingness to substitute one good for the other. This
ratio, being a vertical distance divided by a horizontal distance, is the
slope of the indifference curve and is called the marginal rate
of substitution, MRS.
The marginal rate of substitution is the slope of the indifference curve. It defines the amount of one good the consumer is willing to sacrifice in order to obtain a given increment of the other, while maintaining utility unchanged.
At N, the consumer is willing to sacrifice the amount NF of boarding to get
the same additional amount of jazz. Note that, when he boards less,
as at N, he is willing to give up less boarding than when he has a lot of
it, as at M, in order to get the same additional amount of jazz. His
willingness to substitute diminishes as he moves from M to N: The
quantity NF is less than the quantity MC. In order to reflect this taste
characteristic, the indifference curve has a diminishing
marginal rate of substitution: A flatter slope as we move down along its
surface.
A diminishing marginal rate of substitution reflects a higher marginal value being associated with smaller quantities of any good consumed.
Optimization
We are now in a position to examine how the consumer optimizes—how he gets
to the highest level of satisfaction possible. The constraint on his
behaviour is the affordable set defined in Figure 6.6, the
budget line.
Figure 6.9 displays several of Neal's indifference
curves in conjunction with his budget constraint. We propose that he
maximizes his utility, or satisfaction, at the point E, on the indifference
curve denoted by U3. While points such as F and G are also on the
boundary of the affordable set, they do not yield as much satisfaction as E,
because E lies on a higher indifference curve. The highest possible
level of satisfaction is attained, therefore, when the budget line touches
an indifference curve at just a single point—that is, where the constraint
is tangent to the indifference curve. E is such a point.
This tangency between the budget constraint and an indifference curve
requires that the slopes of each be the same at the point of tangency. We
have already established that the slope of the budget constraint is the
negative of the price ratio (
). The slope of the indifference
curve is the marginal rate of substitution MRS. It follows, therefore,
that the consumer optimizes where the marginal rate of
substitution equals the slope of the price line.
Optimization requires:
 | (6.3) |
A consumer optimum occurs where the chosen consumption bundle is a point such that the price ratio equals the marginal rate of substitution.
Notice the resemblance between this condition and the one derived in the
first section as Equation 6.2. There we argued
that equilibrium requires the ratio of the marginal utilities be same as the
ratio of prices. Here we show that the MRS must equal the ratio of prices.
In fact, with a little mathematics it can be shown that the MRS is indeed
the same as the (negative of the) ratio of the marginal utilities:
. Therefore the two conditions are in essence the same!
However, it was not necessary to assume that an individual can actually
measure his utility in obtaining the result that the MRS should equal the
price ratio in equilibrium. The concept of ordinal utility is sufficient.
Adjusting to income changes
Suppose now that Neal's income changes from $200 to $300. How will this
affect his consumption decisions? In Figure 6.10, this
change is reflected in a parallel outward shift of the budget
constraint. Since no price change occurs, the slope remains constant. By
recomputing the ratio of income to price for each activity, we find that the
new snowboard and jazz intercepts are 10
and 15
,
respectively. Clearly, the consumer can attain a higher level of
satisfaction—at a new tangency to a higher indifference curve—as a
result of the size of the affordable set being expanded. In Figure 6.10,
the new equilibrium is at E1.
Adjusting to price changes
Next, consider the impact of a price change from the initial equilibrium E0
in Figure 6.10. Suppose that jazz now costs more. This
reduces the purchasing power of the given budget of $200. The new jazz
intercept is therefore reduced. The budget constraint
becomes steeper and rotates around the snowboard intercept H, which is
unchanged because its price is constant. The new equilibrium is at E2,
which reflects a lower level of satisfaction because the affordable set has
been reduced by the price increase. As explained in Section 6.2,
E0 and E2 define points on the demand
curve for jazz (J0 and J2): They reflect the consumer response to a
change in the price of jazz with all other things held constant. In
contrast, the price increase for jazz shifts the demand curve for
snowboarding: As far as the demand curve for snowboarding is concerned, a
change in the price of jazz is one of those things other than own-price that
determine its position.
Philanthropy
Individuals in the foregoing analysis aim to maximize their utility, given
that they have a fixed budget. Note that this behavioural assumption does
not rule out the possibility that these same individuals may be
philanthropic – that is, they get utility from the act of giving to their
favourite charity or the United Way or Centre-aide. To see this suppose that
donations give utility to the individual in question – she gets a 'warm
glow' feeling as a result of giving, which is to say she gets utility from
the activity. There is no reason why we cannot put charitable donations on
one axis and some other good or combination of goods on the remaining axis.
At equilibrium, the marginal utility per dollar of contributions to charity
should equal the marginal utility per dollar of expenditure on other goods;
or, stated in terms of ordinal utility, the marginal rate of substitution
between philanthropy and any other good should equal the ratio of their
prices. Evidently the price of a dollar of charitable donations is one
dollar.
6.4 Applications of indifference analysis
Price impacts: Complements and substitutes
The nature of complements and substitutes, defined in Chapter 4,
can be further understood with the help of Figure 6.10.
The new equilibrium E2 has been drawn so that the
increase in the price of jazz results in more snowboarding—the quantity of
S increases to S2 from S0. These goods are substitutes in this
picture, because snowboarding increases in response to an increase in the price of jazz. If the new equilibrium E2 were at a point
yielding a lower level of S than S0, we would conclude that they were
complements.
Cross-price elasticities
Continuing with the same price increase in jazz, we could compute the
percentage change in the quantity of snowboarding demanded as a
result of the percentage change in the jazz price. In this example,
the result would be a positive elasticity value, because the quantity change
in snowboarding and the price change in jazz are both in the same direction,
each being positive.
Policy: Income transfers and price subsidies
Government policies that improve the purchasing power of low-income
households come in two main forms: Pure income transfers and price
subsidies. Social Assistance payments ("welfare") or
Employment Insurance benefits, for example, provide an increase in income
to the needy. Subsidies, on the other hand, enable individuals to purchase
particular goods or services at a lower price—for example, rent or daycare
subsidies.
In contrast to taxes, which reduce the purchasing power of the
consumer, subsidies and income transfers increase purchasing power.
The impact of an income transfer, compared with a pure price subsidy, can be
analyzed using Figures 6.11 and 6.12.
In Figure 6.11, an income transfer increases
income from I1 to I2. The new equilibrium at E2 reflects an
increase in utility, and an increase in the consumption of both
daycare and other goods.
Suppose now that a government program administrator decides that, while
helping this individual to purchase more daycare accords with the intent of
the transfer, she does not intend that government money should be used to
purchase other goods. She therefore decides that a daycare subsidy
program might better meet this objective than a pure income transfer.
A daycare subsidy reduces the price of daycare and therefore rotates
the budget constraint outwards around the intercept on the vertical axis.
At the equilibrium in Figure 6.12, purchases of other
goods change very little, and therefore most of the additional purchasing
power is allocated to daycare.
Let us take the example one stage further. From the initial equilibrium
in Figure 6.12, suppose that, instead of a subsidy
that took the individual to
, we gave an income transfer that
enabled the consumer to purchase the combination
. Such a transfer
is represented in Figure 6.13 by a parallel outward
shift of the budget constraint from
to
, going
through the point
. We now have a
subsidy policy and an alternative income transfer policy, each permitting
the same consumption bundle (
). The interesting aspect of this pair
of possibilities is that the income transfer will enable the consumer to
attain a higher level of satisfaction—for example, at point
—and will also induce her to consume more of the good on the vertical
axis. The higher level of satisfaction comes about because the consumer has
more latitude in allocating the additional real income.
Application Box 6.3 Daycare subsidies in Quebec
The Quebec provincial government subsidizes daycare heavily. In the public-sector network called the "Centres de la petite enfance", families can place their children in daycare for less than $10 per day, while families that use the private sector are permitted a generous tax allowance for their daycare costs. This policy is designed to enable households to limit the share of their income expended on daycare. It is described in Figure 6.13.
The consequences of strong subsidization are not negligible: Excess demand, to such an extent that children are frequently placed on waiting lists for daycare places long before their parents intend to use the service. Annual subsidy costs amount to almost $2 billion per year. At the same time, it has been estimated that the policy has enabled many more parents to enter the workforce than otherwise would have.
The price of giving
Imagine now that the good on the horizontal axis is charitable donations,
rather than daycare, and the government decides that for every dollar given
the individual will see a reduction in their income tax of 50 cents. This is
equivalent to cutting the 'price' of donations in half, because a donation
of one dollar now costs the individual half of that amount. Graphically the
budget constraint rotates outward with the vertical intercept unchanged.
Since donations now cost less the individual has increased spending power as
a result of the price reduction for donations. The price reduction is
designed to increase the attractiveness of donations to the utility
maximizing consumer.