Tutorial 5: Consumer choice
In the preceding tutorials we have looked at the "forest"
of how a market system works. Our exploration of the concepts
of reservation price, supply and demand, and elasticity,
enable us to understand how the market system allocates
resources to satisfy the most highly valued wants. This
exploration has also given us a context in which to explore
comparative statics analysis.
Now we turn our attention to the individual "trees" in
this forest. In this tutorial we will take a more detailed
look at what lies behind the market demand for goods and
services. This exploration will require mastery of
the second analytical technique employed in microeconomics,
optimizing behavior. We will apply this technique
to a model of how, as a consumer, one chooses to allocate
one's limited income to satisfy one's unlimited wants.
This tutorial is divided into three parts. The first part
explores the nature of consumer preferences as modeled by
indifference curves. The second part explores the
constraint imposed on consumers by their income and the
prices of the goods they buy. This constraint is modeled
by a budget line. The third part explores how a commodity
bundle is chosen by a consumer who seeks to maximize the
satisfaction received from the bundle of goods given a budget
constraint.
Consumer Preferences
From all the goods or services available to them, buyers
choose a combination of items we call a market basket.
Consumption of the bundle of goods in a market basket brings
satisfaction to the buyer. Buyers choose between different
bundles of goods, different market baskets, on the basis
of the satisfaction they are expected to bring. Before we
model how consumer's choose from among different market
baskets, we need to first make explicit our assumptions
about how consumer's behave. Our model of consumer's as
buyers is based on four assumptions. Because these assumptions
seem logically correct even without proof, they are often
called axioms.
1. Axiom of Completeness
Given two market baskets, A and B, a consumer will know
whether she prefers A to B (written as A »
B), does not prefers A to B (A « B) or is
indifferent between them (A I B).
When confronted with a choice between two market baskets,
both of which contain desirable goods, a consumer will definitely
know which is preferred, or will definitely know that s/he
would be equally happy with either, i.e., that s/he would
be indifferent between them. Note that such indifference
does not imply that the consumer cannot choose between
the two baskets. Nor does it imply that the consumer finds
both baskets UNdesirable. Rather, indifference implies that
both baskets are equally desirable. This state of indifference
plays a crucial role in our model of consumer choice.
2. Axiom of Greediness
Given two market baskets, A and B, the consumer will always
prefer the basket that has more of at least one item and
no less of the other items.
For example, suppose basket A contains 2 loaves of bread
and 3 bottles of wine, and basket B contains 4 loaves of
bread and 3 bottles of wine. According to the axiom of greediness,
consumers will always prefer basket B (i.e., B »
A) because it has more of one good (bread) and no less of
any other good (wine).
3. Axiom of Transitivity
Given any three market baskets, A, B, and C, if
a consumer indicates that A » B, and B »
C, then, logically, the consumer will indicate that A
» C.
For example, if a consumer reveals that a basket of bread
is preferred to a basket of cheese, and that a basket of
cheese is preferred to a basket of wine, then, logically,
s/he would choose a basket of bread over a basket of wine.
This is an assumption about logical behavior. It states
that consumers choose in a consistent, predictable way,
and that their preferences do not change in "mid choice",
as it were.
Indifference Curves
Armed with these three assumptions (the fourth assumption
is listed below) we can begin to build a model of consumer
choice. To keep the analysis as simple as possible we will
place only two goods in each market basket, food (symbolized
by F) and clothing (symbolized by C). Simplifying consumer
choice in this way allows us to build and manipulate a two-dimensional
graphical model. (Adding more goods will not change the
results, but will make the analysis more complex and require
the use of advanced mathemagics.)
We begin by constructing a two dimensional graph, with
clothing (C units per period) on the y- (vertical) axis,
and food (F units per period) on the x- (horizontal) axis.
Any combination (F, C), makes up a single market basket.
For example, the dot labeled A in Figure 1 below,
indicates a market basket that contains 8 units of
food and 25 units of clothing, i.e., A = (8, 25).
Figure 1
Consumption of this market basket gives the buyer a certain
level of happiness. According to the Axiom of Greediness,
any market basket that contains at least 8 units of food
and more than 25 units of clothing would be preferred
because it would lead to a higher level of satisfaction
(see basket B, for example). Similarly, any market
basket that contains at least 25 units of clothing and more
than 8 units of food would also lead to a higher level of
satisfaction (see basket C). Finally, any market
basket that contains more of both goods, say, basket D,
is clearly preferable to basket A. By the same Axiom,
market baskets E, F and G would be
not preferred to basket A because each contains
less of one or both of the goods.
What about market baskets in the other two regions? Take,
for example baskets x and y. We cannot say with certainty
whether either of these baskets is preferred to or not preferred
to basket A. It is possible that the consumer would be indifferent
between basket A and either of these two baskets. In fact,
the consumer may be indifferent between point A and
any points in these two regions. Why indifferent?
Because any market basket in those regions would contain
more of one good but less of the other. Basket x, for example,
contains more clothing but less food than basket A. Basket
y contains more food but less clothing than A. Because more
of a good increases satisfaction but less of a good decreases
satisfaction (Axiom of Greediness), it may very well
be that the consumer would be indifferent among these three
baskets.
The thick, gray lines extending outward from basket A
divide the chart into four quadrants. These lines help us
clearly demarcate regions with market baskets that are preferred
to A (see preferred region in Figure 2 below) or
not preferred to A (see not preferred region). Until
be have more information, the Axiom of Completeness
allows that baskets in the other two regions may be indifferent
to A (see regions of indifference).
Figure 2
Let's suppose that the consumer is indifferent among
baskets A, x, and y. We can illustrate the set of market
baskets that offer the same level of satisfaction as A by
connecting them with a line going through basket A, as shown
in Figure 3 below. This line shows all the market baskets
offering the consumer the same level of satisfaction. Because
a consumer is indifferent between any two of these baskets,
this line is referred to as an indifference curve.
Figure 3
Because of the location of the regions of indifference,
any line we draw will be negatively sloped. A negatively-sloped
line tells us that if any units of C are removed
from a basket, the consumer must be compensated with
additional units of F in order to remain equally
happy with the new basket.
Marginal Rate of Substitution
Now a negatively-sloped line can take on a number of smooth
shapes. It can be linear, concave, or convex. The shape
it takes tells us something about the rate at which
one is willing to substitute clothing for one more unit
of food.
- A linear indifference curve has a constant slope. As
a result, it tells us that the amount of clothing a consumer
is willing to give up for one more unit of food is constant,
regardless the amount of food s/he already has.
- A concave (concave downward) indifference curve has
a slope that increases as we raise the number of units
of F. This tells us that the amount of clothing a consumer
is willing to give up for one more unit of food increases
the more food s/he already has.
- A convex (concave upward) indifference curve has a slope
that decreases as we raise the number of units of F. This
tells us that the amount of clothing a consumer is willing
to give up for one more unit of food decreases
the more food s/he already has.
Which of these scenarios best describes the way a consumer
would feel? Enter the fourth axiom:
4. Axiom of Substitution
The amount of good C one is willing to trade for one more
unit of F diminishes as the number of units of food consumed
increases.
Thus, the rate at which one is willing to trade C for one
more F, diminishes. Why? Remember that along an indifference
curve, one's level of satisfaction is unchanged because
additional units of food are accompanied by fewer units
of clothing. Moving downward along an indifference curve,
one "pays" for an additional unit of food by giving up one's
clothing. Because clothing is valued for the satisfaction
it brings, the less clothing one has the greater the value
of each remaining unit. Put another way, the opportunity
cost, in terms of clothing given up, of getting more food,
is increasing because the consumer is running out of clothing!
How much one is willing to pay, i.e., how much clothing
one is willing to trade for one more unit of food, varies
according to one's relative preference for food over clothing.
(We'll explore this point in the Excel workbook for this
tutorial...)
For example, Figure 4 (below) shows a single indifference
curve for a consumer. Six different market baskets are highlighted
along the curve, each of which brings the consumer the same
level of happiness, designated U1. The shape of the curve
reveals that as the consumer moves from basket A (4, 45)
to B (6, 30), s/he is willing to trade 7.5 C for 1 F. But
as the composition of the basket changes from B (6, 30)
to C (8, 22.75), s/he is now willing to trade only 3 1/8
C for 1 F. The reduction in willingness to trade continues
in the same manner:
- From C to D (10, 18.25) s/he is only willing to trade
2 1/4 C for 1 F;
- From D to E (12, 15) s/he is only willing to trade 1
5/8 C for 1 F;
- From E to F (14, 13) s/he is only willing to trade 1
C for 1 F.
Figure 4
Thus a consumer's willingness to substitute C for F diminishes
with each additional unit of F received. This behavioral
assumption, which we call the Axiom of Substitution,
is usually referred to as the diminishing marginal
rate of substitution.
Happiness is a Higher Indifference
Curve
So far we have established a plausible way of modeling
the satisfaction received by consuming a bundle of goods.
The model proposes that a negatively sloped, convex line
is all that is needed to show all the bundles, or market
baskets, of two goods that leave a consumer equally happy.
But we also noted that baskets with more of at least one
good, but no less of the other, will make the consumer better
off. Similarly, baskets with less of at least one good,
but no less of the other, will make the consumer worse off.
For example, Figure 5, below, shows three indifference curves
labeled U0, U1, and U2. It illustrates two additional features
of the indifference curve model.
First, starting from basket A, we see that basket B has
more of both food and clothing. As a result, consumption
of the goods in that basket give the consumer more satisfaction
than bundle A. Second, we have drawn an indifference curve
through point B. This indicates that a number of other baskets
could give the consumer the same level of satisfaction.
This leads us to conclude that an indifference curve, such
as U2, drawn above and to the right of another, indicates
a higher level of satisfaction. Similarly, an indifference
curve, such as U0, drawn below and to the left of another,
indicates a lower level of satisfaction.
Figure 5
In fact, pick a point, any point in this (F, C)
space, and one may draw an indifference curve through that
point. [How one draws that new indifference curve
is important, as Good Faith
Effort 6 reveals.] As indifference curves move farther
from the origin, the level of satisfaction from any bundle
on that curve increases. Thus, happiness is a higher indifference
curve!
The level of satisfaction, or happiness, is often referred
to by economists as "utility". And the units we use to "measure"
this happiness are called "utils", hence the symbol U on
each indifference curve in Figures 4 and 5. Note that the
term "measure" is used here to mean simply an ordinal
ranking. Thus, higher indifference curves are given
higher numbers to indicate that baskets on the higher indifference
curve, e.g., U2, give a higher level of satisfaction than
baskets on the lower one, e.g., U1. These days, economists
no longer search for a way to actually measure the level
of one's satisfaction with a bundle of goods.
| Now it's time to
"do the thing".
Click on the following link
to download the Consumer
Choice Workbook. Work through Tutorial
5 Questions 1 - 3 to improve your understanding
of the indifference curve model.
Return here when you have finished.
Need help
downloading the Excel file? |
|
It's true that, with apologies to Charles Schulz, "Happiness
is a higher indifference curve". Thus, a consumer seeks
a market basket that generates the maximum level of happiness.
Graphically, this would be on the indifference curve farthest
away from the origin as possible. However, one's money income
and the prices of the goods impose a limit on the level
of happiness one may attain. The consumer is thus forced
to seek the market basket that generates the maximum attainable
level of happiness.
So, in order to complete our model of consumer choice,
we must develop a model of the consumer's budget constraint.
Continues...
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Indifference Curves