# Microeconomics_4__Besanko

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```are complete, preferences
are transitive, and more is better.
\u2022 Distinguish between ordinal and cardinal ranking of preferences.
\u2022 Apply utility functions as a tool for representing
preferences and analyze the concept of marginal util-
ity and the principle of diminishing marginal utility.
\u2022 Apply utility functions in the analysis of preferences
with a single good and with multiple goods.
\u2022 Construct indifference curves as a way of represent-
ing utility functions in simplified form.
\u2022 Analyze the concept of the marginal rate of substi-
tution of one good for another.
\u2022 Describe and compare some special utility functions.
c03consumerpreferencesandtheconceptofutility.qxd 7/14/10 12:06 PM Page 74
3.1
REPRESENTA-
TIONS OF
PREFERENCES
In a modern economy, consumers can purchase a vast array of goods and services. We
begin by considering a market basket (sometimes called a bundle), defined as a collec-
tion of goods and services that an individual might consume. For example, one basket
of goods might include a pair of jeans, two pairs of shoes, and 5 pounds of chocolate
candy. A second basket might contain two pairs of jeans, one pair of shoes, and 2
pounds of chocolate candy. More generally, a basket may contain specified amounts of
not only jeans, shoes, and chocolate candy, but also housing, electronic goods, tickets
for theatrical and sporting events, and many other items.
To illustrate the idea of a basket, consider a simplified example in which a con-
sumer can purchase only two goods, food and clothing. Seven possible consumption
of food and 30 units of clothing per week. One who chooses basket B instead con-
sumes 60 units of food and 10 units of clothing weekly. A basket might contain only
one good, such as basket J (only food) or basket H (only clothing).
Consumer preferences tell us how an individual would rank (i.e., compare the
desirability of ) any two baskets, assuming the baskets were available at no cost. Of course,
a consumer\u2019s actual choice will ultimately depend on a number of factors in addition
to preferences, including income and what the baskets cost. But for now we will con-
sider only consumer preferences for different baskets.
Our study of consumer preferences begins with three basic assumptions that underlie
the theory of consumer choice. In making these assumptions, we take it for granted
that consumers behave rationally under most circumstances. Later we will discuss sit-
uations in which these assumptions might not be valid.
1. Preferences are complete. That is, the consumer is able to rank any two baskets.
For baskets A and B, for example, the consumer can state her preferences
according to one of the following possibilities:
consumer preferences
Indications of how a con-
sumer would rank (compare
the desirability of) any two
to the consumer at no cost.
FIGURE 3.1 Weekly Baskets of Food and Clothing
Seven possible weekly baskets of food and clothing that
consumers might purchase are illustrated by points A, B,
D, E, G, H, and J.
Un
its
o
f c
lo
th
in
g
Units of food
0
30
20
10
20 40 60
D
G
H E
B
A
J
3.1 REPRESENTATIONS OF PREFERENCES 75
goods and services that an
individual might consume.
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76 CHAPTER 3 CONSUMER PREFERENCES AND THE CONCEPT OF UTIL ITY
She is indifferent between, or equally happy with, baskets A and B (written A B).
2. Preferences are transitive. By this we mean that the consumer makes choices
that are consistent with each other. Suppose that a consumer tells us that she
to prefer basket A to basket E. Using the notation we have just introduced to
describe preferences, we can represent transitivity as follows: If A \ufffd B and if
B \ufffd E, then A \ufffd E.
3. More is better. In other words, having more of a good is better for the consumer.
Suppose the consumer is considering the baskets in Figure 3.1. If more is bet-
ter, she likes more food better than less food and prefers to have more clothing
rather than less clothing. In that case, she would prefer basket A to E or H
because she receives the same amount of clothing with these three baskets, but
more food at A. She would prefer basket A to B or J because she receives the
same amount of food in these three baskets, but more clothing at A. She will
also prefer A to G or D because she receives more food and more clothing
at A than at either of the other two baskets. Therefore, among the seven
about the consumer\u2019s preferences, we do not know how she would rank every
pair of baskets. For example, without further information we do not know
whether she prefers E to G because she would receive more food but less
clothing at G.
ORDINAL AND CARDINAL RANKING
In this book we will refer to two types of rankings: ordinal and cardinal. Ordinal
rankings give us information about the order in which a consumer ranks baskets. For
example, for basket A in Figure 3.1 the consumer buys three times as much food and
three times as much clothing as she does for basket D. We know that the consumer
prefers basket A to D because more is better. However, an ordinal ranking would not
tell us how much more she likes A than D.
Cardinal rankings give us information about the intensity of a consumer\u2019s pref-
erences. With a cardinal ranking, we not only know that she prefers basket A to
basket D, but we can also measure the strength of her preference for A over D. We
can make a quantitative statement, such as \u201cThe consumer likes basket A twice as
an ordinal ranking.
It is usually easy for consumers to answer a question about an ordinal ranking,
such as \u201cWould you prefer a basket with a hamburger and french fries or a basket with
a hot dog and onion rings?\u201d However, consumers often have more difficulty describing
how much more they prefer one basket to another because they have no natural
L
ordinal ranking
Ranking that indicates
whether a consumer prefers
does not contain quantita-
intensity of that preference.
cardinal ranking A
quantitative measure of the
intensity of a preference for
1As noted in the text, the consumer buys three times as much food and clothing at basket A as at D.
However, this does not necessarily mean that the consumer likes basket A exactly three times more than
basket D. Would your own satisfaction triple if you bought three times as much of all goods as you now
do? For most consumers satisfaction would rise, but by less than three times.
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3.2 UTILITY FUNCTIONS 77
3.2
UTILITY
FUNCTIONS
The three assumptions\u2013\u2013preferences are complete, they are transitive, and more is
better\u2013\u2013allow us to represent preferences with a utility function. A utility function
measures the level of satisfaction that a consumer receives from any basket of goods.
We can represent the utility function with algebra or a graph.
PREFERENCES WITH A SINGLE GOOD:
THE CONCEPT OF MARGINAL UTILITY
To illustrate the concept of a utility function, let\u2019s begin with a simple scenario in
which a consumer, Sarah, purchases only one good, hamburgers. Let y denote the
number of hamburgers she purchases each week, and let U( y) measure```