Preferences and Utility
Consumer Behavior
● Theory
of consumer behavior
Description of how consumers allocate incomes
among different goods and services to maximize
their well-being.
Consumer behavior is best understood in these
distinct steps:
1. Consumer Preferences
2. Utility
3. Budget Constraints
4. Consumer Choices
Premises of Consumer Behavior
 Individual preferences determine the amount of
pleasure people derive from the goods and services they
consume.
 Consumers face constraints or limits on their choices.
 Consumers maximize their well-being or pleasure
from consumption, subject to the constraints they face.
Copyright © 2012 Pearson Addison-Wesley. All rights reserved.
Consumer Preferences
 Market Baskets
● Market basket (or bundle)
List with specific
quantities of one or more goods.
ALTERNATIVE MARKET BASKETS
MARKET BASKET
UNITS OF FOOD
UNITS OF CLOTHING
A
20
30
B
10
50
D
40
20
E
30
40
G
10
20
H
10
40
To explain the theory of consumer behavior, we will
ask whether consumers prefer one market basket to
another.
Axioms of Consumer’s Behavior
 1) Completeness
 2) Transitivity
 3) Continuity
 4) More is Better.
Axioms of Consumer’s Behavior
 1) Completeness
 Preferences are assumed to be complete.
 In other words, consumers can compare and rank
all possible baskets.
 if A and B are any two market baskets, an individual
can always specify exactly one of these possibilities:
 A is preferred to B
 B is preferred to A
 A and B are equally attractive
Note that:
 These preferences ignore costs conditions.
Axioms of Rational Choice
2) Transitivity
 Preferences are transitive.
 Transitivity means that
 if a consumer prefers basket A to basket B
and basket B to basket C, then the
consumer also prefers A to C
Axioms of Rational Choice
 3) Continuity
 if A is preferred to B, then situations
suitably “close to” A must also be
preferred to B
Axioms of Rational Choice
 4) More Is Better - all else being the same, more of a
commodity is better than less of it (always wanting
more is known as nonsatiation).
 Marginal utilities is positive for all commodities.
 Good - a commodity for which more is preferred to
less, at least at some levels of consumption.

Goods are assumed to be desirable—i.e., to be good.
 Bad - something for which less is preferred to more,
such as pollution.
Utility
 Given these assumptions, it is possible to show that
people are able to rank all possible situations from
least desirable to most.
 Economists call this ranking utility
 if A is preferred to B, then
U(A) > U(B)
Utility:
Nonuniqueness of utility measures
 Utility rankings are ordinal in nature
 they record the relative desirability of
commodity bundles
 it makes no sense to consider how much
more utility is gained from A than from B
 It is also impossible to compare utilities
between people
Utility:
The ceteris paribus assumption
 Utility is affected by
 the consumption of physical commodities
 psychological attitudes
 peer group pressures
 personal experiences
 the general cultural environment
 Economists generally devote attention to
quantifiable options while holding constant
the other things that affect utility
 ceteris paribus assumption
Utility from consumption of goods
 Assume that an individual must choose among
consumption goods x1, x2,…, xn
 We can show his rankings using a utility function
of the form:
utility = U(x1, x2,…, xn; other things)
 Often “other things” are held constant
utility = U(x1, x2,…, xn)
 We can assume the individual is considering two
goods, x and y
utility = U(x,y)
Economic Goods
 In the utility function, the variables are assumed to be
“goods”
 more is preferred to less
Quantity of y
Preferred to x*, y*
?
y*
Worse
than
x*, y*
?
Quantity of x
x*
Economic Goods using market
baskets
•Because more of
each good is
preferred to less, we
can compare market
baskets in the shaded
areas.
•Basket A is clearly
preferred to basket G,
while E is clearly
preferred to A.
•However, A cannot
be compared with B,
D, or H without
additional information.
AN INDIFFERENCE CURVE
The indifference curve
U1 that passes
through market
basket A shows all
baskets that give the
consumer the same
level of satisfaction as
does market basket
A; these include
baskets B and D.
Our consumer prefers
basket E, which lies
above U1, to A, but
prefers A to H or G,
which lie below U1.
Indifference Curves
 An indifference curve shows a set of consumption
bundles among which the individual is indifferent
Quantity of y
Combinations (x1, y1) and (x2, y2)
provide the same level of utility
y1
y2
U1
Quantity of x
x1
x2
Properties of Indifference Maps
1.
2.
3.
4.
Bundles on indifference curves farther from the
origin are preferred to those on indifference curves
closer to the origin.
There is an indifference curve through every
possible bundle.
Indifference curves cannot cross.
Indifference curves slope downward.
Marginal Rate of Substitution
 The slope of the indifference curve at any point is
called the marginal rate of substitution (MRS).
 Its value will have a negative sign.
Quantity of y
dy
MRS 
dx U U1
y1
y2
U1
Quantity of x
x1
x2
Marginal Rate of Substitution
 MRS changes as x and y change
 reflects the individual’s willingness to trade y
for x
At (x1, y1), the indifference curve is steeper.
The person would be willing to give up more
y to gain additional units of x
Quantity of y
At (x2, y2), the indifference curve
is flatter. The person would be
willing to give up less y to gain
additional units of x
y1
y2
U1
Quantity of x
x1
x2
Marginal Rate of Substitution
Example: U = Ax2+By2; MUx=2Ax; MUy=2By
(where: A and B positive)
MRSx,y = MUx/MUy
= 2Ax/2By
= Ax/By
Marginal utilities are positive (for positive x and y)
Marginal utility of x increases in x;
Marginal utility of y increases in y
21
Indifference Curve Map
 Each point must have an indifference curve
through it
Quantity of y
Increasing utility
U3
U2
U1
U1 < U2 < U3
Quantity of x
Transitivity
 Can two of an individual’s indifference curves
intersect?
Quantity of y
The individual is indifferent between A and C.
The individual is indifferent between B and C.
Transitivity suggests that the individual
should be indifferent between A and B
C
B
A
U2
U1
But B is preferred to A
because B contains more
x and y than A
Quantity of x
Impossible Indifference Curves
Transitivity
Impossible Indifference Curves
B, Burritos per semester
 Lisa is indifferent
between e and a, and
also between e and b…
 so by transitivity she
e
b
a
I1
I0
Z, Pizzas per semester
should also be indifferent
between a and b…
 but this is impossible,
since b must be preferred
to a given it has more of
both goods.
 Lisa is indifferent
between b and a since
both points are in the
same indifference curve…
 But this contradicts the
“more is better”
assumption.
 Why?
 As, b has more of both and
hence it should be
preferred over a.
B, Burritos per semester
Impossible Indifference Curves (cont.)
b
a
I
Z, Pizzas per semester
B, Burritos per semester
Impossible Indifference Curves (cont.)
 Consumer is
indifferent between b
and a since both points
are in the same
indifference curve…
b
 But this contradicts the
a
I
Z, Pizzas per semester
“more is better”
assumption since b has
more of both and hence
it should be preferred
over a.
Types of Ranking:
Students take an exam. After the exam, the
students are ranked according to their performance.
• 1) An ordinal ranking lists the students in order of
their performance (i.e., Harry did best, Joe did
second best, Betty did third best, and so on).
• 2) A cardinal ranking gives the mark of the exam,
based on an absolute marking standard (i.e.,
Harry got 80, Joe got 75, Betty got 74 and so
on).
• 3) Alternatively, if the exam were graded on a
curve, the marks would be an ordinal ranking.
THE MARGINAL RATE OF
SUBSTITUTION
The magnitude of the
slope of an indifference
curve measures the
consumer’s marginal
rate of substitution
(MRS) between two
goods.
In this figure, the MRS
between clothing (C) and
food (F) falls from 6
(between A and B) to 4
(between B and D) to 2
(between D and E) to 1
(between E and G).
The Marginal Rate of Substitution
● Marginal
rate of substitution (MRS) Maximum
amount of a good that a consumer is willing to give
up in order to obtain one additional unit of another
good.
CONVEXITY
The decline in the MRS reflects the assumption
regarding consumer preferences: a diminishing
marginal rate of substitution.
When the MRS diminishes along an indifference
curve, the curve is convex.
MARGINAL UTLITIES AND MARGINAL RATE OF
SUBISITUTION
 The general equation for an indifference curve is
U(x1,x2)  k, a constant
 Totally differentiating this identity gives
U
U
dx1 
dx2  0
 x1
 x2
rearranging
d x2
 U /  x1
 
d x1
 U /  x2
This is the MRS.
MU’s and MRS: An example
Suppose U(x1,x2) = x1x2. Then

MU 
x


MU 
x

1
2
x
so MRS 
MU x
MU
1
2
U
 (1)( x2 )  x2
x1
U
 ( x1 )(1)  x1
x2
d x2
 U /  x1
x2



d x1
 U /  x2
x1
MU’s and MRS: An example
U(x1,x2) = x1x2;
x2
8
x2
MRS  
x1
MRS(1,8) = -(8/1) = -8
MRS(6,6) = -(6/6) = -1.
6
U = 36
1
6
U=8
x1
UTILITY
Example U(x1,x2)= x1.x2 =16
X1
1
2
3
4
5
X2
16
8
5.3
4
3.2
As X1  MRS  (in absolute terms),
preferences
MRS
(-) 8
(-) 2.7
(-) 1.3
(-) 0.8
i.e convex
MONOTONIC TRANSFORMATIONS AND
MRS
 Applying a monotonic transformation to a
utility function representing a preference
relation simply creates another utility function
representing the same preference relation.
 What happens to marginal rates-of-substitution
when a monotonic transformation is applied?
MONOTONIC TRANSFORMATIONS AND
MRS
 For U(x1,x2) = x1x2 the MRS = (-) x2/x1
 Create V = U2; i.e. = x12x22 What is the MRS for V?
2
 V /  x1
2 x1 x2
x2
MRS  


2
 V /  x2
x1
2 x1 x2
which is the same as the MRS for U.
Special Functional Forms
1)Cobb – Douglas Utility
2)Perfect Substitutes
3)Perfect Complements
4)CES Utility: includes
the other three as special
cases
5)Quasi linear
Special Functional Forms
1. Cobb-Douglas: U = Axy
where:  +  =, > or < than 1; A, , positive constants
MUX = Ax-1y
Ax -1
MUY =  y
MRSx,y = (y)/(x)
“Standard” case
Note: marginal rate of substitute only depends on the ratio
of X and y not on the total amounts of X and y.
So indifference curves for different levels of Utility look identical
38
to each other no matter how far away from the origin they are.
Special Functional Forms
y
Example: Cobb-Douglas
All curves are “hyperbolic”,
asymptoting to, but never
touching any axis.
Preference Direction
IC2
IC1
x
39
Special Functional Forms
Perfect Substitutes: U = Ax + By
Where: A, B positive constants
MUx = A
MUy = B
MRSx,y = A/B
1 unit of x is equal to B/A units of y everywhere
(constant MRS).
40
Perfect Substitution Indifference
Curves
The indifference curves will
x2
x1 + x 2 = 5
13
x1 + x2 = 9
9
be linear.
The MRS will be constant
along the indifference curve.
x1 + x2 = 13
5
V(x1,x2) = x1 + x2.
5
9
13
All are linear and parallel.
x1
Special Functional Forms
Perfect Complements: U = A min(x,y)
where: A is a positive constant.
MUx = 0 or A
MUy = 0 or A
MRSx,y is 0 or infinite or undefined (corner)
42
Perfect Complementarity Indifference
Curves :
Fixed Proportion of Consuming Goods
45o
x2
W(x1,x2) = min{x1,x2}
min{x1,x2} = 8
8
min{x1,x2} = 5
5
3
min{x1,x2} = 3
3
5
8
x1
All are right-angled with vertices on a ray from the origin.
Only by choosing more of the two goods together can utility
be increased.
Imperfect Substitutes
 The standard-
shaped, convex
indifference curve in
panel lies between
these two extreme
examples.
B
 Convex indifference
I
Z
curves show that a
consumer views two
goods as imperfect
substitutes.
Special Functional Forms
U = v(x) + Ay Where: A is a positive constant.
U(x1,x2) = f(x1) + x2 is linear in just x2 and is called
quasi-linear.
MUx = v’(x) = V(x)/x, where  small MUy = A
E.g.
U(x1,x2) = 2x11/2 + x2.
"The only thing that determines your personal trade-off
between x and y is how much x you already have."
*can be used to "add up" utilities across individuals*
45
Special Functional Forms
y
Example: Quasi-linear Preferences
• (consumption of beverages)
Each curve is a vertically
shifted copy of the others.
IC2
IC1
•
•
0
IC’s have same slopes
on any vertical line
x
46
3.2 Curvature of Indifference
Curves
 Imperfect Substitutes
• Between extreme examples of perfect substitutes and perfect
complements are standard-shaped, convex indifference curves.
• Cobb-Douglas utility
function
(e.g.
)
indifference curves
never hit the axes.
• Quasilinear utility
function
(e.g.
)
indifference curves
hit one of the axes.
 DOUBT next slides
Examples of Utility Functions
 CES Utility (Constant elasticity of substitution)
utility = U(x,y) = x/ + y/
when   1,   0 and
utility = U(x,y) = ln x + ln y
when  = 0
 Perfect substitutes   = 1
 Cobb-Douglas   = 0
 Perfect complements   = -
 Doubt all three
Examples of Utility Functions
 For the CES utility function, the elasticity of
substitution () is equal to 1/(1 - )
 Perfect substitutes   = 
 Fixed proportions (perfect complements)   = 0