PPA 723: Managerial
Economics
Lecture 5:
Indifference Curves
Managerial Economics, Lecture 5: Indifference Curves
Outline
Properties of Consumer Preferences
Indifference Curves
Managerial Economics, Lecture 5: Indifference Curves
Tastes
Individual tastes (preferences)
determine the pleasure people derive
from different goods and services
Our objective is to determine how a
consumer’s tastes influence its
decisions (positive analysis), not to
judge tastes (normative).
Managerial Economics, Lecture 5: Indifference Curves
Standard Assumptions About
Consumer Preferences
1. Completeness
2. Transitivity
3. More is better
Managerial Economics, Lecture 5: Indifference Curves
Assumption 1: Completeness
Consumer can rank any two bundles of
goods
Only one of the following is true: The
consumer
prefers Bundle x to Bundle y
prefers Bundle y to Bundle x
is indifferent between the two bundles
Managerial Economics, Lecture 5: Indifference Curves
Assumption 2: Transitivity (Rationality)
A consumer's preference over bundles
is consistent:
If a consumer prefers Bundle z to Bundle y
and Bundle y to Bundle x
Then that consumer prefers Bundle z to
Bundle x
Managerial Economics, Lecture 5: Indifference Curves
Assumption 3: More is Better
More of a good is better than less of it.
Good: commodity for which more is
preferred to less at least at some
levels of consumption
Bad: something for which less is
preferred to more, such as pollution
Consumers are not satiated.
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.1a Bundles of Pizzas and Burritos Lisa Might Consume
(a) Ranking Regions
B, Burritos
per semester
c
25
A
f
20
15
e
a
d
10
b
B
0
15
25 30
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.1b Bundles of Pizzas and Burritos Lisa Might Consume
(b) Indifference Curve
B, Burritos
per semester
25
c
f
20
e
15
a
10
0
d
b
I
15
25 30
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.1c Bundles of Pizzas and Burritos Lisa Might Consume
(c) Preference Map
B, Burritos
per semester
25
c
f
20
e
15
10
I2
d
I1
I0
0
15
25 30
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Indifference Curve Properties
1. Bundles on indifference curves farther
from the origin are preferred to those
on indifference curves closer to the
origin.
2. There is an indifference curve through
every possible bundle.
3. Indifference curves cannot cross.
4. Indifference curves are “thin”.
5. Indifference curves slope down.
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.2a Impossible Indifference Curves
(a) Crossing
B, Burritos
per semester
e
b
a
I1
I0
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.2b Impossible Indifference Curves
(b) Upward Sloping
B, Burritos
per semester
b
a
I
Z
, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Willingness to Substitute
Downward-sloping indifference curve 
consumer is willing to substitute one
good for the other.
Marginal rate of substitution (MRS) of
burritos (rise) for pizza (run), is slope of
indifference curve:
B
MRS 
Z
Managerial Economics, Lecture 5: Indifference Curves
Marginal Rate of Substitution
B, Burritos
per semester
MRS = B/Z
B
Z
I
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
MRS Varies Along an
Indifference Curve
Indifference curves bow away from the
origin (called convex).
Indicates diminishing marginal rate of
substitution (MRS).
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.3a Marginal Rate of Substitution
(a) Indifference Curve
Convex to the Origin
B , Burritos
per semester
a
8
–3
5
3
2
0
b
1
–2
c
1
–1
d
1
3 4 5
I
6
Z , Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Unlikely Outcome:
Concave Indifference Curve
If indifference curve bows toward the
origin (concave),
Then (implausibly) the consumer has an
increasing MRS.
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.3b Marginal Rate of Substitution
B, Burritos
per semester
(b) Implausible Indifference Curve
that is Concave to the Origin
a
7
–2
b
5
1
–3
c
2
1
I
0
3
4 5
6
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.4a Perfect Substitutes
Coke, Cans
per week
4
3
2
1
I1
0
I2
I3
I4
1
2
3
4
Pepsi, Cans per week
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.4b Perfect Complements
Ice cream,
Scoops per week
e
3
d
2
a
1
0
1
c
b
I3
I2
I1
2
3
Pie, Slices per week
Managerial Economics, Lecture 5: Indifference Curves
Figure 4.4c Imperfect Substitutes
B, Burritos
per semester
I
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Utility
 Utility is a number that reflects the relative
rankings of various bundles of goods
 If Lisa prefers bundle A to B, then utility from
A must be greater than utility from B
 A utility function is a:
 relationship between a utility measure and every
possible bundle of good
 succinct summary of information in an indifference
curve map
Managerial Economics, Lecture 5: Indifference Curves
Utility and Marginal Utility
The marginal utility of Z is:
U
MU Z 
Z
MUZ is the change in utility from a small
increase in Z holding B fixed
Managerial Economics, Lecture 5: Indifference Curves
Utility
U, Utils
350
Utility function, U (10, Z )
250
230
0
 Z =1
1
2
3
4
U = 20
5
6
7
8
9
10
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Marginal Utility
MU Z, Marginal
utility of pizza
130
20
0
MUZ
1
2
3
4
5
6
7
8
9
10
Z, Pizzas per semester
Managerial Economics, Lecture 5: Indifference Curves
Totals, Margins, and Averages
Economic analysis often depends on the
distinction between a total, a average,
and a margin.
In the case of utility



U = total utility
U/Z = average utility of Z
MUZ = U/Z = marginal utility of Z
Managerial Economics, Lecture 5: Indifference Curves
Utility and the Marginal Rate
of Substitution
Let A = the good on the vertical axis
and B = the good on the horizontal axis,
Then (note the inversion):
MU B
A
MRS 

B
MU A
Managerial Economics, Lecture 5: Indifference Curves
Marginal Rate of Substitution
Quantity of A
Give up
one unit
of A
Gain MUA units of utility,
which can “buy”
MUA / MUB Units of B
A
MRS = A/B = - MUB/MUA
B
I
Quantity of B
Managerial Economics, Lecture 5: Indifference Curves
Deriving the Marginal Rate of Substitution
U  0  A( MU A )  B( MU B )
 MU A  B( MU B )
MU A
B  
MU B
MU B
A
1
MRS 


B MU A / MU B
MU A