Chapter 3
UTILITIES
INDIFFERENCE CURVES
Budget line
2
Good 2
150
100
50
Good 1
0
50
100
150
Points on the budget line indicate all the bundles of goods that the
consumer can afford.
Indifference Curve
3
 Indifference curve: locus of bundles that provide the
consumer with the same level of satisfaction
Indifference curves
4
Good 2 (x 2)
a b
20
w
140
100
0
10
Good 1 (x 1)
Points on the same indifference curve represent bundles yielding the
same amount of utility.
Indifference Curves
5
 Indifference map
 Set of indifference curves for a consumer


Every bundle
 On an indifference curve
Indifference curves

Farther from origin ->Higher utility
The Shape of Indifference Curves
6
 Indifference curves
 Cannot slope upward


Cannot cross each other


Nonsatiation assumption
Transitivity and nonsatiation assumptions
Farther from the origin – higher utility
Nonsatiation assumption
 Cannot cross each other


Are bowed in toward the origin
Convexity assumption
 Farther from the origin - higher utility

Indifference curves cannot slope upward
7
Good 2 (x 2)
E
B
x
a
D
0
y
C
Good 1 (x 1)
If an indifference curve ran from a to x, then bundle x would be no better
than bundle a despite containing more of both goods. This upward slope
of the indifference curve would be a violation of the nonsatiation
assumption.
Indifference curves cannot cross each other
8
Good 2 (x 2)
a
b
I1
c
I2
Good 1 (x 1)
0
If indifference curves I1 and I2 crossed at a, then by transitivity of preferences
bundle b would be no better than bundle c despite containing more of both
goods. This crossing of indifference curves would be a violation of the
nonsatiation assumption
Farther from the origin -> higher utility
9
Good 2 (x 2)
a
0
w
Bundle w must be
preferred to bundle a
because it contains
more of both goods
Good 1 (x 1)
Bowed-in
(b)
(a)
10
Good 2 (x 2)
Good 2 (x 2)
a
a
c
c
b
b
0
Good 1 (x 1)
(a) Bowed-out indifference curves violate
convexity of preferences. Bundle c is a
weighted average of bundles a and b, but
yields lower utility level because it is on an
indifference curve that is closer to the origin.
0
Good 1 (x 1)
(b) Bowed-in indifference curves
satisfy the convexity of preferences.
Bundle c, a weighted average of
bundles a and b, yields a higher
utility level
The Marginal Rate of Substitution
11
 Marginal rate of substitution (MRS)
 Particular point on indifference map
 One consumer
 Ratio of exchanging goods

Same utility
 MRS = - ∆x2 / ∆x1
The Marginal Rate of Substitution
12
 Diminishing marginal rate of substitution
 From convexity
 Move along the indifference curve
Same utility level
 MRS decreases

Convex preferences and the MRS
13
Good 2 (x 2)
100
a
+∆x2
-∆x1
60
b
-∆x1
+∆x2
c
10
9
0
d
I1
10 20
100 110
Good 1 (x 1)
As the consumer is given bundles containing more and more of
good 2, she values an individual unit of good 2 less and less
Indifference Curves and Tastes
14
 Flat indifference curves
 Goods that yield no utility
 Straight-line indifference curves
 Goods that are perfect substitutes
MRS - constant along an indifference curve
 In a two-good world
 Indifference curve - straight line

(b)
(a)
15
Good
Good 2 (x 2)
2 (x 2)
+∆x2
a
10
9
5
4
0
Good 1 (x 1)
(a) Flat indifference curves. The good
measured on the horizontal axis is
yielding no utility for the consumer.
0
-∆x1
+∆x2
-∆x1
3
8 11
Good 1 (x 1)
(b) Straight-line indifference curves:
perfect substitutes. The same amount
of good 2 is always needed to
compensate the consumer for the
loss of one unit of good 1.
Indifference Curves and Tastes
16
 Right-angle indifference curves
 Goods that are perfect complements
Must be consumed in a fixed ratio to produce utility
 In a two-good world
 Right angle indifference curves

 Bowed-out indifference curves
 Nonconvex preferences
(d)
(c)
17
Good
2 (x 2)
Good 2 (x 2)
11
10
0
+∆x2
+∆x2
-∆x1
b +∆x
2
-∆x1
a
-∆x1
b
c
a
5 6
I1
Good 1 (x 1)
0
Good 1 (x 1)
(c) Right-angle indifference curves:
(d) Bowed-out indifference curves:
perfect complements. Adding any
nonconvex preferences and the MRS. As the
amount of only one good to bundle a consumer is given bundles containing more
yields no additional utility.
and more of good 2, he values an individual
unit of good 2 more and more.
Perfect substitutes
18
Pepsi
0
Coke
Mary’s marginal rate of substitution is constant at any bundle of
Pepsi and Coke.
Optimal Consumption Bundle
19
 Optimal consumption bundle
 Maximize consumer’s utility


Within the economically feasible set
Best bundle

According to consumer’s preferences
 Characteristics of optimal bundles
 Indifference curve tangent to budget line
Slope of indifference curve = MRS = -∆x2/∆x1
 Slope of budget line = price ratio = p1/p2
 MRS = p1/p2

The optimal consumption bundle
20
Good 2 (x 2)
B
x
+1
-3
z
-4
e
k
+1
m
n
F
0
B’
Good 1 (x 1)
At the optimal point e, the indifference curve is tangent to the boundary
BB’ of the economically feasible consumption set.