Transcript x 1
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.