Indifference Curves
Introductory Microeconomics
1
Example:
 To encourage education, a government is considering
three different options:
 A lump-sum cash to kids of school age.
 A matching subsidy to each dollar the kids spend on
schooling.
 Provide education for free.
 Which is better?
2
Three Steps Involved In The Study Of
Consumer Behavior.
1) We will study consumer preferences.
 To describe how and why people prefer one good
to another.
2) Then we will turn to budget constraints.
 People have limited incomes.
3) Finally, we will combine consumer preferences and
budget constraints to determine consumer choices.
 What combination of goods will consumers buy
to maximize their satisfaction?
3
Market basket defined
 A market basket is a collection of one or more
commodities.
 One market basket may be preferred over another
market basket containing a different combination of
goods.
4
Three Basic Assumptions of Consumer
Preferences
 Preferences are complete.
 Give me any two baskets of goods (A and B), I will be able
to tell you on of the followings:
I prefer A to B
I prefer B to A
I am indifferent between A and B
 Preferences are transitive.
 If I prefer A to B and B to C, I must also prefer A to C.
 Non-satiation: Consumers always prefer more of any good to
less.
Indifference curves represent all combinations of market baskets that
provide the same level of satisfaction to a person.
5
Preferences over market basket
Market
Basket
A
B
D
E
G
H
Units of
Food
20
10
40
30
10
10
Units of
Clothing
30
50
20
40
20
40
Observations based on more
good is preferred to less
E is preferred to
G A H
Similarly, A, E, B, H, D are
all preferred to G
…
Much easier to see in a graph.
6
Preferences over market basket
Easier to see in a graph
Clothing
(units per week)
50
B
40
H
The consumer prefers
A to all combinations
in the blue box, while
all those in the pink
box are preferred to A.
E
A
30
D
G
20
10
10
20
30
40
Food
(units per week)
7
Preferences over market basket
Easier to see in a graph
Clothing
(units per week)
B
50
H
E
40
For example:
Combination B,A, & D
yield the same satisfaction
•E is preferred to U1
•U1 is preferred to H & G
A
30
D
20
U1
G
10
10
20
30
40
Food
(units per week)
8
Preferences over market basket
Clothing
(units
per
50
week)
B
Indifference curves slope downward to the right.
If it sloped upward it would violate the assumption
that more of any commodity is preferred to less.
H
E
40
A
30
Any market basket lying above and
to the right of an indifference curve
is preferred to any market basket
that lies on the indifference curve.
D
20
U1
G
10
10
20
30
40
Food
(units per week)
9
Indifference map
Clothing
(units
per
week)
 An indifference map is a set of
indifference curves that describes a
person’s preferences for all
combinations of two commodities.
 Each indifference curve in the
map shows the market baskets
among which the person is
indifferent.
D
B
A
U2
U1
U3
Market basket A
is preferred to B.
Market basket B is
preferred to D.
Food
(units per week)
10
Indifference Curves Cannot Cross
Clothing
(units per week)
If crossed
U2
U1
the consumer should be indifferent
between A, B and D. However, B contains
more of both goods than D. Thus, given
transitivity assumption, the assumption
of more is preferred to less is violated.
A
B
D
Food
(units per week)
11
The amount of clothing given up for unit of food
decreases with amount of food
A
Clothing 16
(units
per week) 14
12
Observation: The amount
of clothing given up for
a unit of food decreases
from 6 to 1
-6
10
B
1
8
Question: Does this
relation hold for giving
up food to get clothing?
-4
D
6
1
-2
4
E
G
1 -1
1
2
1
2
3
4
5
Food
(units per week)
12
Marginal Rate of Substitution
A
Clothing 16
(units
per week) 14
12
The marginal rate of substitution
(MRS) quantifies the amount of one
good a consumer will give up to
obtain more of another good
MRS = 6
-6
10
1
8
MRS is measured by
the slope of the
indifference curve
B
-4
D
6
MRS = 2
1
-2
4
E
G
1 -1
MRS = - C / F
1
2
1
2
3
4
5
Food
(units per week)
13
Assumption: Diminishing Marginal Rate of Substitution
Clothing 16
(units
per
14
week)
12
Along an indifference curve there is a
diminishing marginal rate of
substitution.
A
MRS = 6
Example: the MRS for AB was 6, while
that for DE was 2
-6
10
B
1
8
-4
D
6
MRS = 2
1
-2
4
E
G
1 -1
That is, consumers prefer a
balanced market basket.
1
2
1
2
3
4
Indifference curves are convex
because as more of one good
is consumed, a consumer
would prefer to give up fewer
units of a second good to get
additional units of the first one.
5
Food
(units per week)
14
Perfect Substitutes
Apple
Juice
(glasses) 4
Perfect
Substitutes
3
Two goods are perfect
substitutes when the marginal
rate of substitution of one good
for the other is constant.
2
1
0
1
2
3
4
Orange Juice
(glasses)
15
Perfect Complements
Left
Shoes
4
Perfect
Complements
3
Two goods are perfect
complements when
the indifference
curves for the goods
are shaped as right
angles.
2
1
0
1
2
3
4
Right Shoes
16
BADS
 Things for which less is preferred to more
 Examples
Air pollution
Asbestos
How does the indifference curve over
1. Two bads
2. One good and one bad
look like?
17
Utility and utility functions
 Utility: Numerical score representing the satisfaction that a
consumer gets from a given market basket.
 Utility Functions
 Assume:
The utility function for food (F) and clothing (C)
U(F,C) = F + 2C
Market Baskets: F units C units U(F,C) = F + 2C
A
8
3
8 + 2(3) = 14
B
6
4
6 + 2(4) = 14
C
4
4
4 + 2(4) = 12
The consumer is indifferent between A & B
The consumer prefers A & B to C
18
Utility Functions & Indifference Curves
Clothing
(units
per week)
Assume: U = FC
Market Basket
U = FC
C
25 = 2.5(10)
A
25 = 5(5)
B
25 = 10(2.5)
15
C
10
U3 = 100 (Preferred to U2)
A
5
B
0
5
10
U2 = 50 (Preferred to U1)
U1 = 25
Food
15
(units per week)
19
Ordinal Versus Cardinal Utility
 Ordinal Utility Function: places market baskets in
the order of most preferred to least preferred, but it
does not indicate how much one market basket is
preferred to another.
 Cardinal Utility Function: utility function describing
the extent to which one market basket is preferred
to another.
 Ordinal Versus Cardinal Rankings
 an ordinal ranking is sufficient to explain how
most individual decisions are made.
20
Budget Constraints
 Budget constraints limit an individual’s ability to
consume in light of the prices they must pay for
various goods and services.
 The budget line indicates all combinations of two
commodities for which total money spent equals
total income.
21
The Budget Line
 Let F equal the amount of food purchased, and C is
the amount of clothing.
 Price of food = Pf and price of clothing = Pc
 Then Pf F is the amount of money spent on food,
and Pc C is the amount of money spent on clothing.
Pf F + Pc C = I
22
Budget Constraints
Market Basket Food (F) Clothing (C) Total Spending
Pf = ($1) Pc = ($2)
PfF + PcC = I
A
B
D
E
G
0
20
40
60
80
40
30
20
10
0
$80
$80
$80
$80
$80
23
Budget Constraints
Clothing
(units
per week)
(I/PC) = 40
Pc = $2
Pf = $1
I = $80
Budget Line F + 2C = $80
A
B
30
As consumption moves along a
budget line from the intercept, the
consumer spends less on one item
and more on the other.
D
20
E
10
G
0
20
40
60
80 = (I/PF)
Food
(units per week)
24
Budget Constraints
Clothing
(units
per week)
(I/PC) = 40
A
The vertical intercept (I/PC),
illustrates the maximum amount of C
that can be purchased with income I.
Pc = $2
Pf = $1
I = $80
B
30
Budget Line F + 2C = $80
D
20
E
10
G
0
20
40
60
80 = (I/PF)
The horizontal intercept (I/PF),
illustrates the maximum amount of F
that can be purchased with income I.
Food
(units per week)
25
Budget Constraints
Clothing
(units
per week)
(I/PC) = 40
Pc = $2
Budget Line F + 2C = $80
A
I = $80
1
Slope  C/F   - PF/P C
2
B
30
Pf = $1
10
D
The slope of the line measures the relative cost
of food and clothing. The slope is the negative
of the ratio of the prices of the two goods.
20
20
E
10
The slope indicates the rate at which the
two goods can be substituted without
changing the amount of money spent.
G
0
20
40
60
80 = (I/PF)
Food
(units per week)
26
Effects of Changes in Income
Clothing
(units
per week)
A increase in
income shifts
the budget line
outward
80
60
A decrease in
income shifts
the budget line
inward
40
20
L3
L2
L1
(I =$40)
0
40
(I = $80)
80
120
(I = $160)
160
Food
(units per week)
27
Effects of Changes in Prices
Clothing
(units
per week)
An increase in the
price of food to
$2.00 changes
the slope of the
budget line and
rotates it inward.
A decrease in the
price of food to
$.50 changes
the slope of the
budget line and
rotates it outward.
40
L3
L1
L2
(PF = 1)
(PF = 2)
40
80
(PF = 1/2)
120
160
Food
(units per week)
28
Effects of Changes in Prices
Clothing
(units
per week)
Pc = $2
Pf = $1
I = $80
If the two goods decrease in price,
but the ratio of the two prices is
unchanged, the slope will not
change.
80
Same as an increase in income
60
40
20
If the two goods increase in
price, but the ratio of the two
prices is unchanged, the slope
will not change.
L1
Same as a decrease in income.
L3
L2
Pc = $4, Pf =$2
0
40
80
120
Pc = $1, Pf=$0.5
160
Food (units per week)
29
Consumer Choice
 Consumers choose a combination of goods that will
maximize the satisfaction they can achieve, given
the limited budget available to them.
 The maximizing market basket must satisfy two
conditions:
1) It must be located on the budget line.
2) Must give the consumer the most preferred
combination of goods and services.
30
Consumer Choice
Clothing
(units per
week)
Pc = $2
Pf = $1
I = $80
40
Market basket D
cannot be attained
given the current
budget constraint.
D
30
20
U3
Budget Line
0
20
40
80
Food (units per week)
31
Consumer Choice
Clothing
(units per
week)
Pc = $2
Pf = $1
Point B does not maximize satisfaction
because there exist a point A which is attainable
and yields a higher satisfaction.
40
30
I = $80
Note that the MRS -(-10/10) = 1
is greater than the price ratio (1/2).
B
-10C
A
Budget Line
20
U1
+10F
0
20
40
80
Food (units per week)
32
Consumer Choice
Recall, the slope of an indifference curve is:
Further, the slope of the budget line is:
MRS  
Slope  
C
F
PF
PC
Therefore, it can be said that satisfaction is maximized where:
PF
MRS 
PC
33
Example: Matching vs. Non-matching grant
from the federal government
 Local official has a preference on police spending (by
taxing its citizens) and private consumption (by its
citizens).
 The budget line represents the total amount of
resources available for the public spending and private
spending.
 A non-matching grant from the federal government is
simply a check from the federal government.
 A matching grant from the federal government is
offered as a subsidy of the local spending.
34
Choosing between a non-matching and
matching grant to fund police expenditures
Non-matching Grant
Private
Expenditures ($)
Before Grant
Budget line: PQ
A: Preference maximizing
market basket
Expenditure
OR: Private
OS: Police
T
P
B
U
A
R
After Grant
• Budget line: TV
•B: Preference maximizing
market basket
•Expenditure
•OU: Private
•OZ: Police
U3
U1
O
S
Z
Q
V
Police
Expenditures ($)
35
Choosing between a non-matching and
matching grant to fund police expenditures
Matching Grant
Private
Expenditures ($)
T
Before Grant
Budget line: PQ
A: Preference maximizing
market basket
P
W
R
A
C
U2
U1
O
S
X
Q
After Grant
•C: Preference maximizing
market basket
Expenditures
•OW: Private
•OX: Police
R
Police ($)
36
Choosing between a non-matching and
matching grant to fund police expenditures
Private
Expenditures ($)
Matching vs. Non-Matching Grant
Nonmatching Grant
•Point B
•OU: Private expenditure
•OZ: Police expenditure
Matching Grant
•Point C
•OW: Private expenditure
•OX: Police expenditure
T
P
U
W
B
A
C
U3
U2
U1
O
Z X
Q
Note that the amount of grant
at point B and C are the same.
R
Police ($)
37
Example: A College Trust Fund
 Suppose Jane Doe’s parents set up a trust fund for her
college education.
 Originally, the money must be used for education.
 If part of the money could be used for the purchase of
other goods, her preferred consumption bundle
changes.
38
A College Trust Fund
Other
Consumption
($)
A College Trust Fund
A: Consumption before the trust fund
The trust fund shifts the budget line
B: Requirement that the trust fund
must be spent on education
U3
C: If the trust could be spent on
other goods
C
P
A
B
U2
U1
Q
Education ($)
39
End
40