Ka-fu Wong University of Hong Kong

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Ka-fu WongUniversity of Hong Kong
Indifference Curves
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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?

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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?

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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.

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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.
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Preferences over market basket
Units of Food
Units of Clothing
Market Basket
Observations based on more good is preferred to
less
E is preferred to

• A 20 30
• B 10 50
• D 40 20
• E 30 40
• G 10 20
• H 10 40

A
H
G
Similarly, A, E, B, H, D are all preferred to G

Much easier to see in a graph.
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Preferences over market basketEasier to see in a
graph
Clothing (units per week)
50
40
30
20
10
Food (units per week)
10
20
30
40
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Preferences over market basket Easier to see in
a graph
Clothing (units per week)

• For example
• Combination B,A, D
• yield the same satisfaction
• E is preferred to U1
• U1 is preferred to H G

50
40
30
20
U1
10
Food (units per week)
10
20
30
40
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Preferences over market basket
Clothing (units per week)
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.
50
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.
40
30
20
U1
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Food (units per week)
10
20
30
40
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Indifference map
Clothing (units per week)

• An indifference map is a set of indifference
  curves that describes a persons preferences for
  all combinations of two commodities.
• Each indifference curve in the map shows the
  market baskets among which the person is
  indifferent.

Food (units per week)
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Indifference Curves Cannot Cross
Clothing (units per week)
If crossed
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)
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The amount of clothing given up for unit of food
decreases with amount of food
Clothing (units per week)
16
14
12
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Question Does this relation hold for giving up
food to get clothing?
8
6
4
2
Food (units per week)
2
3
4
5
1
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Marginal Rate of Substitution
A
Clothing (units per week)
The marginal rate of substitution (MRS)
quantifies the amount of one good a consumer will
give up to obtain more of another good
16
14
MRS 6
-6
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MRS is measured by the slope of the indifference
curve
10
B
1
8
-4
D
MRS 2
6
1
E
MRS - ?C / ?F
-2
G
4
1
-1
1
2
Food (units per week)
2
3
4
5
1
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Assumption Diminishing Marginal Rate of
Substitution
Along an indifference curve there is a
diminishing marginal rate of substitution.
A
Clothing (units per week)
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MRS 6
Example the MRS for AB was 6, while that for DE
was 2
-6
12
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B
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.
1
8
-4
D
MRS 2
6
1
E
-2
G
4
1
-1
That is, consumers prefer a balanced market
basket.
1
2
Food (units per week)
2
3
4
5
1
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Perfect Substitutes
Apple Juice (glasses)
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Perfect Substitutes
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Two goods are perfect substitutes when the
marginal rate of substitution of one good for the
other is constant.
2
1
Orange Juice (glasses)
2
3
4
1
0
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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
2
3
4
1
0
Right Shoes
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BADS

• Things for which less is preferred to more
• Examples
• Air pollution
• Asbestos

• How does the indifference curve over
• Two bads
• One good and one bad
• look like?

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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

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Utility Functions Indifference Curves
Clothing (units per week)
15
10
5
Food (units per week)
10
15
5
0
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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.

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Budget Constraints

• Budget constraints limit an individuals 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.

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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
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Budget Constraints
Market Basket Food (F) Clothing (C) Total
Spending Pf (1) Pc (2) PfF PcC I

• A 0 40 80
• B 20 30 80
• D 40 20 80
• E 60 10 80
• G 80 0 80

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Budget Constraints
Clothing (units per week)
Pc 2 Pf 1 I 80
(I/PC) 40
As consumption moves along a budget line from the
intercept, the consumer spends less on one item
and more on the other.
30
20
10
Food (units per week)
40
60
80 (I/PF)
20
0
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Budget Constraints
Clothing (units per week)
The vertical intercept (I/PC), illustrates the
maximum amount of C that can be purchased with
income I.
A
(I/PC) 40
Pc 2 Pf 1 I 80
B
30
D
20
E
The horizontal intercept (I/PF), illustrates the
maximum amount of F that can be purchased with
income I.
10
G
Food (units per week)
80 (I/PF)
40
60
20
0
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Budget Constraints
Clothing (units per week)
Pc 2 Pf 1 I 80
(I/PC) 40
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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.
10
20
20
The slope indicates the rate at which the two
goods can be substituted without changing the
amount of money spent.
10
Food (units per week)
40
60
80 (I/PF)
20
0
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Effects of Changes in Income
Clothing (units per week)
80
60
40
20
Food (units per week)
80
120
160
40
0
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Effects of Changes in Prices
Clothing (units per week)
40
Food (units per week)
80
120
160
40
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Effects of Changes in Prices
Clothing (units per week)
If the two goods decrease in price, but the ratio
of the two prices is unchanged, the slope will
not change. Same as an increase in income
80
Pc 2 Pf 1 I 80
60
If the two goods increase in price, but the ratio
of the two prices is unchanged, the slope will
not change. Same as a decrease in income.
40
L1
L3
20
L2
Pc 1, Pf0.5
Pc 4, Pf 2
80
120
160
40
0
Food (units per week)
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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.

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Consumer Choice
Clothing (units per week)
Pc 2 Pf 1 I 80
40
30
20
40
80
20
0
Food (units per week)
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Consumer Choice
Clothing (units per week)
Point B does not maximize satisfaction because
there exist a point A which is attainable and
yields a higher satisfaction.
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Note that the MRS -(-10/10) 1 is greater than
the price ratio (1/2).
30
-10C
A
20
10F
40
80
20
0
Food (units per week)
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Consumer Choice

• Recall, the slope of an indifference curve is

Further, the slope of the budget line is
Therefore, it can be said that satisfaction is
maximized where
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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.

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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
P
A
R
Police Expenditures ()
O
S
Q
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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
A
R
O
Q
S
Police ()
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Choosing between a non-matching and matching
grant to fund police expenditures
Matching vs. Non-Matching Grant
Private Expenditures ()

• Nonmatching Grant
• Point B
• OU Private expenditure
• OZ Police expenditure
• Matching Grant
• Point C
• OW Private expenditure
• OX Police expenditure

T
P
B
U
W
A
C
Note that the amount of grant at point B and C
are the same.
U2
X
O
Q
R
Z
Police ()
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Example A College Trust Fund

• Suppose Jane Does 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.

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A College Trust Fund
A College Trust Fund
Other Consumption ()
Education ()
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End