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

commodities.

is a collection of one or more  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 E A

30 20 10

G D

10 20 30 The consumer prefers A to all combinations in the blue box, while all those in the pink box are preferred to A. 40 Food (units per week) 7

Preferences over market basket

Easier to see in a graph Clothing (units per week) 50

B

For example: Combination B,A, & D yield the same satisfaction

•

E is preferred to U

1

•

U 1

is preferred to H & G 40

H E A

30 20

G D U 1

10 10 20 30 40 Food (units per week) 8

Clothing (units per week) 50 40 30

Preferences over market basket

H 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.

A E

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.

20

G D U 1

10 10 20 30 40 Food (units per week) 9

Clothing (units per week)

Indifference map

D B



An indifference map indifference curves that describes a person ’ is a set of s preferences for all combinations of two commodities.



Each indifference curve in the map shows the market baskets among which the person is indifferent.

A U 3 U 2

Market basket A is preferred to B. Market basket B is preferred to D.

U 1

Food (units per week) 10

Indifference Curves Cannot Cross

Clothing (units per week)

U 2 U 1

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) 11

The amount of clothing given up for unit of food decreases with amount of food

Clothing (units per week) 16 14 12 10 8 6 4 2 -6

A

Observation: The amount of clothing given up for a unit of food decreases from 6 to 1 1 -4

B D

1 -2 1 -1

E

1

G

Question : Does this relation hold for giving up food to get clothing?

1 2 3 4 5 Food (units per week) 12

Marginal Rate of Substitution

Clothing (units per week) 16 14 12 10 8 6 4 2 -6 1

A

1 -4 2

B

MRS = 6 The marginal rate of substitution (MRS) quantifies the amount of one good a consumer will give up to obtain more of another good MRS is measured by the slope of the indifference curve 1 -2

D

1 -1 MRS = 2

E G

1

MRS = -



C /



F

3 4 5 Food (units per week) 13

Assumption: Diminishing Marginal Rate of Substitution

Clothing 16 (units per week) 14 12 10 8 6 4 2 -6 1

A

1 -4 2 MRS = 6

B

1 -2 3

D

1 -1 4 Along an indifference curve there is a

diminishing marginal rate of substitution.

Example: the MRS for AB was 6, while that for DE was 2 MRS = 2

E G

1 5 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. That is, consumers prefer a balanced market basket.

Food (units per week) 14

Perfect Substitutes

Apple Juice (glasses) 4 Perfect Substitutes 3 2 Two goods are perfect substitutes when the marginal rate of substitution of one good for the other is constant.

1 0 1 2 3 4 Orange Juice (glasses) 15

Left Shoes 4

Perfect Complements

3 2 1 0 1 2 3 Perfect Complements 4 Two goods are perfect complements when the indifference curves for the goods are shaped as right angles .

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 ) 15 10

C

Assume: U = FC

Market Basket U = FC C 25 = 2.5(10) A 25 = 5(5) B 25 = 10(2.5)

5 0 5

A B

10 15

U 3

= 100 (Preferred to U

2

)

U 2

= 50 (Preferred to U

1

)

U 1

= 25 Food (units per week) 19

Ordinal Versus Cardinal Utility

  Ordinal Utility Function: preferred to another.

places market baskets in the order of most preferred to least preferred, but it does not indicate how much one market basket is Cardinal Utility Function: to another.

utility function describing the extent to which one market basket is preferred  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 various goods and services.

’ s ability to consume in light of the prices they must pay for The budget line commodities for which total money spent equals total income.

indicates all combinations of two

21

The Budget Line

   Let F equal the amount of food purchased, and C is the amount of clothing.

Price of food = P f Then and P c P f C F and price of clothing = P c is the amount of money spent on food, is the amount of money spent on clothing.

P

f

F + P

c

C = I

22

Budget Constraints

Market Basket Food (F) Clothing (C) Total Spending

P f

= ($1)

P c

= ($2)

P f F + P c C = 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/P

C

) = 40

A Pc = $2 P f = $1 I = $80

Budget Line F + 2C = $80

B

30 20

D

As consumption moves along a budget line from the intercept, the consumer spends less on one item and more on the other.

E

10 0 20 40 60

G

80 = (I/P

F

) Food (units per week) 24

Budget Constraints

Clothing (units per week ) (I/P

C

) = 40

A

The vertical intercept (I/PC), illustrates the maximum amount of C that can be purchased with income I.

Pc = $2 P f = $1 I = $80 B

30 Budget Line F + 2C = $80

D

20 10 0 20 40 60

E G

80 = (I/P

F

) 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/P

C

) = 40 30 20 10

A

10

Pc = $2 P f = $1 I = $80

Budget Line F + 2C = $80

Slope   C/  F  1 2  P F /P C

B 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

E

The slope indicates the rate at which the two goods can be substituted without changing the amount of money spent.

0 20 40 60

G

80 = (I/P

F

) Food (units per week) 26

Effects of Changes in Income

Clothing (units per week) 80 A increase in income shifts the budget line outward 60 40 A decrease in income shifts the budget line inward 20

L 3

0 (I =$40)

L 1

(I = $80) 40 80 120

L 2

160 (I = $160) Food (units per week) 27

Effects of Changes in Prices

Clothing (units per week) (P

F

= 2) 40

L 3

40 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.

L 1

(P

F

= 1) 80 120

L 2

(P

F

= 1/2) 160 Food (units per week) 28

Effects of Changes in Prices

Clothing (units per week) 80

Pc = $2 P f = $1 I = $80

60 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 40 20 0

L 3 L 1

40

P c = $4, P f =$2

80 120 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.

L 2 P c = $1, P f =$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) 40

Pc = $2 P f = $1 I = $80

30

D

Market basket D cannot be attained given the current budget constraint.

20 0 20 40

U 3

Budget Line 80 Food (units per week) 31

Consumer Choice

Clothing (units per week) 40 -10C 30

Pc = $2 P f = $1 I = $80 B

Point B does not maximize satisfaction because there exist a point A which is attainable and yields a higher satisfaction .

Note that the MRS -(-10/10) = 1 is greater than the price ratio (1/2).

A Budget Line 20 0 20 +10F 40

U 1

80 Food (units per week) 32

Consumer Choice

Recall, the slope of an indifference curve is:

MRS

  

C



F

Further, the slope of the budget line is:

Slope

 

P F P C

Therefore, it can be said that satisfaction is maximized where:

MRS



P P C F

33

Example: Matching vs. Non-matching grant from the federal government

    Local official has a taxing its citizens) and private consumption (by its citizens).

preference on police spending (by The budget line resources available for the public spending and private spending.

represents the total amount of 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

Private Expenditures ($)

T P U R O S A Z B

Non-matching Grant Before Grant Budget line: PQ A: Preference maximizing market basket Expenditure OR: Private OS: Police

U 3 Q U 1 V

•

After Grant Budget line: TV

•

B: Preference maximizing market basket

•

Expenditure

•

OU: Private

•

OZ: Police Police Expenditures ($) 35

Choosing between a non-matching and matching grant to fund police expenditures

Private Expenditures ($)

T

Matching Grant

P

Before Grant Budget line: PQ A: Preference maximizing market basket

W R A C U 2 U 1

After Grant

•

C: Preference maximizing market basket Expenditures

•

OW: Private

•

OX: Police

O S X Q R

Police ($) 36

Choosing between a non-matching and matching grant to fund police expenditures

Private Expenditures ($)

T P U W

Matching vs. Non-Matching Grant

B A C

Nonmatching Grant

•

Point B

•

OU: Private expenditure

•

OZ: Police expenditure Matching Grant

•

Point C

•

OW: Private expenditure

•

OX: Police expenditure

U 3 U 2 U 1 Note that the amount of grant at point B and C are the same.

O Z X Q 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 ($)

P

A College Trust Fund

A C B

A: Consumption before the trust fund The trust fund shifts the budget line B: Requirement that the trust fund must be spent on education

U 3 U 2

C: If the trust could be spent on other goods

Q U 1

Education ($) 39

End 40