1 Introductory Microeconomics Indifference Curves

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Introductory Microeconomics

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

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

Market Basket

Units of Food

Units of Clothing

E is preferred to

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

…

Much easier to see in a graph.

Observations based on more good is preferred to less

G A H

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Preferences over market basketEasier to see in a graph

The consumer prefersA to all combinationsin the blue box, whileall those in the pinkbox are preferred to A.

Food(units per week)

10

20

30

40

10 20 30 40

Clothing(units per week)

50

G

A

EH

B

D

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Preferences over market basket Easier to see in a graph

U1

For example: Combination B,A, & Dyield the same satisfaction•E is preferred to U1

•U1 is preferred to H & G


10

20

30

40

10 20 30 40


50

G

D

A

EH

B

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Preferences over market basket

U1


10

20

30

40

10 20 30 40

Clothing(units

per week)

50

G

D

A

EH

B

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.

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.

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Indifference map

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.

U2

U3


Clothing(units

per week)

U1

AB

D

Market basket Ais preferred to B.Market basket B ispreferred to D.

Market basket Ais preferred to B.Market basket B ispreferred to D.

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Indifference Curves Cannot Cross

U1U2



A

D

B

If crossedthe 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.

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

A

B

D

EG-1

-6

1

1

-4

-21

1

Observation: The amountof clothing given up for a unit of food decreasesfrom 6 to 1


Clothing(units

per week)

2 3 4 51

2

4

6

8

10

12

14

16

Question: Does thisrelation hold for givingup food to get clothing?

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Marginal Rate of Substitution


Clothing(units

per week)

2 3 4 51

2

4

6

8

10

12

14

16 A

B

D

EG

-6

1

1

11

-4

-2-1

MRS = 6

MRS = 2

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

MRS = - C / F

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Assumption: Diminishing Marginal Rate of Substitution


Clothing(units

per week)

2 3 4 51

2

4

6

8

10

12

14

16 A

B

D

EG

-6

1

1

11

-4

-2-1

MRS = 6

MRS = 2

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

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.

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Perfect Substitutes

Orange Juice(glasses)

Apple Juice

(glasses)

2 3 41

1

2

3

4

0

PerfectSubstitutes

PerfectSubstitutes

Two goods are perfect substitutes when the marginal rate of substitution of one good for the other is constant.

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Perfect Complements

Two goods are perfect complements when the indifference curves for the goods are shaped as right angles.

Right Shoes

LeftShoes

2 3 41

1

2

3

4

0

PerfectComplements

PerfectComplements

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BADS

Things for which less is preferred to more Examples

Air pollutionAsbestos

How does the indifference curve over1. Two bads 2. One good and one badlook 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

Food(units per week)10 155

5

10

15

0

Clothing(units

per week)

U1 = 25

U2 = 50 (Preferred to U1)

U3 = 100 (Preferred to U2)A

B

C

Assume: U = FCMarket Basket U = FC

C 25 = 2.5(10)A 25 = 5(5)B 25 = 10(2.5)

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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 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.

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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

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

Market Basket Food (F) Clothing (C) Total SpendingPf = ($1) Pc = ($2) PfF + PcC = I

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Budget Constraints

Budget Line F + 2C = $80(I/PC) = 40

Food(units per week)40 60 80 = (I/PF)20

10

20

30

0

A

B

D

E

G

Clothing(units

per week)

Pc = $2 Pf = $1 I = $80

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

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Budget Constraints

Budget Line F + 2C = $80

(I/PC) = 40


10

20

30

0

A

B

D

E

G

Clothing(units

per week)

Pc = $2 Pf = $1 I = $80

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

The horizontal intercept (I/PF), illustrates the maximum amount of F that can be purchased with income I.

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Budget Constraints

Budget Line F + 2C = $80

CF/PP- 2

1- FC/ Slope

10

20

(I/PC) = 40


10

20

30

0

A

B

D

E

G

Clothing(units

per week)

Pc = $2 Pf = $1 I = $80

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.

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

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Effects of Changes in Income


Clothing(units

per week)

80 120 16040

20

40

60

80

0

A increase inincome shiftsthe budget lineoutward

A increase inincome shiftsthe budget lineoutward

(I = $160)(I = $160)L2L2

(I = $80)

L1

L3

(I =$40)

A decrease inincome shiftsthe budget lineinward

A decrease inincome shiftsthe budget lineinward

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Effects of Changes in Prices


Clothing(units

per week)

80 120 16040

40

(PF = 1)

L1

An increase in theprice of food to$2.00 changesthe slope of thebudget line androtates it inward.

L3

(PF = 2)(PF = 1/2)

L2

A decrease in theprice of food to$.50 changesthe slope of thebudget line androtates it outward.

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Effects of Changes in Prices

Food (units per week)

Clothing(units

per week)

80 120 16040

20

40

60

80

0

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

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

Pc = $1, Pf=$0.5Pc = $1, Pf=$0.5L2L2

L1

L3

Pc = $4, Pf =$2

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.

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.

Pc = $2 Pf = $1 I = $80

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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

Budget Line

U3

D Market basket D cannot be attainedgiven the currentbudget constraint.

Pc = $2 Pf = $1 I = $80


Clothing(units per

week)

40 8020

20

30

40

0

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Consumer Choice


Clothing(units per

week)

40 8020

20

30

40

0

U1

B

Budget Line

Pc = $2 Pf = $1 I = $80

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

-10C

+10F

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

A

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Consumer Choice

Recall, the slope of an indifference curve is:

F

CMRS

C

F

P

PSlope Further, the slope of the budget line is:

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

C

F

P

PMRS

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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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Before Grant Budget line: PQA: Preference maximizing market basket Expenditure

OR: PrivateOS: Police

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

V

T

U3

U1

After Grant• Budget line: TV•B: Preference maximizing market basket •Expenditure

•OU: Private•OZ: Police

BU

Z

R

Non-matching GrantNon-matching Grant

P

PoliceExpenditures ($)

PrivateExpenditures ($)

O S Q

A

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


P

R

U2

T

U1

Matching GrantMatching Grant

Police ($)


O QS

R

After Grant•C: Preference maximizing market basketExpenditures

•OW: Private•OX: Police

C

X

W A

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T

U3

U1

Nonmatching Grant•Point B

•OU: Private expenditure•OZ: Police expenditure

Matching Grant•Point C

•OW: Private expenditure•OX: Police expenditure

W

X

Matching vs. Non-Matching GrantMatching vs. Non-Matching Grant

P

Police ($)


O Q

A

U2

C

R

BU

Z

Note that the amount of grant at point B and C are the same.

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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.

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A College Trust Fund

The trust fund shifts the budget line

P

Q Education ($)

OtherConsumption

($)

U2

A College Trust FundA College Trust Fund

A

U1

A: Consumption before the trust fund

C

U3 C: If the trust could be spent on other goodsB

B: Requirement that the trust fund must be spent on education

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1 Introductory Microeconomics Indifference Curves