indifference curve

PPA 723: Managerial Economics

Lecture 5:

Indifference Curves

The Maxwell School, Syracuse UniversityProfessor John Yinger

Managerial Economics, Lecture 5: Indifference Curves

Outline

Properties of Consumer Preferences

Indifference Curves


Tastes

Individual tastes (preferences) determine the pleasure people derive from different goods and services

Our objective is to determine how a consumer’s tastes influence its decisions (positive analysis), not to judge tastes (normative).


Standard Assumptions About Consumer Preferences

1. Completeness

2. Transitivity

3. More is better


Assumption 1: Completeness

Consumer can rank any two bundles of goods

Only one of the following is true: The consumer prefers Bundle x to Bundle yprefers Bundle y to Bundle xis indifferent between the two bundles


Assumption 2: Transitivity (Rationality)

A consumer's preference over bundles is consistent:

If a consumer prefers Bundle z to Bundle y and Bundle y to Bundle x

Then that consumer prefers Bundle z to Bundle x


Assumption 3: More is Better

More of a good is better than less of it.

Good: commodity for which more is preferred to less at least at some levels of consumption

Bad: something for which less is preferred to more, such as pollution

Consumers are not satiated.


Figure 4.1a Bundles of Pizzas and Burritos Lisa Might Consume

B, Burritosper semester

(a) Ranking Regions

302515

Z, Pizzas per semester

25

20

15

10

0

da

b

e

c

f

A

B


Figure 4.1b Bundles of Pizzas and Burritos Lisa Might Consume


(b) Indifference Curve

302515


25

20

15

10

0

da

bI

e

c

f


Figure 4.1c Bundles of Pizzas and Burritos Lisa Might Consume


(c) Preference Map

302515


25

20

15

10

0

d

I0

I 1

I 2

e

c

f


Indifference Curve Properties

1. Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin.

2. There is an indifference curve through every possible bundle.

3. Indifference curves cannot cross.4. Indifference curves are “thin”.5. Indifference curves slope down.

Two Indifferent Managerial Economics, Lecture 5: Indifference Curves

Figure 4.2a Impossible Indifference Curves


(a) Crossing


I 1

I0a

be


Figure 4.2b Impossible Indifference Curves


(b) Upward Sloping

Z , Pizzas per semester

I

a

b


Willingness to Substitute

Downward-sloping indifference curve consumer is willing to substitute one good for the other.

Marginal rate of substitution (MRS) of burritos (rise) for pizza (run), is slope of indifference curve:

BMRS

Z


B , Burritosper semester


I

B

Z

MRS = B/Z

Marginal Rate of Substitution


MRS Varies Along an Indifference Curve

Indifference curves bow away from the origin (called convex).

Indicates diminishing marginal rate of substitution (MRS).


Figure 4.3a Marginal Rate of Substitution


(a) Indifference CurveConvex to the Origin

5

3

8

1–1

1

12

0

–2

–3

3 4 5 6


a

b

c

d

I


Unlikely Outcome:Concave Indifference Curve

If indifference curve bows toward the origin (concave),

Then (implausibly) the consumer has an increasing MRS.


Figure 4.3b Marginal Rate of Substitution


(b) Implausible Indifference Curvethat is Concave to the Origin

5

7

1

1

2

0

–2

–3

3 4 5 6


a

b

c

I


Figure 4.4a Perfect Substitutes

Coke, Cansper week

1 2 3 4

Pepsi, Cans per week

1

0

2

3

4

I 1 I2 I3 I 4


Figure 4.4b Perfect Complements

Ice cream,Scoops per week

1 2 3

Pie, Slices per week

1

2

3

0

I 1

I 2

I 3

a

d

e c

b


Figure 4.4c Imperfect Substitutes



I


Utility Utility is a number that reflects the relative

rankings of various bundles of goods

If Lisa prefers bundle A to B, then utility from A must be greater than utility from B

A utility function is a: relationship between a utility measure and every

possible bundle of goodsuccinct summary of information in an indifference

curve map


Utility and Marginal Utility

The marginal utility of Z is:

MUZ is the change in utility from a small increase in Z holding B fixed

Z

UMU

Z


U , Utils

U = 20

Utility function, U (10, Z )

Z = 1

10987654321


0

350

250

Utility

230


, MarginalMUZ utility of pizza

MUZ

10987654321


0

130

Marginal Utility

20


Economic analysis often depends on the distinction between a total, a average, and a margin.

In the case of utility U = total utility U/Z = average utility of Z MUZ = marginal utility of Z

Totals, Margins, and Averages


Utility and the Marginal Rate of Substitution

Let A = the good on the vertical axis and B = the good on the horizontal axis,

Then (note the inversion):

A

BA

MU

US

BMR

M

I

Give upone unit

of A

B

MRS = A/B = - MUB/MUA

Marginal Rate of Substitution

Quantity of A

Quantity of B

Gain MUA units of utility,which can “buy”

MUA / MUB Units of B

A


0 ( ) ( )

( )A B

A B

U A MU B MU

MU B MU

A

B

MUB

MU

1

/B

A B A

MUAMRS

B MU MU MU

Deriving the Marginal Rate of Substitution

indifference curve

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