Spring Indifference Curve Analysis

7/31/2019 Spring Indifference Curve Analysis

1/22

Indifference Curve Analysis

1. Develop indifference curves

2. Develop budget constraint

3. Some basic analysis: a. changes in

prices; b. changes in income;

c. the Engels Curve

4. The Food Stamps Problem


2/22

Indifference curve:

A collection of points for which the

consumer is indifference between

each of them and some referencepoint.

Typically shown in the context of a two

good world on a two-dimensional graph.


3/22

.

A

.

E

.F

.

B

C

.D

OG

Food

Indifference

curve

What sense does the indifference

curve make? A heuristic approach.


4/22

The axiomatic approach to indifference

curves is a search for a minimum setof assumptions regarding consumer

behavior through which to generate

indifference curves.

Standard axioms:

1. More is preferred to lessnonsatiation

2. Completenessall points in a relation

3. TransitivityA B; B C; A C


5/22

Food

Og

U1U2

A

.

B

.C

Why indifference curves

cannot cross (and still obey

the axioms for preferences).

.


6/22

A

B

U1

U1

OG

Food

The axioms imply that indifference

curves must be unbroken, ie

continuous.


7/22

These two sets of indifference curves represent people

who differ in their relative willingness to trade

food for medicine. Which one is hungry? Careful.


8/22

The budget equation:

B = pogOG + pfF

OG = B/pogpf/pogF

Meaning: The budget equation will depict

a curve in OG-Food space that is downward

sloping (note: its derivativepf/pog is

negative).


9/22

OG

FoodB/p f

If budget is B, then the most OGpossible to buy is B/p and similarly

the most Food possible is B/p . The

budget constraint connects these

two intercepts.

o,

f

Budget constraint


10/22

. E

UE

Food

OG

Budgetline

Consumer equilibrium

in indifference curve analysis


11/22

Applying calculus to find an expression

for the slope of the other curve, the

indifference curve:

OG/F = - (U/F) /(U/OG)

or, using an equivalent notation:

OG/F = - MUf/MUog


12/22

. E

UE

Food

OG

Budgetline

Consumer equilibrium

in indifference curve analysis

At an equilibrium, tangency implies thatthe slope of the budget constraint equals

the slope of the indifference curve: Hence,


13/22

Consumer equilibrium requires that

pf/pog = MUf/MUog

or

MUf/pf = MUog /pog

In words: The marginal utility per dollarof expenditure must be equal for each good.


14/22


15/22

.

.

.E3E2

E1

Food

OG

F1 F3

As income increases, Food demandedincreases. This is shown in indifference

curve analysis as successive, new

equilibria.


16/22

Engels Curve

Food

Income

F1 F2 F3

Consider the shape of the Engels

Curve as related to the income

elasticity of demand.


17/22

End of the portion prior to

the Group project on the Food Stamps

Problem.


18/22


19/22

OG

Food

AB

C D0

When the eligible person is given A

worth of Food Stamps, this extends

her budge constraint to ABD.

Food Stamps Problembudget constraint


20/22

OG

Food

AB

C D0


.

.

EE

A case of a Food Stampsrecipient for whom the Stamps

could just as well have been

in cash (rather than in-kind).


21/22

OG

Food

A B

C D0


A case of a Food Stampsrecipient for whom the Stamps

could just as well have been

in cash (rather than in-kind).

.E

UFStamps

Ucash

.

E


22/22

Discussion Questions:

1. Would this analysis make good policy?

2. What do we know about the behavior of

the poor and how do we know this?

3. If we would say that giving cash would

make bad policy, is ones criticism basedon an efficiency argument? An equity

argument? A paternalistic argument?

Documents

Spring Indifference Curve Analysis