Indifference Curve Analysis 1. Develop indifference curves 2. Develop budget constraint 3. Some basic analysis: a. changes in prices; b. changes in income;

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

Indifference curve:

A collection of points for which the consumer is indifference between each of them and some reference point.

Typically shown in the context of a two good world on a two-dimensional graph.

.A

.E

.F

.B

C

.D

O G

Fo o d

Ind iffe re nc e c urve

Wha t se nse d o e s the ind iffe re nc e c urve m a ke ? A he uristic a p p ro a c h.

The axiomatic approach to indifference curves is a search for a minimum set of assumptions regarding consumer behavior through which to generate indifference curves.

Standard axioms:

1. More is preferred to less—nonsatiation2. Completeness—all points in a relation3. Transitivity– A B; B C; A C

Fo o d

O g

U1

U2

A.

B. C

Why ind iffe re nc e c urve s c a nno t c ro ss (a nd still o b e y the a xio m s fo r p re fe re nc e s).

.

A

B

U1

U1

O G

Food

The a xio m s im p ly tha t ind iffe re nc ec urve s m ust b e unb ro ke n, iec o ntinuo us.

These two sets of indifference curves represent people who differ in their relative willingness to trade food for medicine. Which one is hungry? Careful.

The budget equation:

B = pogOG + pfF

OG = B/pog – pf/pogF

Meaning: The budget equation will depict a curve in OG-Food space that is downward sloping (note: its derivative –pf/pog is negative).

O G

Fo o dB/p f

If b ud g e t is B, the n the m o st O G p o ssib le to b uy is B/p a nd sim ila rlythe m o st Fo o d p o ssib le is B/p . Theb ud g e t c o nstra int c o nne c ts the se two inte rc e p ts.

o ,

f

Bud g e t c o nstra int

. E

UE

Food

O G

Bud g et line

C o nsum e r e q uilib riumin ind iffe re nc e c urve a na lysis

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

. E

UE

Food

O G

Bud g et line

C o nsum e r e q uilib riumin ind iffe re nc e c urve a na lysis

At an equilibrium, tangency implies that the slope of the budget constraint equals the slope of the indifference curve: Hence,

Consumer equilibrium requires that

pf/pog = MUf /MUog

or

MUf /pf = MUog /pog

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

..

. E3E2

E1

Fo o d

O G

F1 F3

As inc o m e inc re a se s, Fo o d d e m a nd e dinc re a se s. This is sho wn in ind iffe re nc ec urve a na lysis a s suc c e ssive , ne we q uilib ria .

Eng e l’s C urve

Fo o d

Inc o m e

F1 F 2F 3

C o nsid e r the sha p e o f the Eng e lsC urve a s re la te d to the inc o m ee la stic ity o f d e m a nd .

End of the portion prior to

the Group project on the Food Stamps

Problem.

O G

Fo o d

AB

C D0

Whe n the e lig ib le p e rso n is g ive n ABwo rth o f Fo o d Sta m p s, this e xte nd she r b ud g e c o nstra int to ABD.

Fo o d Sta m p s Pro b le m b ud g e t c o nstra int

O G

Fo o d

AB

C D0

Fo o d Sta m p s Pro b le m b ud g e t c o nstra int

..

EE’

A c a se o f a Fo o d Sta m p sre c ip ie nt fo r who m the Sta m p sc o uld just a s we ll ha ve b e e n in c a sh (ra the r tha n “in-kind ”).

O G

Fo o d

A B

C D0

Fo o d Sta m p s Pro b le m b ud g e t c o nstra int

A c a se o f a Fo o d Sta m p sre c ip ie nt fo r who m the Sta m p sc o uld just a s we ll ha ve b e e n in c a sh (ra the r tha n “in-kind ”).

.E

UFSta m p s

U c a sh

.E’’

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 one’s criticism based on an efficiency argument? An equity argument? A paternalistic argument?