# Develop indifference curves

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```					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.
OG
Indifference
.B         curve
D
.
A
.
.E
C            .F

Food
What sense does the indifference
curve make? A heuristic approach.
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—nonsatiation
2. Completeness—all points in a relation
3. Transitivity– A  B; B  C;  A  C
Og

.A
.C
.     U1
B     U2
Food
Why indifference curves
cannot cross (and still obey
the axioms for preferences).
OG
U1

B

A           U1

Food
he
T axioms imply that indifference
curves must be unbroken, ie
continuous.
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).
OG

Budget constraint

Food
B/p f
,
If budget is B then the most OG
possible to buy is B/p o, and similarly
the most Food possible is B/p f . T he
budget constraint connects these
two intercepts.
OG

. E
Budget
UE      line

Food
Consumer equilibrium
in indifference curve analysis
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
OG

. E
Budget
UE      line

Food
Consumer equilibrium
in indifference curve analysis

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.
OG

E
E2 . 3
.
.E1

Food
F1       F3

As income increases, Food demanded
his
increases. T is shown in indifference
curve analysis as successive, new
equilibria.
Income

Engel’s Curve

Food
F1   F2    F3

Consider the shape of the Engels
Curve as related to the income
elasticity of demand.

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 views: 13 posted: 1/15/2012 language: pages: 16