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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
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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.
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.
A
.
E
.F
.
B
C
.D
OG
Food
Indifference
curve
What sense does the indifference
curve make? A heuristic approach.
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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
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Food
Og
U1U2
A
.
B
.C
Why indifference curves
cannot cross (and still obey
the axioms for preferences).
.
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A
B
U1
U1
OG
Food
The axioms imply that indifference
curves must be unbroken, ie
continuous.
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These two sets of indifference curves represent people
who differ in their relative willingness to trade
food for medicine. Which one is hungry? Careful.
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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).
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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
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. E
UE
Food
OG
Budgetline
Consumer equilibrium
in indifference curve analysis
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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
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. 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,
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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.
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.
.
.E3E2
E1
Food
OG
F1 F3
As income increases, Food demandedincreases. This is shown in indifference
curve analysis as successive, new
equilibria.
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Engels Curve
Food
Income
F1 F2 F3
Consider the shape of the Engels
Curve as related to the income
elasticity of demand.
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End of the portion prior to
the Group project on the Food Stamps
Problem.
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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
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OG
Food
AB
C D0
Food Stamps Problembudget constraint
.
.
EE
A case of a Food Stampsrecipient for whom the Stamps
could just as well have been
in cash (rather than in-kind).
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OG
Food
A B
C D0
Food Stamps Problembudget constraint
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
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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?