Lecture 4 - Theory of Choice and Individual Demand
David Autor
14.03 Microeconomic Theory and Public Policy, Fall 2005
Agenda
1. Utility maximization
2. Indirect utility function
3. Application: Gift giving — Waldfogel paper
4. Expenditure function
5. Relationship between Expenditure function and Indirect utility function
6. Demand functions
7. Application: Food stamps — Whitmore paper
8. Income and substitution e
ff
ects
9. Normal and inferior goods
10. Compensated and uncompensated demand (Hicksian, Marshallian)
11. Application: Gi
ff
en goods — Jensen and Miller paper
Roadmap:
1

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Axioms of consumer
preference
Primal
Dual
Min p
x
x+ p
y
y
s.t. U(x,y) > U
Indirect Utility function
U*= V(p
x
, p
y
, I)
Expenditure function
E*= E(p
x
, p
y
, U)
Max U(x,y)
s.t. p
x
x+ p
y
y < I
Marshallian demand
X = d
x
(p
x
, p
y
, I) =
(by Roy’s identity)
Hicksian demand
X = h
x
(p
x
, p
y
, U) =
(by Shepard’s lemma)
Slutsky equation
I
V
p
V
x
∂
∂
∂
∂
−
/
/
x
p
E
∂
∂
−
1
Theory of consumer choice
1.1
Utility maximization subject to budget constraint
Ingredients
:
•
Utility function (preferences)
•
Budget constraint
•
Price vector
Consumer’s problem
Maximize utility subject to budget constraint
Characteristics of solution
:
•
Budget exhaustion (non-satiation)
•
For most solutions: psychic trade-o
ff
= monetary payo
ff
2

•
Psychic trade-o
ff
is MRS
•
Monetary trade-o
ff
is the price ratio
From a visual point of view utility maximization corresponds to the following point:
(Note that the slope of the budget set is equal to
−
p
x
p
y
)
B
A
D
C
x
y
IC
1
IC
2
IC
3
What’s wrong with some of these points?
We can see that
A
P
B
,
A
I
D
,
C
P
A
. Why should one choose
A
?
The slope of the indi
ff
erence curves is given by the MRS
1.1.1
Interior and corner solutions [Optional]
There are two types of solution to this problem.
1. Interior solution
2. Corner solution
3

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