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February 4, 2010
1
L
OGISTICS
Read this week
Chapter 2 (static consumptionleisure framework)
Read for next week
Chapter 3 and Chapter 4 (consumptionsavings framework)
The foundation for virtually all of the analytical frameworks the rest
of the semester
Recitations this week
Review consumptionleisure framework
Work through parts of Practice Problem Set 2
Numerical examples of the consumptionleisure theory
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View Full Document C
ONSUMPTION
L
EISURE
M
ODEL
(C
ONTINUED
)
F
EBRUARY 4, 2010
February 4, 2010
3
C
ONSUMER
O
PTIMIZATION
The Graphics of the ConsumptionLeisure Model
Consumer’s decision problem:
maximize utility subject to budget
constraint
–
bring together both
cost
side and
benefit
side
Choose
c
and
l
subject to
Plot budget line
Superimpose indifference map
At the optimal choice
(1
)
168(1
)
Pc
t Wl
t W
leisure
c
slope = (1
t
)
W
/
P
168
optimal choice (
c*,l*
)
( *, *)
)
( *, *)
l
c
u c l
tW
u c l
P
CONSUMPTIONLEISURE
OPTIMALITY CONDITION
 key building block of modern
macro models
MRS (between
consumption
and leisure)
Aftertax real
wage
IMPORTANT:
the
larger is (1
t
)
W
/
P
,
the steeper is the
budget line
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View Full Document February 4, 2010
4
R
EAL
W
AGE
Macro Fundamentals
W
/
P
a key variable for macroeconomic analysis
Unit Analysis (i.e., analyze algebraic units of variables)
Units(
W
) = $/hour of work
Units(
P
) = $/unit of consumption
Units(
W
/
P
) =
Economic decisions depend on
real
wages (
W
/
P
), not nominal
wages (
W)
Measures the purchasing power of (nominal) wage earnings…
…which is presumably what people most care about
$
$
unit of consumption
hour of work
$
hour of work
$
unit of consumption
unit of consumption
hour of work
Will sometimes denote
using
w
(lower
case…)
February 4, 2010
5
C
ONSUMER
O
PTIMIZATION
The Graphics of the ConsumptionLeisure Model
Consumer’s decision problem:
maximize utility subject to budget
constraint
–
bring together both
cost
side and
benefit
side
Choose
c
and
l
subject to
Plot budget line
Superimpose indifference map
At the optimal choice
(1
)
168(1
)
Pc
t Wl
t W
leisure
c
slope = (1
t
)
W
/
P
168
optimal choice (
c*,l*
)
( *, *)
)
( *, *)
l
c
u c l
tW
u c l
P
CONSUMPTIONLEISURE
OPTIMALITY CONDITION
 key building block of modern
macro models
MRS (between
consumption
and leisure)
Aftertax real
wage
Derive consumptionleisure
optimality condition using
Lagrange analysis
IMPORTANT:
the
larger is (1
t
)
W
/
P
,
the steeper is the
budget line
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View Full Document February 4, 2010
6
L
AGRANGE
A
NALYSIS
The Mathematics of the ConsumptionLeisure Model
Apply Lagrange tools to consumptionleisure optimization
Objective function:
u
(
c
,
l
)
Constraint:
g(c,l
) = 168(1
t
)
W
–
Pc
–
(1
t
)
Wl = 0
Step 1:
Construct Lagrange function
Step 2:
Compute firstorder conditions with respect to
c
,
l
,
λ
Step 3:
Solve (with focus on eliminating multiplier)
( , , )
( , )
168(1
)
(1
)
L c l
u c l
t W
Pc
t Wl
**
( , )
)
( , )
l
l
u c l
tW
u c l
P
CONSUMPTIONLEISURE
OPTIMALITY CONDITION
MRS (between
consumption and leisure)
Aftertax real
wage
February 4, 2010
7
M
ICRO
L
EVEL
L
ABOR
S
UPPLY
Labor Supply in the Micro
An experiment:
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This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.
 Spring '11
 chugh

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