Intermediate Macroeconomics

.
2 kinds of variables
-
exogenous
:
determined outside the model ,
taken as given
-
endogenous : determined inside a model
.
variables : denoted w/ latin Letters
.
timing notation : time is discrete ( t -
l is one variable in the past ,
t is present ,
t ti is
one period in the future )
X
t
t -
I +
t
t + I
t t I
.
parameter : fixed value governing mathematical relationships
)
Basic
Accounting
.
GDP :
current dollar Value of all final goods E services produced within a
country during
a particular period of time
-
measure of production Er a flow concept
-
production =
income =
expenditure
-
income approach :
GDP t
=
wages +
t interest +
t
rent +
t
profitt
-
expenditure approach :
GD Pt =
Consumption et investment t
t
government t
t
net exports t
log GDP
O
✓~
t
Real vs .
Nominal
-
GDP is defined in current dollar prices
. -
instead ,
want a
' '
real
"
measure of GDP
GDP t
= E- i
Pet Yet
in a single good world , something real is denominated in goods
.
solution :
"
constant dollar
"
GDP
rea , app
-
Value quantities of
goods at different points in time using base
year prices
✓ =
R GDP + + h
T E
Pett Y
let thI t th
implicatehffatorG Dpt
E Pet th Teeth
RGD Pt
=
EP et Yett h

( nominal )
Pt th Yt th
=
GDR
C P1 =
Epetth Yet
t th
E Pet Yet
.
inflation :
rate of growth of price index
Variable Notation
.
Y
+ + h
=
Ptth Ytth
Peth
exogenous
→ model →
endogenous

Measurement
.
l nominal ) GD Pt
=
Ei Pet Yet year
t $ current
-
Production = Income =
Expenditures
.
Real GD Pt
=
E I Peb Yet I
Yt year
b $ constant
.pt =
E- I Pet Yet
( ,
Pt Yt
U
implicit, Fop price
§ ,
Plb Y It
I t
.
Cpl +
=
PEP
'
= El Pet X lb =
F- I Peb X lb
Labor Market
Ut
.
Ut =
U ±
t E t
.
Production Function :
Yt =
At FL Kt ,
Nt )
I I
-
he :
avg .
hours per worker ht Et
T T
-
E t
:
# of employed workers intensive extensive
-
Ut :
# of unemployed workers
-
left :
Total # of workers =
Ut t
E .
L
-
Lt :
# of people L population )
.
Ut =
It
left
.
lfpe =
Lt
.
epopt =
Et
Lt

Ch 4 ,
S ,
6 , 7
Growth
.
growth :
growth in real GDP over long time horizons L decades )
-
long run :
frequencies of time measured in decades
*
US Real GDP per capita
In It On avg .
,
I .
8% growth per year
t
.
Rule of 70
.
Key Question : What accounts for this growth ?
-
production function :
Ye .
-
At F ( Kt ,
N t )
-
in a mechanical sense , can only be 2 things :
-
factor accumulation :
more inputs
-
productivity growth :
more output given the same inputs
.
It =
At
Fluke
' .
Nt )
Nw!
=
At FL
' ⇐
Int ,
I )
.
In = In
At t
Lyke
t '
Nt )
NN!
= In At F (
Kt
Int ,
I ) → In At t In FL Kt I Nt ,
1) t In N t ht
.
Stylized Facts
-
output per worker
grows at approx .
constant rate over time
-
capital per worker grows at approx . constant rate over time
'
¥ : a In ( III ) =
constant
2
¥ :
I 1h
(¥1 ) =
constantI In Yt -
I In E z
I
constant3
÷ :
k¥ 2
Constant23
4
WYN a
constant 4th We
= -
a In 7¥
=
Ll In
Ye E e
+
labor Share ↳ Et Ne
S R :
R t
I constant 6 I In wt I constant
return on capital
Rt Kt
I =
I -
¥
Yt
- in
0.33 O .
66

-
Stylized Facts :
Cross -
Section
-
there are
large differences in income per person across countries
-
there are
large differences in income growth per person across countries
-
Strong correlation btw
being rich E having a
highly educated population
-
quality adjusted hours are higher → increases factors of production
-
rich countries can afford more education

So low Model
So low Model
-
main implication :
productivity is
key
-
productivity is only means for sustained growth L not factor accumulation )
-
productivity key to
understanding cross -
country income differences L not level
of capital )
downside of model :
takes productivity to be
exogenous
ModelBasics
.
time runs from t to infinity
.
representative household E firm
.
only I
good
Representative Firm
Yt =
At FCK t ,
Nt I
I F ( O ,
N ) =
FCK ,
O ) =
O
2
Fn =
En 70 ,
Fic 70
3
Finn
=
LO ,
Fick CO
↳
diminishing marginal product
4 F ( JK ,
8 N ) =
8 F Lk ,
N )
↳
homogeneous of degree I in K E N
↳ constant returns
FCK ,
N ) = Fk K t
Fn N
w w
Rt W t
Production Function : Yt =
At FCK t ,
N t )
Kt :
capital
N t
:
hours of work
At :
productivity
Representative Firm
.
Max
Kt , Nt 10 At F ( K t .
N t
) -
R t
K t
-
Wt N t
'
Kt :
A t Fk ( Kt ,
N t I
-
Rt =
O
A t Fk ( K t ,
N t ) =
Rt
.
Nt :
At FN L Kt ,
N t
) =
w t
.
has production function ,
hires labor and rents capital
.
MC =
MR

F ( Kt ,
Nt ) =
Ktt Nt
' -
a
FN =
L I -
x ) ke
-
NEX 30
Fic
=
x Kt
' -
I
Nt
'
-470
Fun =L -
x ) ( I -
a) KENI
- -
'
LO
Fick =
a ( x -
I ) Kt
' -
Z
Net
- a
LO
FL 8kt , 8 Nt ) = ( 8kt )
-
L 8 Nt )
' -
a
= 8*+1
-
^
KENT
' -
d
=
JFL Ke , Nt )
Kt :
Af
(Kent )
" '
=
Rt
Nt :
At Ll -
x ) ( It =
We
Household :
I
Yt =
At FL Kt .
Nt )
3
It =
S Yt OES El investment
4
Ct =
( I -
S ) Yt Consumption
C t
t
It
=
Yt
' '
resource constraint
' '
Nt =
N
Z
Ktt ,
=
It
t
( I -
8) Kt OE SEI
-
-
capital in depreciation
next period rate
5
Wt =
At FN ( Kt ,
Nt )
6
Rt =
At Fk ( Kt ,
Nt )
Ktt I
=
Sit t
( I -
8) Kt
Kt + I
=
s AtFL Kt ,
Nt ) t
Ll -
8) Kt
Kt =
# capital per worker
Nt
f ( k ) I FLIN ,
1) =
Fl kN )
N
w
k
Kt +1=5 At F L Kt ,
Nt ) t
Ll -
8) Kt
Nt Nt Nt
ktt ,
=
SA tf ( Kt ) t
LI -
8) Kt
- -
investment depreciation
per worker per worker

kttl
SA tf ( Kt ) t
LI -
8) Kt
""
ktt ,
=
Kt =k*
"
steady state
"
↳
capital stock will
converge to this point
450 )
I*
Kt
Iim
kso f
'
( k )=cs inada conditions
Iim
k→cs f
'
Lk )=O
Llktt , =sAfLkt ) -
8kt → when 4kt +1=0 ,
then SAFLK ) =
Sk
investment depreciation
invests 8k depreciation
depree .
SAFCK ) investment
- I
k* k
I Yt AFL Kt ,
Nt )
Nt Nt
Yt
=
Af L Kt )
2 ktt ,
=
it t
( I -
8) Kt
3 It SAF L Kt , Nt )
Nt Nt
it =
SAFLKT )
4
Ct
=
( I -
5) A f ( Kt )
5
Wt=AfLkt
) -
Af't
Kt ) Kt
6 Rt =
Af 'Lkt)

Cobb -
Douglas F=K
-
N
' - a
f=kYt=AtkE
kttI=SAtkEt( I -
8) Kt
k*=SAtk*
a
t
( I -
8) k*
8k*=SAtk*k*=(sgAt
)
y*= Akka
C
*
=
( I -
S )Ak*a
[
*
=sAk*×
R*=qAk*k
-
I )
W*=( I -
a) Ak*d
Change in A* ( constant Value of At )
kttl ktt ,
= Kt
-
.
SA 'kFtLl -
f) let
-
' ' '
SAKE t ( I -
8) Kt
F450 )
I l
k* k**
Kt
Increase in
Productivity
kt+,=sAflktlt( I -
81kt Att Ao
→
A ,
ktti Kt y
yt=AtfLkt )
KY - y ,* -
-- -
- * *
ko •
Yo
I I I I l
IKEk ,* Kt
tttlttztime t time
same for consumption's
investment

Real wage :
Wt
=
At FN ( Kt ,
Nt )
w We
=
Atf ( Kt ) -
Atf
'
L Kt ) Kt
R
Rt =
Atf
'
( Kt )
- •
WE Rot
I I
t
time t
time
Increase in
savings
k
t so
→
s ,
SoCs ,
y i
ttl
*
i.
* -
y ,
-
- -
A yo
*
• i o*
I l I I l
IKEk ,* Kt t ttlttz time t time
C W R
a
W ,
*
-
c.
*
-
(
Rot •

-
*
Co Wo* • RF -
I l I l I
t time t ttittz time t
time
Remarks :
.
neither
changes in A 't
Or changes in s →
sustained increases in
growth
.
Sustained growth must come from increases in productivity
-
no upper limit on A
'
key assm :
diminishing returns to capital
Golden Rule
.
optimal s ?
.
higher s
.
more capital →
more output → more consumption
.
consume a smaller fraction of output → less consumption

Max consumption : A
*
f
'
Lk *
) = 8
8k =
s A f Ck )
#
A f Ck )
c
8k
V

Augmented Solow Model
Yt-Atflkt.Z.int
)
Z :
labor augmenting technological progress a
"
productivity
"
ktti
ZN :
efficiency units of labor n
Zt=( ltz )t ( Zo
-
I )
ktti
Nt =
( I the )t
-I =z!pty,
per efficiency unit variables
It + ,
=
SAF l It )t( I -
8) It
,
( It E) ( t.in ) n* n
k Kt
Itt ,
-
It =I*
kttl
=
( It Z )
Kt
Ktti= It t
( I -
81kt
It -_
Sit
Ct '
( I -
SI Yt
^
n
ktti Itt ,
-_
ke
Htt , =sAF( Kt ,ZtNt ) +
( I -
8) Kt
sttflktltll
-
Slice
Itt ,
= It -
( Ith )(
Itz
)
ZtNt Zt Nt ZLNT
Zttl Ntt i
Kttl
It Nt
- -
=SAF( LINE ,
1) t
( I -
8) It
-
Zttl Nttl
( ltzkltnlktt ,
-_
SAFL It )t u -
8) It
( ltzlllth
)Itti=SAf(It )t t I -
8) It
( ltz )( Ith ) ( It ZI ( Itn )
I
^
E*=It Kt
Ett , =It=k* ( Ith )( It -2
)E*=sAfLI*
) t Ll -
8) kn*
Kttl Kt I L Ith )( ltz ) -
LI -
8) ]k*=sAfLE* )
ZttINtti=ZtNt
tlthtztnz
-
1+8
]k*=sAf(I*
)
Kttl
=
ZttINtt , [
htzthzt
8
]k*=sAfLE*)
Kt Zt Nt Int
-2+8=5
'AfLkn* )
=
( ltz )( Ith )
ht
-2+8 ( NZ )
kttl
=
( Itz ) SAfLk* )
Kt
-
¥

^yt=AfLkt )
it =sy^t
[ t
-
-
( I -
stye
Itt , =y^t=y*
Yeti YE
ZttiNtti= Zent
Yttl
=/ + z
kttl
=
It Z
Yt Kt
n n
kttl =
Kt
n
y^ttI Yt
Kttl Kt
Zttl Nttl Zt Nt Kttl
=
Kt
= →
Yttl Yt Yttl Yt
Zttl Nttl Ze Nt
Max
K ,N AFCK ,2tN ) -
Wt N -
Rtk
AFklkt.2-Ntt-R-LAFnlkt.INT/2t=WtF(K.2N)=2NfLk
)
Fk ( K ,ZN)=ZNf' ( I ) .
In =
fi ( E )
FN ( K ,
-2N )2=2fCI)tZNf'( I )
-
¥Nk=2f( E ) -
fi ( I )
.
=
ZALE ) -
fi (E) I )
Rt =
Af
.
( It )
Wt=AzLf( It) -
f
'
(Et )Et )
Rtt , =Rt=R*
Wtt ,
=
( I +
2) Wt
E labor share
Wt Nt
=
(1+12)
Wt Nth
Ye Yeti

^
kttl
SAH It t LI -
8) I
AI l
n
^*n
n*k .
=
Kt k ,
kickmy
ny=AfLI ) MW
ki -
yay -
✓
- •
.:*
T• Ogi o
I
t
t t
Ink
my R
( return /to z
• •
✓•
12
t t t
Yt -
AF ( Kt ,ZtNt )
^yt=Af( It ) output per efficiency unit
yt=2tyt
'
-
Ztttflkt ) output per capita

Understanding cross-country Income Differences
.
3 hypotheses
.
countries initially endowed with different levels of capital
.
countries have different savings rates
.
countries have different productivity levels
.
most plausible :
differences in
productivity
Convergence
.
2 countries w/ same
steady state
.
country 2 has less capital
k
9
92
- k ,
=k*
#
'
z €O
k
z
.
condition
convergence is somewhat likely
s
Differences in s and A
*
.
most countries have different steady States
y:: t :: Is: E
.
I :
US ,
2 :
Mexico
*
- 4-1 = 4 Sz = 4 S
,
yz*
If x =
'
13 →
Sz Would have to be 0.0625 times s ,
.
probably not due to
savings
.
rich countries are highly productive
Productivity
.
drives Solow
.
sustained growth cause
.
causeslarge income differences
.
residual in Solow model

Factors Influencing Productivity
'
knowledge E education
.
climate
.
geography
.
institutions
'
finance
.
degree of openness
.
infrastructure
Policy Implications
.
promote productivity

Consumption
GLS Ch . 9
Microeconomics of Macro
.
now move from
long run to medium G short run
.
in long run ,
didn't model decision -
making
.
decision rules of
optimizing agents G equilibrium
.
only 2 periods C t G t t I l
.
representative agents :
one household E one firm
.
unrealistic ,
but helpful
Consumption
.
largest expenditure category in GDP
.
study representative household
.
household receives
exogenous amounts of income
.
must decide how to divide income
.
everything real
Basics
.
income :
Yt E Yet ,
exogenous
.
consume :
Ct E Ctt I
.
St =
Ye -
Ct can be negative
.
earns I
pays real interest rate rt
Budget Constraints
C t
t
St E Yt
( t + ,
t
Sit ,
-
St I Yt + I
+
rt St
.
St is savings stock
.
Stt ,
-
St is
saving flow
.
rt St
:
income earned on stock of savings brought into ttl
.
household wouldn't want Seti 70 b/c no t t 2
.
household would like Seti SO die in debt
-
Stt I
=
O ( no Ponzi )
.
Assume budget constraints hold with
equality E eliminate St , leaving
:
C t
t
fit't
=
Yt t
YI're I BC

Ctt ,
=
Yt t it ( It rt ) St
St =
C ttl
-
Yeti
I t
rt
C t
t
St =
Yt
( t
+
Cttl -
Ttt I
= y
I t
rt
t
C t
t = Yet YI're
Preferences
.
U L C t )
.
U' L Ct ) 70 monotonicity
.
U'
'
Let KO
diminishing marginal utility
4 U
'
- L
Ct Ct
.
Ex utility equation
:
U ( Ctl =
In Ct
U
'
( Ct ) = It
U
"
( Ctl =
-
LIZ
Lifetime Utility
U =
U ( Ct ) t
BU ( Ctn )
where Bsl discount factor
.
patient
:
BY
.
impatient :B NO
B=¥e e is discount rate
Max
Ct .
Ceti U ( C t ) t
BU ( Ctt , )
S .
t . Ct
t
Ceti ( It re )
-
'
=
Yt t
Yi ( It rt )
-
'
Ctt ,
=
Ht
t
Ytt ,
( It rt )
-
'
-
Ceti ) ( It rt )
Ctt ,
=
( ( Yt -
Ct ) ( It rt ) t
Yet ,
)
MEI U ( Cet ) t
BU ( ( Ytctkltrt) t
Yeti )

U' L Ct ) t BU
'
( Ctt ,
)( -
It ( ltrt ) =
O
U' L Ctl =
Blltrtlu
'
I
Cttiteuler
Equation
.
EX :
U=lnCtt Blncttl
U' ( Ctl =
B ( It Rtl U' ( C ttl )
Et =
Blithe ,
Ceti
=
Blltrt )
C t
C ttl
=
It rt
C t I t
P
lnctti-lnct-lhlltrtl.tn ( Ite )
Tre -
e
n
Cttl
slope -_
-
U' ( Ct )
Slope Be
:
-
Litre )
Htrtlytt
BU
'
( C ttt )
Yttl
" "
:÷÷¥.
III:O.
www..io#cutiiins,
Yo-
B U' l Ctt i
)dCtH=U'
( Ct )dCt same onindiff .
Yt Yet
Ct
dctil=
-
U' C Ct ) -
MRS Curve
dct BU
'
( Ctti )
marginal rate of substitution
MRS
=MUe
MUTTI
u
'
( C t )
Cttl ^ Cttl ^
Ctt ,
a
It ft =
If borrower ,
RT is bad
BU
'
( Ctti )
If saver ,
rt is good
Consumption Function n
Ce
=
cut .
Yet , .
rt ) it .
-
•.e'
I:# ¥ ,
-
.
+ t -
-
( Itr , ) f
-
( ltro )
# I I
) I ) I >
Smooth
¥141
YEYt
'
Ct Ye Ct
Yeo Ct
Substitution us .
Income Effect

( t t I Cttl
borrower saver
%
it
.
I
•
µ
c " t " -
•[Co ,
ttl
-
• Co , ttl
-
•
Yo
,
ttt
-
•
-
( Itr , , t )
-
lltro ,
t )
(
-
l Ith 't )
(
-
Citro ,
t )
I I Ige
' '
I I I
Yo ,
t Cut Co . t
Ct G. t Co ,
t Yo ,
t Ct
Consumption Function
C t
=
Cd ( Yt ,
Yeti ,
rt )
+ t -
↳ assuming certain preferences
actually ambiguous
U =
In Ct t
Bln Ct
⇐tot
=
Yt t → Ceti =
( Yt
-
Ct ) l It rt ) tutti
( t t I
Ct
=
BC It rt )
( Yt -
Ct ) L It rt ) tutti =
B ( It rt ) Ct
( Yt -
Ct ) t
t= Bct
Yet Ft =
Ct ( I +
B )
C t
.
-
( Yet Yt I ( It 135
'
dct
=
Tis dYtt¥¥ d Yeti
÷t=¥
"
marginal propensity to consume
"
L MPC ) , always positive
If given a dollar ,
how much would be spent today ?
It =
-1-1 always positive
Htt I It rt It B
ft =
¥3Fitz always negative
substitution effect dominates income effect
Permanent Income Hypothesis
.
permanent income :
present value of lifetime income
1. Consumption forward -
looking .
Consumption Should not react to
changes in income
that were predictable in the past
2. MPC Cl
3. Longer you live ,
the lower the MPC

* Make sure to know :
I . wealth L GLS Ch .
9.4 .
I )
2. permanent VS .
transitory changes in income ( GLS Ch .
9.4 .
2)
Consumption Under
Uncertainty
.
future income is uncertain
'
two possible values : Y It i
I Y
'
Eti.
E ( Yt , ,
) =p Y Eti t
Ll -
p ) Y
'
Eti
Ct t
St =
Yt
C I .
, ,
=
Y tht,
t
St l I t
rt )
C
IF
Y It,
t
St l I t
rt )
ETUI =
U L Ct ) t
BE tu L Ctn ) ] expected utility
IF U L Ctl t
B I p u ( C tht,
) t
l I -
p ) U (
Ctu
) )
Msf
×
U L Ye
-
St ) t
B L p U ( Y tht,
t
St L I tr ) ) t
LI -
p ) u ( Y It ,
t
St L I t
rt ) ) )
-
U
'
( Yt -
S t ) t
B p U
'
( C htt,
) ( I t
rt ) t
B ( I -
p ) U
'
( Chet ,
) ( I t
rt ) =
O
U
'
C Ct I =
B Ll t rt ) Et U
'tCe t I ) I Euler equation
÷ =
B ( It rt ) Ip ÷ ,
t
( I -
p )
÷ ,
] l when log utility )
.
If U
' "
70 ,
then increased uncertainty over future income results in decreased Ct
Random Walk Hypothesis
.
uncertain future income ,
U
' ' '
= O
,
B l It rt ) =
I
.
Euler Equation :
Et Ctt D= Ct
.
consumption expected to be constant
.
Consumption Should not react to changes in Ytt I which were predictable
↳ retirement ,
social
security
↳
generally fails
-
potential evidence of liquidity constraints

Equilibrium ( Ch 11 )
'
3 modes of economic analysis
:
I .
Decision Theory
2. Partial Equilibrium
3 .
General Equilibrium
.
competitive equilibrium : set of prices and allocations where all agents are
acting according to
their optimal decision rules ,
taking prices as given . and all markets
simultaneously clear
Comp .
Equilibrium in Endowment Economy
.
no
endogenous production
.
Optimal decision rule :
consumption function
.
market :
market for saving ,
St
.
price
:
rt
.
market -
clearing
:
Ye =
Ct
.
allocations : Ct Er Ct ti
↳
no saving ,
consume at endowment point
.
L total agents w/ identical preferences
.
index households by j
.
each household can borrow I save at same real interest rate , rt
.
optimal decision rule :
Ct L j I = Cd ( Yt L j ) ,
Yt ti l j ) , rt )
.
Aggregate saving
= O :
St =
,
St Cj , = O One
agent 'S
saving must be another 's
borrowing
,
( Yt Lj I -
Ct l jl ) =
O →
,
Yt Lj ) =
,
Ct Lj )
.
Suppose all
agents have same endowment levels
.
normalize total number of agents to L =
I
↳
average equals aggregate
↳ Ct =
Cd ( Yt ,
Y t ti . rt )
↳ Yt =
Ct
.
Total desired expenditure
:
YI =
Cd L Yt .
Yt ti ,
rt )
.
Assume Cd ( O ,
Yt t I ,
r ) > O
.
Since MPC s I , one point where income equals expenditure

yat
Yea =
Yt
YET =
Cd ( Yt ,
Yeti ,
r
, t
)
✓ d
-
I i. t
YET =
Cd ( Yt ,
Yeti ,
to , t
)
✓ d YET =
Cd ( Yt ,
Yeti ,
rz, t
)
to , t
-
f
household optimization✓ d
-
'
zit
IS curve is
every combo of every rt E income
, i , u
given that level of income today ,
want to
U u
I t
I
zit Yo ,
t hit consume all income
todayr
K ,
t
-
to ,
t
-
.
ri ,
t
-
1
IS
I U
I t
rt
Ys Curve
Ys
yat
Yea =
Yt
YET =
Cd ( Yt ,
Ytti ,
ro , t
)
v
Yt
✓ d
to ,
t I 0 , t
-
I ✓
It
Yo ,
t
rt
YS
r -
O ,
t
IS
U YEI
0 .
t

ya
supply shock TYT
t
Yea =
Yt
YET =
Cd ( Yt ,
Ytti ,
ri
, t
)
YET =
Cd ( Yt ,
Ytti ,
ro , t
)
Yo,dt -
T
Yt
rt
✓ U I
r -
O ,
t
r , ,
t -
IS
I
v
U U I t
I
O .
t
I
I
,
t
ya
demand Shock TY th
t
Yea =
Yt
YET =
Cd ( Yt ,
Yi,
ttl ,
to , t
)
YET =
Cd ( Yt ,
Ytti ,
ro , t
)
Yo,dt -
Tt
* =
Cdc
I ✓
It
Yo ,
t
rt
YS
•
y
to ,
t
-
→
IS IS
'
U YtI
0 .
t

.
market clearing
:
Ct =
Yt
.
corresponds to a single rt
↳ measure of how plentiful the future is expected to be relative to the present
-
if rt T ,
then expect Yt ti
T
-
if rt I ,
then expect Yeti I
-
if uncertainty increases , rtt
Example with
Log Utility
:
I t
rt =
I Yt t I
B Yt
rt proportional to expected income growth
I
Agents w/ Diff .
Endowments
.
L , of
agent I .
Lz Of agent 2
.
identical preferences Uj =
In Ct Cj I t
Blog Ct ti C j )
.
Yt L I I =
I , Yt L 21=0
Ct L j I t =
Ye L j ) t
¥4 )
.
Yeti ( 17=0 ,
Yet , (2) =
I
I t
rt
Ct (1) =
-1
Ct Lj I =
[ Ytlj It
II t
B
C t (2) .
-
1-
1-
Yt =
Ct ⇐
§ St ( j 1=0
I t
B I t
rt
Yt =L ,
Yt L I ) t
Lz Yt L 2) =L ,
Ll ) t
Lz I O ) =L ,
Ct =
⇒ t
-4-1
I t
B I t
rt
L .
= t
¥
B ( It rt I =
¥ Howe
Yt + I
=
Lz
B ( It rt ) =
YEI
'
1- =
B LI t
rt )
-1Euler Eqn
Ct Lj ) Ct ti Lj )
C t ti l I )
=
B ( It rt ) =
Ct L j ) Ct
I t
rt =
-1€B L .
.
rt does not depend on distribution across
agents

Equilibrium with Production and Endogenous Labor
Supply C Ch 121
Production Er Labor supply
-
endogenous production . investment ,
E labor
supply
Firm
Yt =
At FL Kt ,
Nt I
.
At is
exogenous
.
Zt
=
I
1. both inputs needed
2. Fk > O Fu > O If increase K or N ,
increase Ye
3 .
Fkk SO Fun CO ↳ falls over time I
diminishing marginal returns I
4. T FCK ,
N ) =
FLY K ,
TN ) constant returns to scale
Capital Accumulation
.
firm makes investment decision l in Solow ,
households make decision )
.
borrow from bank at rate rt
.
current capital Kt is
exogenous
da accumulates according to :
Htt ,
=
I
t
t
( I -
8) Kt same as in Solow
Firm Profit Maximization 2 choices :
how much labor .
investment
.
firm hires labor Nt and Ntt , at
wages Wt and Wt ti
.
borrows B 't at real interest rate rt to finance investment I t
.
profits paid as dividends to owners
Firm Dividends
Dt =
Yt -
Wt Nt t
Bt
-
I t no price b/c real
=
Yt -
Wt N t
←
labor costs
← repayment to bank
Dtt I
=
Yttt -
Wtt ,
N t ti
-
I t ti
-
LIt
rt I I t
=
Ytt I
-
Wtt , N t ti
t
( I -
8) Kt ti
-
( Itrt )It
T
scrap value of capital stock
Firm Valuation E Profit Maximization
.
Value of firm :
NPV of flow of dividends :
Vt =
D. it
¥ Dt ti
Max
Nt . Nt ti ,
It Dt
t
tf Dtt I
Where :
Dt
=
At FL Kt ,
N t ) -
wt Nt
Dtt I
=
At ti F ( K t ti ,
N t ti ) + ( I t
8) Kt ti
-
Wtt ,
Nt ti
-
( I t rt ) I t
K t t I
=
It t
LI -
8 ) Kt

Max
Nt ,
Ntti ,
It Dt t
Ft D th
f
K th
=
( I -
8) K t
t
It
At F ( Kt . Nt )
-
Wt Nt t ( Att ,
FL Kt ti .
Ntt , ) -
Wtt , Ntt i
-
L Itrt )Itt
LI
-
8) Kt ti )
I+
rt
-
I 1
At t ( Kt . Nt )
-
Wt Nt t ( Att ,
FL Kt ti .
Ntt , ) -
Wtt , Ntt ,
-
L Itrt ) ( Kt ti
-
It-
8) Kt ) t
(
t -
8) Kt ti
I+
rt
Nt :
At FN ( Kt ,
N t ) =
Wt
Nt ti
:
At ti FN ( Kt ti ,
N t ti ) =
Wtt , K MC =
marginal benefit
I t
rt I t rt
Kt ti
:
Att I Fk ( K t ti , Ntti ) t
( I -
8) =
I t
rt It =
K t ti
-
( I -
8) Kt
HttHtt¥
At ti Fk ( Kt ti ,
N t ti
) =
rt t
8 =
Rtt ,
Labor Demand
Wt Nt =
Nd ( Wt ,
At ,
Kt )
¢ marginal benefit
-
t t
Wt
Of labor
If At Or Kt T
→
Nt = Nd ( Wt ,
At , Kt )
Nt Nt
Investment Demand
rt It
=
I
d
( rt . At ti ,
Kt )
rt
-
t
-
If At ti T or Kt t
→
It .
-
I
d
( rt ,
A t ti ,
Kt )
It It
Household
-
representative household w/ preferences over consumption and labor
.
leisure is Lt = I -
Nt
.
lifetime utility :
U =
U I Ct .
I -
Nt ) t
BU ( Ctu ,
I -
N t ti
)
.
ex of period Utility functions :
U = In Ct t
01h ( I -
Nt )
t
Otis a labor
supply shock b/c it shifts utility from leisure
( dis utility for labor )

Budget Constraints
.
household faces flow budget constraints for period t and ttl ,
but now income is partly
endogenous
endog . exog .
( t
t
St E Wt Nt t
Dt
( ttl
t
#-
St I Wtt I Ntt i
t
Dtt I
t
rt St
I BC :
C t
t
-1ft =
Wt Nt +
Dft .
,
Wtt IN ttt
t
Dtt I
I t rt
Max
Ct .
Ctn , Nt ,
tutti U ( Ct ,
I -
Nt ) t
BU L Ctti ,
I -
N th )
subject to IBC
( tt I
=
( wt Nt t
Dt
-
C t ) ( It rt ) t
Wtt , Nt ti
t
Dtti
Max
Ct ,
Nt , Ntt , U ( Ct ,
I -
N t ) t
B U l ( Wt Ntt Dt
-
Ct ) ( It rt ) t
Wtt , N ttl
t
Dtti ,
I -
N t ti
)
a-
Ct
:
Uc ( Ct .
I -
Nt ) -
B Uc l Ctti ,
I -
N t ti ) ( It rt 1=0 ( Ct ,
I -
N t ) t
B Fda ,
( Cti , ,
I -
Net , ) FEET
'
=
O
Uc L Ct .
I -
Nt ) =
BUC ( Ceti ,
I -
Ntt , ) ( It rt )
Nt : -
UN ( Ct ,
I -
N t ) t
BUC ( Ctn ,
I -
Ntt ,
) Wt ( I trt 1=0
( Ct .
Lt )
NttBITE,
C Ctn .
I -
Ntt ,
=
O
UN ( Ct ,
I -
N t ) =
Uc ( Ct ,
I -
Nt ) Wt
* -
I Clt rt ) Wt
Nt ti
:
UN ( Ct ti ,
I -
Nt ti
) =
Uc ( Ce ,
I -
Ntti )
C t ti
-
S t
=
Wtt i Nt ti
t
Dtti t
rt St
Lt t
Nt =
I
Lt ti
+
Ntt ,
=/
or
C t
t
Wt Lt t
St =
Wt
t
Dt
C t ti
-
St t
Wti i L t ti
=
Wth
t
Dtt I
u C C ,
L ) =
log C t
0109L If W T # = -
w
Ct Ct Uc
⇐-
W¥u( c ,
L , =
k
TYPEu ( C ,
L ) =
k
¥
ofI I
I Lt I Lt
Ct =
Cd ( Yt
;, ,
Y , ,
r±
) Assume consumption driven by aggregate income
Labor Supply
.
substitution effect dominates income effect
.
if preferences :
U ( C ,
I -
N ) =
In ( C t O In I I -
N ) )
↳ labor supply only depends on
wage da distaste for labor ( O )
Uc =
¥4 -
N )
Uh =
Cto In ( I -
N )
'
FON
=
TEN =
w → N = It fu

Labor
Supply Curve
N t
=
N
s
( W t ,
O )
Wt t
-
→
If Ot
N t
Market Clearing
.
St =
It
.
savings by households borrowed by firms to purchase new capital L investment )
.
period t resource constraint :
Yt =
Ct t
I t
.
Y t + ,
=
( t ti
t
I t t I
Equilibrium , period t
.
Conditions :
Ct =
(
d
( Yt ,
Yeti .
rt )
Nt =
Ns L Wt .
Ot ) household Side
N t
=
Nd ( We ,
At ,
Kt ) firm side
I
t
= Id ( rt ,
At ti ,
K t )
Yt =
At F L Kt ,
N t )
Yt =
C.L
t I t
.
endogenous variables :
Ct .
Nt .
Yt ,
It ,
W t ,
rt
.
exogenous Variables : At ,
At ti ,
Kt ,
Ot
↳
quasi
-
exogenous
:
Yt ti ,
K th
Competitive Equilibrium
.
2
prices
:
rt ( intertemporal price of goods ) and We ( price of labor )
.
Wt adjusts SO that market clears ( Ns = Nd )
.
rt adjusts to clear market ( St =
It )
.
endowment
economy is special case where Nt is fixed G It =
O

Neoclassical Model
.
optimizing agents and frictionless markets
.
emphasizes supply shocks (
Changes in At Or Ot )
.
medium
run
Equilibrium conditions
C t
=
Cd ( YI,
Y #I ,rt ) optimizing by
Nt =
N
S
( Wt ,
O e )
households
+ -
N t
=
Nd ( W t ,
At ,
Kt ) firm
It =
I
d
( rt ,
At + , ,
ke )
optimizes
Yt =
At FL Kt ,
N t ) tech constraint
+ t
Yt =
Ct t
It resource constraint I market
clearing conditions
↳ s =
I in production economy
Graphical Analysis
.
IS curve :
set of ( re ,
Yt ) where household E. firm behave out i
many Wrt consumption E
investment demand E income equals expenditure
.
YS curve :
set of ( rt ,
Yt ) where household E firm behave
optimally ,
labor market
Clears ,
and production function holds
-
summarizes labor supply ,
demand ,
and production function
.
general equilibrium :
on both IS and Ys curves
simultaneously
IS Curve
.
Y I =
Cd L Yt .
Yet , , re ) and Id ( rt ,
Att I ,
Kt )
.
Y of =
Y t
.
graph set of ( rt ,
Yt ) where this holds
y
d Ted =
Yt
t
Y of =
Cd ( Ye ,
Yeti ,
rt ) t I
d
( rt , At ti .
K t )
ya
0 ,
t
Cd ( O , Yeti ,
rt ) t Id ( rt .
At ti ,
Kt ) •
u v
I 0 , t I t

y
d Ted =
Yt
t
Y f =
Cd ( Ye ,
Yeti ,
ri
,
t ) t I
d
(
K
, t ,
At ti .
K t )
Y of =
Cd ( Ye ,
Yeti ,
ro, t ) t I
d
(
ro
,
t ,
At ti .
K t )
Y of =
Cd ( Ye ,
Yeti , rz ,
t ) t I
d
(
Vz
,
t ,
At ti .
K t )
•
Ti , t ( to , t L r2 , t
YZ ,
t
YO , t Yi , t
Ye
rt
T2 , t
ro .
t
.
in production ,
IS curve is flatter b/c response from consumption
r , ,
t
is
and investment
.
If Att , T ,
IS →
.
If K t I .
IS →
Yt
Ys Curve
.
begin by plotting labor demand a supply .
Find Nt where these intersect .
.
given this Nt ,
determine Yt from production function
.
rt irrelevant for labor demand , supply ,
and production function under our assumptions :
Ys curve is still Vertical as in endowment economy
.
could generate an upward
-
sloping Ys curve ,
and for IS shocks ,
if we considered
effect of rt on labor supply
y S
wt
Labor Market rt
NS ( W t ,
O t )
If At T
,
Ys →
T2 ,
t
If Ot T ,
Y
s
→
to ,
t
Wo ,
t
If K t
T ,
Y S →
V. ,
t
Nd ( Wt ,
A t ,
K t )
No ,
t N t
YE
Yt Yt Yt =
Yt
-
( Kt ,
Nt )
Yo ,
t
y
At t
No , t N t
Yo , t Yt

General Equilibrium
.
economy must be on both IS E Ys curves
.
intersection jointly determines Yt , rt ,
Nt .
and Wt
.
figure out split between Ct and It , given Yt Grt by looking at consumption and
investment demand functions
Ytd YI =
Yt
YET =
Cd ( Yt ,
Yeti ,
rt ) t
I
d
( rt ,
At ti ,
Kt )
Y t
y S
wt
Labor Market rt
NS ( W t ,
O t )
T2 ,
t
to ,
t
Wo ,
t
V , it
IS
Nd L W t ,
A t ,
K t )
No ,
t N t
YE
Yt Yt Yt =
Yt
-
( Kt ,
Nt )
Yo ,
t
y
At t
No , t N t
Yo , t Yt
Effects of Changes in
Exogenous Variables
.
At ,
Ot .
and K t affect position of Ys curve
.
A th E Kt affect IS curve
.
Figure out how Ys da IS curve Shift ,
determine new rt .
Use this to figure out how other
exogenous variables react
.
a complication arises :
changes in It affect ktti ,
Which affects Yeti ,
and hence Ct
.
we ignore these effects -
size of capital stock is
large relative to investment ,
and in
medium run can treat capital stock as approximately fixed ( unlike
long run where we
Study capital accumulation )
.
Y tt ,
will therefore only be affected by changes in exogenous variables dated ttl :
Att , .
"
Pseudo -
exogenous
"
in sense we will treat it as unaffected by time t
exogenous shocks

Ytd
YF=Yt
Supply Shock Att
Ytd=Cd( Yt ,
Yeti .tt/tld(rt.AttI ,
Kt )
Yt
YS
wt
Labor Market rt
NS ( Wt ,
Ot )
T2 ,
t
To ,t
Wo ,t
Vi it
IS
Nd ( Wt ,
At , Kt )
No ,t Nt YE
Yt Yt Yt =
Yt
tflkt.NL )
Yo ,t
F-No , t Nt Yo ,t Yt
Atta T
Ytd YI =
Yt
a z
Ytd=Cd( Yt ,
Yeti .tt/tld(rt.AttI ,
Kt )
I V
u In graph ,
Can 't tell if Ct EltIt
YS
we
Labor Market re increase or decrease
NS ( Wt ,
Ot )
T2 ,
t
•
r
to ,t
→ •
Wo ,t
Vi it
IS
Nd ( Wt ,
At , Kt )
No ,t Nt YE
Yt Yt Yt =
Yt
tflkt.NL )
Yo ,t
(
A
No , t Nt Yo ,t Yt

Supply vs .
Demand
.
with a vertical Ys curve , output is
completely supply
-
determined
.
"
demand Shocks
"
l shocks which Shift the IS curve ) affect composition of output and
rt ,
but not the level of output
-
neoclassical model emphasizes supply shocks l productivity and labor preference I as
main source of fluctuations
.
Can
get demand Shocks to impact output if Ys is upward
-
sloping ( because interest
rate affects labor supply ) ,
but doesn't
change the fact that model Still needs to be
predominantly driven
by supply
-
shocks to make predictions which are more or less
consistent with data
Qualitative Effects of Changes in
Exogenous Variables
Variable T At T Ot T Att t
Yt t
-
O
Ct t
.
?
It t
-
?
N t
t
-
O
Wt
+ t
O
rt
-
t t

Fiscal Policy
.
fiscal policy refers to government spending da taxes
.
key result :
Ricardian Equivalence
-
the manner in which a
government finances its
spending
is irrelevant
.
government spending multiplier
Adding Government to the Environment
.
government spending in both periods is
exogenous
.
budget constraints :
G I Tt t
BE
G It,
t
rt Bto I Tt ti
t
B ft ,
-
BE
-
BE :
stock of
government debt issued in t and carried into t t I
-
BE ,
=
O
.
I BC :
Gt t
Gt 'T
Tt +
Tt t I
I t
rt I t
rt
.
government 's
budget must balance in an intertemporal present value sense
Value of Firm :
PDV of flow of dividends :
Vt '
-
Dt t
,
! rt
Dt ti
Max
Nt ,
Ntti ,
It Dt
t
¥t Dtt ,
Where Dt =
At F l Kt ,
Nt ) -
Wt Nt
Dtt ,
=
A th F ( Kt ti ,
N t ti ) + ( I t
8) Ktt I
-
W th N t ti
-
l I t rt ) It
Household Preferences
.
Representative households :
U =
U ( Ct ,
I -
N t ) t
BU ( Ct ti ,
I -
N t -
I
) th ( G t ) t
Bh L Gt ti
)
-
can
ignore
-
household gets utility from government spending via ht .
)
Household Budget Constraint
C. t
t
St I W t N t
t
Dt
-
Tt
( t t I
t
S t ti
-
St I wt ti
N t ti
t
D t ti
-
Ttt I
t
rt St
-
Tt da Ttt , are given
C t
t = W t N t t D t
-
To +
Wtt IN t t I
t
Dt ti
-
Ttt I
I t
rt

Household Optimization
.
FOC :
Uc ( Ct ,
I -
N t ) =
B Ll t rt ) Uc ( Ct ti ,
I -
Nt ti )
U L ( Ct ,
I -
N t I =
Wt Uc L Ct ,
I -
Nt )
U L
( Ct ti ,
I -
N t ti ) =
Wtt , Uc ( C ttl ,
I -
N th
)
.
IBC :
C
t
t =
Wt Nt t
Dt t
Wt " N
,
Dtt '
-
Tt -
Ittf
( t
t =
Wt N t
t
D t
-
Gt +
Wt ti Nt ti
t
Dt ti
-
Gt + ,
I t
rt
.
C t
=
(
d
( Yt
-
G t ,
Yeti -
Gt ti , rt )
+ t -
Ricardian Equivalence
BE =
( Tt ti
-
G t ti
)
.
Issuing debt equivalent to
raising future taxes
.
Assumptions :
.
taxes are lump sums
.
no
borrowing constraints
-
households forward -
looking
-
no
overlapping generations
Fiscal Policy in an Endowment Equilibrium Model
.
market
clearing
:
St
-
Be =
It
aggregate is private t
public savings
Yt
-
Tt -
Ct
-
( Gt
-
Tt I =
It
↳ Yt =
Ct t
Gt t
It
C t
=
Cd ( Yt
-
Gt ,
Yt -
I
-
Ge ti ,
rt ) l I )
Nt =
Ns ( Wt , Ot ) ( 2)
Nt = Nd ( Wt , At ,
Ke ) I 3)
It =
Id ( rt ,
At ti ,
K t ) ( 4)
Ye =
At FL Kt ,
N t ) ( S )
Yt =
C t
t
It t
Gt ( 6)

Government Spending Multiplier
Y I = Cd ( Y e
-
Gt ,
Y t +1
-
Gt + , , rt ) t I
d
( rt ,
Att I .
K t ) t
Gt
Y I =
Yt
↳ Ye =
Cd ( Y e
-
Gt ,
Yt + ,
-
Gt + , , rt ) t I
d
( rt ,
Att I .
K t ) t
Gt
Differentiate :
d Yt
=
Ift Ld Yt -
d Gt ) t
d Gt
→
d Yt =
d Gt
-
MPC
Holding rt fixed , output would Change one
-
for -
one with government spending
↳ multiplier would be 1 L horizontal Shift of IS curve to a
change in Gt I
Without Ricardian Equivalence
.
If household is not forward -
looking
Yt =
Cd ( Yt -
Tt ,
rt ) t
Id ( rt ,
Att I ,
Kt I t
Gt
d Yt
=
FEI d Yt t
d Gt
et
d Gt
=
1¥ ) I
Multiplier is greater than I
( assumes no Ricardian Equivalence and fixed rt I
Rounds of Spending
dY_t = I +
Mpc t
M PG t MPC
3
t . . .
=
-1 W/O Ricardian Equivalence
d Gt I -
MPC
dd =
( I -
M PC ) t MPC ( I -
MPC ) t MPC
2
( I -
M PC ) t . . .
= =
I w/ Ricardian EquivalenceI -
M PC
Gt T
y
d Ted =
Yt
t
Y I =
Cd ( Ye -
G , ,
t ,
Yt + ,
-
Gt ti , ro ,
t
) t
I
d
( to , t ,
At ti ,
K t ) t
G I , t
+
f Y I =
Cd ( Ye -
Go,
t ,
Yet ,
-
Gt ti ,
ro,
t
) t
I
d
( to , t ,
At ti ,
K t ) t
Go it
=
C
d
( Ye -
G , ,
t ,
Yt + ,
-
Gt ti , ri,
t
) t
I
d
( r , it ,
At ti ,
K t ) t
G I it
•
•
YE
rt
•
r
to ,
t →
•• IS
'
IS
Yt

Crowding Out
-
TGT has no effect on Ys
.
dcttdlt = -
dGt
.
rt must rise
.
TGtt ,
→
rtt
.
Multiplier is O ( assumption of Vertical Ys in neoclassical model where Yt can 't react
tort )
Demand Shock :
Tatti
Yt Yf=Yt
d
YI = Cd ( Yt -
Gt ,
Yeti
-
GO.tt
'
,
bit )
q
t Id ( ro ,t ,
Attl ,
Ktlt Gt
t
YI = Cd ( Yt -
Gt ,
Yeti
-
Gi
tti ,
r it )
+ Id ( r , ,t ,
Atti ,
Ktlt
'
Gt
"
YI = Cd ( Yt -
Gt ,
Ytti
-
Gi,
tti ,
bit )
+ Id ( ro ,t ,
Attl ,
Ktlt Gt
Yt
Wt Ns ( Wt , Ot ) rt ✓
Is
To ,t
-
r , ,t
-
←
IS
Ndlwt ,
At ,
Kt ) IS
'
Nt Yt
Yt Yt
Kt ,
Ntl
y
At FC
- r
No ,t
Nt Yo ,t Yt
Exogenous Shock
Variable TAT TOT Tatti 9Gt Totti
Yt t -
O O O
Ct t -
?
- -
It t
-
?
-
t
Nt t -
O O O
Wt
+ t
O O O
rt
.
t t t
-

Money in the Neoclassical Model
Money
.
asset
-
medium of
exchange
-
store of Value
-
unit of account
.
liquid
New Variables
.
Mt :
stock of
money
.
Pt :
price of goods
.
it :
nominal interest rate
Nominal Budget Constraints
.
period t :
Pt Ct t
Pt St t
Mt E Pt We Nt
-
Pt Tt t
Pt Dt
-
Period ttt :
Ptt IC t t I
t
Ptt , St ti
-
Pt St t
Mt ti
-
Mt I Ptt I Wt ti N th
-
Pt ti Tt ti
t
it Pt S t
t
Pt ti Dtt I
.
terminal conditions :
St ti
=
O ,
Mt ti
=
O
Ct t S t
t =
Wt Nt -
Tt t
Dt real Value
( t ti
-
¥¥ St =
Wt ti
N t t I
-
Ttt I
t
Dt ti
t
it
,
S t
t
¥7
.
Yet : real money balances
Fisher Relationship
I t
rt = I I t
it )
Ptt I
.
expected inflation :
I t
tf ,
=
¥
Pt
.
Fisher relationship
rt =
it
-
IT It ,

Real IBC
C t t I
=
Wtt , Ntt I
t
Dt ti
-
Ttt ,
t
¥7 t
( I t it ) ( III ) St
C t t I
=
Wtt , Nt ti
t
Dt ti
-
Ttt ,
t
( I t
rt ) St
t
IIII EI
St =
I
t rt ( C t ti
-
Wtt ,
N t ti
-
D t ti
t
Tt ti )
-
I t
'
it FI
Preferences
.
lifetime utility
U =
U ( Ct ,
I -
N t ) t
V FI t
BU ( C th ,
I -
Nti , )
.
household solves I subject to IBC ) :
Max
Ct ,
Nt .
Ceti ,
N t ti ,
Mtl Pt
{ U ( Ct ,
I -
N t ) t
V ( FI ) t
Bu ( C t ti ,
I -
N t ti ) }
Optimality Conditions
.
FOC for consumption Er labor :
Uc ( C t ,
I -
N t ) =
B ( I t
rt ) Uc ( C t ti ,
I -
N t ti )
U L l Ct ,
I -
N t I =
Wt U c ( Ct ,
I
-
N t ) Same for Nt ti
.
FOC for money
:
v
'
I I =
Ucl Ct ,
I -
Ntl
.
Shortcut for higher Ct requiring higher Mtl Pt to facilitate extra I
bigger transactions
.
if no utility benefit from
holding money ,
V
'
l .
7=0 ,
then would
only hold if it =
O :
money dominated as a store of value by bonds if it 70
Optimal Decision Rules
.
Ct =
(
d
( Y t
-
Gt ,
Y t ti
-
Gt ti
)
.
N t
=
Ns ( W t .
O t )
.
M t
=
Pt Md l It,
It )
Or M t
=
Pt Md ( rt IITEti ,
YI )
Government
.
government
' '
prints
"
money
Pt Gt I Pt Tt t
Pt B to t
Mt
P t ti Gt ti
t
it Pt B E t
Mt I P t ti Tt ti
-
Pt Bt
G
Ptt I G t ti
t
( I t i t
) Pt Bt
G t
Mt I Pt ti Tt ti
Government 's IBC
.
Combining 2 flow budget constraints da
using the Fisher relationship ,
we get
:
Gt t =
Tt t t .
TMI

Equilibrium Conditions
( t
=
Cd ( Y t
-
G t ,
Yt ti
-
G t ti ,
rt I ( I )
N t
=
Ns ( Wt ,
Ot ) I 2)
Nt =
Nd ( wt ,
At ,
Kt ) ( 3)
It =
Id ( rt ,
At ti ,
K t ) ( 4 )
Yt =
At F ( Kt ,
N t I ( 5 )
Yt =
C t
t
I t
t
Gt ( 6 )
Mt =
Pt Md l it .
Yt )
{7g! } new
rt =
it
-
IT Eti
.
Endogenous Variables :
Ya ,
Ct ,
It ,
Nt .
Wt ,
rt . Pe .
it
.
New Exogenous Variables :
Mt and IT ft ,
Classical Dichotomy
.
first 6 equations use 6 real endogenous variables E no nominal Variables
↳ real endogenous variables are determined independently of nominal Variables
.
known as classical dichotomy
.
don't need to know nominal Variables to determine real Variables .
but converse
not true ( nominal variables will be affected by real variables )

Money Market Equilibrium
Pt MS Mt
Pt Md ( to , t
t
Itf , ,
Yo , t )
Pt =
Md ( rt t IT ft , ,
Yt )
If Yt T Md T Ptt ( shifts right )
Po , t I I I I l
tf rt T
'
,
Mdt Pt T ( shifts left )
Mo , t Mt
Increase Money Supply ( T Me ) no effect on real Variables
Pt MS Ms
'
Pt Md ( to , t
t
IT ft I ,
Yo , t )
P l
, I I I I I '
Po, t I I I I I
→
Mo , t Mt
Increase in At →
towers Pt household wants to hold more
money since rt t
Pt MS
Pt Md ( to , t
t
IT ft I ,
Yo , t )
→
Po , t I I I I l
P , ,
t
I I I l l
Mo , t Mt
Real Shocks
.
At T :
rt d Yt T Md →
Ptt
.
Ot T :
rt T Yet Md ←
Pt T
.
Att ,
T Or Gt T or G t + it :
rt T ,
no effect on Yt
.
Money demand shifts left 4 price level rises
.
IT Ft,
T :
it T L by same amount )
.
money demand pivots in ,
so price level increases

Gt 'T
Ted
YI=Yt
Positive demand Shock
Tt Cd ( Yt -
Gt ,
Yet ,
-
Gen ,
rt ) t Id ( rt , Atta ,
Kt ) +
Gt
-
MPCCI
Yt
YS
wt
Labor Market rt
NS ( Wt ,
Ot )
✓
I
,
t I I I l l •
r
To ,t
s •
Wo ,t
IS
'
IS
Nd ( Wt ,
At , Kt )
No ,
t
Nt YE
Yt Yt Yt =
Yt
-
( Kt ,Nt )
Yo ,t
(
Att
No , t Nt Yo , t Yt
Pt MS
Pt Md ( to .tt/Tfti ,
Yost )
P ,
,
t
I I I I l ①
Po , t I I I I I
Mot Mt
Qualitative Effects
Exogenous Shock
Variable TAT TOT Tatti TGT Totti Tht TITE 't
Yt t -
O O O O O
C t
t -
?
- -
O 0
It
t -
?
-
+
O O
Nt t
-
O O O O O
Wt
t +
O O O O O
rt
-
+ t t -
O O
it
-
+ t t -
O
+
Pt - t + + -
t +

New Keynesian Models
.
nominal
rigidities
-
wages and I or prices are im perfectly flexible
.
means :
.
Money is non
-
neutral L no classical dichotomy )
.
demand Shocks can affect employment G output
.
equilibrium of the model is inefficient Er there is scope for
policy to improve
outcomes in short run
Demand 4 Supply
.
demand side of the neoclassical da new
Keynesian model are the same
.
differences arise on the
supply side
.
2 basic variants :
price stickiness or nominal wage stickiness
Simple Sticky Price Model
.
Pt =
Ft is now
exogenous
.
firm has to hire labor to meet demand at F rather than maximizing firm value
Partial
Sticky Price Model
.
Pt =
PI t T ( Yt
-
Yet ) where 710
.
Y tf the hypothetical equilibrium level of output in neoclassical model
-
nests simple sticky price model L 8=0 ) and neoclassical model ( 8
→ as I
-
again replace labor demand curve w/ modified expression for price level
Simple Sticky Price Model Partial Sticky Price Model
C t
=
Cd ( Y t
-
G t ,
Yt ti
-
G t ti ,
rt I Ct =
Cd ( Y t
-
G t ,
Yt ti
-
G t ti ,
rt I
N t
=
Ns ( Wt ,
Ot ) N t
=
Ns ( Wt ,
Ot )
Pt =
Ft Pt =
Ft t
Y ( Yt
-
Y E )
I
t
=
I
d
( rt ,
At ti ,
K t ) I
t
=
I
d
( rt ,
At ti ,
K t )
Yt =
At F ( Kt ,
N t I Yt =
At F l Kt ,
N t I
u u
I t
=
C t
t
I t
t
G t I t
=
C t
t
I t
t
G t
Mt =
Pt Md ( it ,
Yt ) Mt =
Pt Md ( it ,
Yt )
rt =
it
-
IT It , rt =
it
-
IT Eti

Graphing the Equilibrium
.
use
aggregate demand LAD ) E aggregate supply ( AS )
( t
=
( d
( Yt -
Gt ,
Yet I
-
Gt ti .
rt )
-
AD :
, g
{ It
=
Id ( rt ,
At ti ,
ft ,
K t )
Yt =
Ct t
It t
Gt
( M
{
Mt =
Pt Md ( it ,
Yt I
rt
=
it
-
IT Eti
.
Classical dichotomy no longer applies
IS da LM curves
.
IS curve :
set of ( rt ,
Yt ) where first 3 conditions hold
Yt =
Cd ( Yt -
Gt ,
Yt + ,
-
Gt ti , rt ) t
I
d
( rt ,
At ti ,
K t ) t
Gt
.
LM Curve :
combos of Lrt ,
Ye ) that satisfy last 2 equations
Mt =
Pt Md ( rt
t
IT ft , ,
Yt )
-
upward Sloping
-
LM curve will Shift if Mt .
Pt .
or IT tea Change
-
rule of thumb :
LM curve shifts in the same direction as real balances
,
FI
Deriving the LM Curve
rt Ms
rt LM
Yi ,
t ) YO , t
•
To , t •
Me =
Po , e
Md ( rt t
Teo , t t , ,
Yi. t
)
Mt =
Po , e
Md ( rt t
Teo , t t , ,
Yo . t
)
Mo , t
Mt
Yo , t Yi ,
t YE
Shift in LM Curve : T Mt
rt Ms M s
'
rt
LM ( Mo ,
t )
LM I M i ,
t )
ro ,
t
r I
,
t
.
M t
=
Po ,
t Md ( rt
t
IT E. t + I ,
Yo , t
)
M o
,
t Mi , t M t Yo ,
t
Yt

IS -
LM Curves
rt
LM ( M o , t ,
Po , t ,
IT E . t t ,
)
To ,
t
I S ( G o ,
t
,
Yo , t t I
,
A o
,
t t I ,
K o ,
t )
v
v
I 0 , t I t
The AD Curve
.
What if Yo , t
¥ Ys when IS = LM ?
.
LM took Pt as given ,
can still adjust Pt to shift L rt ,
Yt I
point where IS =
LM
-
The AD curve is the set of ( Pt .
Y t ) pairs where the
economy is both oh the IS da LM curves
-
Pt determines position of LM Curve which determines a Yt where the LM curve intersects the IS
curve ; a
higher Pt means LM curve shifts in ,
which results in a lower Yt →
AD curve is downward
Sloping
Deriving the AD curve
rt LM ( M o
,
t ,
P2,
t
, Teo,
t ti )
L M ( M o
,
t ,
Po,
t
, Teo,
t ti )
L M ( M o
,
t ,
P I ,
t
, Teo,
t t , )
I S ( G o , t ,
Yo , t t I ,
G o , t ti , A O ,
t t I
,
KO , t )
Yt
Pt
Pz ,
t
Po ,
t
I
Pi ,
t
AD
Yt

Shifts of the AD Curve
.
The AD Curve will Shift if either the IS or the LM curves shift I for reason other than Pt Which
would be a movement along the AD curve )
.
AD curve will shift right if :
-
Att .
or G t increase ( IS shifts I
-
Me or IT Et ,
increase ( LM shifts )
'
Gt ti
decreases US shifts )
The
Supply side
.
AS curve :
set of ( Pt ,
Ye ) that is consistent w/ the production function ,
some notion of labor
market equilibrium ,
and
any exogenous restriction on nominal price or wage adjustment
.
AS curve would be vertical in neoclassical model
Neoclassical Equilibrium
rt
L M ( M o ,
t
,
IT 8 .
t -
I ,
Po ,
t )
ro , t
÷Wt
NS ( Wt , Oo , t I Pt AS
Wo ,
t p -
O , t
Nd ( Wt ,
A o ,
t ,
Kt ) AD
N t
Yo , t Yt
Yt =
A o ,
t F ( ke ,
N t )
Yt
Yo ,
t
-
-I
No , t
Yt
Simple Sticky Price Model
.
Pt =
Ft →
exogenous
.
firm cannot optimally choose labor condition
.
AS curve will be horizontal at Et ,
can only shift if Ft changes exogenously

Simple Sticky price Equilibrium
rt
L MIMO ,t ,
ITE .
t -
I ,
Po ,
t )
ro , t
÷Wt
NS ( Wt , Oo ,t
) Pt
Pat
-
AS
AD
Nt Yo ,t Yt
Yt =Ao,tF( ke ,
Nt )
Yt
" " t
!I
No , t
Yt
Partial
Sticky Price Model
-
output gap :Pt=FttV( Yt
-
Yet )
.
AS curve will be upward sloping with Slope determined by V
.
Asf :
hypothetical neoclassical AS curve
Partial Sticky Price Equilibrium rt
L MIMO ,t ,
ITE .
t -
I ,
Po ,
t )
ro , t
÷Wt
NS ( Wt , Oo .tl Pt
Asf
AS
Wo ,t Po ,t=Ft -
Nd ( Wt ,Ao,t ,
Ko , t ) AD
Nt Yo ,t Yt
Yt =Ao,tF( ke ,
Nt )
Yt
" " t
!I
No , t
Yt

Monetary Non -
Neutrality
.
New
Keynesian model output is ( fully or
partially ) demand determined
.
If Mtt ,
LM→ ,
Yet , rtt.CTT.NET ,
Wtt
Mtt :
Simple Sticky Price
rt
L MIMO ,t ,
Po ,
t )
L MLM it ,
Po ,
t )
ro , t
→
÷Wt
NS ( Wt ,
@ o.tl Pt
Wi ,t
→
Wait
Po ,t
-
AS
AD
'
AD
Nt Yo ,t Yt
Yo 't
"
=
A " " " " " Nt " " "
I
Nott Ni ,t
Yo ,tY , ,t
Yt
rt
Mt 'T :
Partial Sticky Price LMCMo.t.po.tl
L MLM , ,t ,
P , ,t )
ro , t
I
LMC Mist,
Po ,
t )
÷Wt
NS ( Wt ,
@ o.tl Pt
Asf
AS
wilt
Wo ,t Po ,t=Ft -
•
AD
Ndlwt.Ao.t.ko.tl AD
Nt Yo ,t Yt
Yo 't !" t
=
A " " Ft " "
N "
¥
I
No , 't Ni ,
t
Yt

Monetary Non -
Neutrality
.
change in money supply affects real variables in New Keynesian model
.
as 8 gets smaller LAS curve
gets flatter ) ,
has bigger effect on real Variables
.
8=0
:
simple sticky price
.
y → as :
neoclassical
Supply Shocks
.
At Or Ot Or Kt Shocks cause AS curve to shift
.
If price level is
sticky , output reacts less to
supply shocks
At T :
neoclassical
rt
LM ( Mo ,
t
,
Po .
t )
L M ( M o ,
t
,
Po ,
t )
ro , t
→
÷Wt
NS ( Wt , Oo , t I Pt AS AS
'
Wi it .
Wo ,
t
Po
, t
-
→
Nd ( Wt , Ai,
t ,
Kt ) P , it →
Nd ( Wt ,
A o ,
t ,
Kt ) AD
N t
yo .
iii.'
n . ,
¥
" " t Y t
I
No , t
Yo ,
t Y , it
Yt

Att :
simple sticky price
rt
L MIMO ,t ,
ITE .
t -
I ,
Po ,
t )
ro , t
÷Wt
NS ( Wt , Oo ,t
) Pt
Wo ,t
Wit
Po ,t
-
AS
AD
Nt
% .
iii.n . ,
¥
" a t 't
I
No , t
Yt
Att :
partial sticky price
rt
( ML Mo ,t ,
Post )
L M ( Mo ,t ,
Pi , t )
to , t
r , ,t
÷Wt
NS ( Wt ,
@ o.tl Pt Asf
Asta's
AS
Po ,t=FtWo ,t -
Ndlwt ,A , ,t ,
Ko , t ) Pitt
-
•
ii.!
" "
. . . .
"
)Yt=Ao,tF( ke ,
Nt ) Yt
Yo 't ✓
, Pt =
Ft t
Y ( Yt -
Ttt )
No , t
Yt
p Asf Asf
'
AS AS
'
t
Ft >
L
o•
AD
Ytf Y, ,tYtf
'
Ye

Economy Reacts Differently to Supply Shocks
.
As 830 ( stickier prices )
, output L and other real Variables ) under -
react more
.
In simple sticky price ,
if Atl ,
Ntt
.
In partial simple sticky price ,
if Att ,
Nt ?
rt LMLMO ,t ,
Po ,
t )
Positive IS Shock :
Neoclassical →
ri ,
t
← LMLMO ,t ,
Po ,
t )
ro , t
Is
IS
'
Yt
Wt
NS ( Wt , Oo , t ) Pt AS
Pi ,t
-
•
r
Wo ,
t p - >
o ,t →
AD
'
Ndlwt ,
Ao ,t ,
Kt ) AD
Nt Yo , t Yt
Yt =Ao,tF( ke ,
Nt )
Yt
" " t
!I
No , t
Yt
rt
Positive IS Shock :
Simple Sticky LMCMO.t.po.tl
→
✓
i. t
to , t
IS IS
'
Yt
Wt
NS ( Wt , @o.t ) Pt
W , ,t
→
Wo ,t
Po ,t
-
AS
AD
'
AD
Nt Yo , t Yt
Yt =Ao,tF( ke ,
Nt )
Yt
" " t
!I 1
No , t N , ,tNt Yo ,t Yi ,
t Yt

rt
Positive IS Shock :
partial Sticky Price
→
LMI Mat ,
Ritt
←
LM ( Mo ,
t
,
Po ,
t )
ro , t
Is
IS
'
Y .
L
Wt
NS ( Wt , Oo , t ) Pt AS
f
AS
W i
,
t
Pi ,
t
Wo ,
t -
Po , t
= Ft
→
AD
'
Nd ( Wt ,
Ao , t ,
Ko , t ) AD
N t
Yo , t Yt
Yt =
A o ,
t F ( ke ,
Nt )
Yt
Yo ,
t
-
-I
No ,
t Ni , t Yo ,
t Yi , t
Yt
Demand Shocks
'
the flatter the AS curve ,
the more output reacts to the IS shocks
.
rt Under -
reacts relative to neoclassical case
Conclusion
.
Nk is same as neoclassical model except Pt is not perfectly flexible
.
AS curve is non -
vertical G not on labor demand curve
-
money is non -
neutral ,
demand shocks matter , and economy reacts
differently to
supply shocks
l

Dynamics in New Keynesian Model
Dynamics
'
AS curve :
Pt =
It t
V I Ye
-
YE )
where YE is the
' '
flexible price
"
level Of output
.
if firm could
freely set price ,
it would do so such that on its labor demand curve ,
which would entail Yt =
Ttt
'
Output gap
:
Yt -
Y tf
rt LM I Me ,
Po .
t )
Negative Output Gap
LM I Me ,
Pott)
Firms would like to lower price rat
ro.tt
I
¥Wt
Ns ( Wt , Ot )
Pt Asf As
f-
Wo , t Fo .
t -
Wo ,
t
Po , t
-
Nd ( Wt ,
At ,
Kt )
Pott
AD
Nt Yt
Yt At Fl Kt ,
N t ) Ye Ye =
Yt
-I I I I
No , t Not, t
Nt Yo ,
t Yo ,
tf Yt
Transition from Short Run to Medium Run
-
with a negative output gap ,
the firm is producing less than it would like to
↳
a friction I menu costs )
prevent the firm from
lowering price to close
gap
.
given equilibrium we ,
firm would like to hire more labor ,
but that would require more
demand for output ,
which would require a lower Pt
.
In
long run ,
Ft will adjust to close
gap by shifting AS curve

rt LM I Me ,
Po .tl
Closing a
Negative Output Gap
LM I Me ,
Pott)
To ,t
→
rot,
I =LM ( Mt ,
P , .tl
IS
Yt
wt
Ns ( Wt , Oi )
Pt Asf As
f- AS
'
Wo , t Fo ,t
-
→
Wo ,t
Post -
Ndlwt ,
At ,
Kt )
Pott
AD
Nt Yt
Yt At Flkt ,
Nt ) Ye Ye =
Yt
-I I I I
No , t Nott Nt Yo ,tYo .tt Yt
Dynamic Response to Shocks
.
assume the economy initially sits in neoclassical equilibrium
'
then something exogenous changes and causes either the AD or AS to shift
↳
non
-
zero output gap in short run
↳
puts pressure on
Ftto shift
Monetary Shock :
Mtl
rt LM (
Mo
,
t.po.tl-LMIMi.t.pz.tl
LMLM.t.PI.tl
rz ,t= rat -
LM ( M , ,t,
Po ,
t )
r , ,t
-
←
←
- IS
Yt
wt
Ns ( Wt , Oz )
pt Asf
AS
'Ag
Wi ,
t
-
Pz ,t=Fz,t
-
• rt
P , ,t
-
•
r
Wo ,t
Po ,t=Fot
-
>
=Wz,t AD
'
Ndlwt ,
At ,
Kt ) AD
Nt Yt
Yt At Flkt ,
Nt ) Ye Ye =
Yt
-I I I I
No ,t N ,
,
't
Nt Yo
,tY, ,t
Yt
=Nz,t =Yz,t

Monetary Neutrality I Short Run vs .
Medium Run )
.
short run :
non -
neutral
.
AD shifts when Mt Changes ,
causing Yt LE. other real Variables ) to
change
↳
puts pressure on Ft
.
medium run :
neutral G Classical dichotomy holds
.
Ft adjusts to Close output gap
→ neoclassical equilibrium
Supply Shock :
Att
rt LM I
Mo
,
t ,
Po .
t )
LM I Mo,
t ,
P .
t )
ro ,
t -
→ LM I Mo,
t ,
P
'
,
t )
ri ,
t
→
rz ,
t
-
¥Wt
NS ( Wt , Ot )
Pt Asf Asf
'
As
→
→ AS
'
W 2 ,
t
Wo ,
t
Po it
= PT,
t
-
→ AS
' '
Nd Lwt ,
A
, it ,
Kt ) P . it •
Wi ,
t o
Pz ,
t = Fz ,
t
Nd Lwt ,
Ao,
t ,
Kt ) AD
Nt Yt
y ,
-
l Ke ,
Nt )
Ye Ye =
Yt
" t T
Ao,
t Fl Kt ,
N t )
neg .
Output
gap
-
I I I I I I
Ni ,
t No ,
t Nz , t
Nt Yo ,
t
Yi , t Yz , t
Yt
= Yo.tt =
Yi .tt
Supply Shock Dynamics
.
Output under -
reacts to At in short run
.
as prices get more flexible ( AS curve is
steeper ) , output reacts more
.
price level falls ,
but not
enough (
neg .
output gap )
.
in new short run
eqm
:
firm would like to produce more ,
but must lower price
-
downward pressure on Ft
.
eventually restore to neoclassical eqm

LM I
Mo
,
t ,
Pz
.
t )
rt LM I Mo,
t ,
P ,
t )
IS Shock :
At ti
T →
←
c LM I M t ,
Po .
t )•
O ,
ro ,
t -
IS
'
¥We
NS ( Wt , Ot )
pt Asf AS
'Ag←
W , it
-
P2
.EE?E•
r
.
,
Wo ,
t
Po , t
= To ,
t
-
A D
'
Nd Lwt ,
At ,
Kt ) AD
Nt Yt
Yt At Fl Kt ,
Nt ) Ye Ye =
Yt
-I I I I
No ,
t Ni
, t
Nt Yo ,
t Yi ,
t Yt
IS Shock Dynamics
.
After positive IS Shock ,
Yt E Pt rise
.
at new equilibrium , pos .
output gap
.
firm wants to reduce labor → need Ptt
↳ AS curve shifts in →
neoclassical
eqm
Phillips Curve
.
relationship btw output gap L change in prices
Pt
-
Pt -
,
=
Ft -
Pt -
i
t
T L Yt -
Ttt ) where Pt -
, is normalized to I
- -
actual inflation exp .
prev .
inflation
ITE = :
inflation rate expected to
Obtain b/w t
-
I E t
ITT =
ITE t V ( Yt -
YE )
Monetary Policy Cannot Permanently Increase Output !
.
can
temporarily raise output by increasing Mt
↳ but in med .
run ,
this puts upward pressure on prices da the effect goes away
↳
only results in
higher inflation

rt LM (
Mo,t
,
Po
,t)=LM(
M ,
,t ,
Pi ,
t
)
Fully Anticipated Increase in Mt so that
← LM I M ,
,
t.PO.tl
Pt also rises r , ,e= rat -
→
IS
Yt
we
Ns ( Wt , Ot )
Pt AS
AS
←
Wo ,t
-
Po ,t=PO,t →
AD
AD
Nt Yt
Yt At Flkt ,Nt ) Ye Ye =
Yt
-I 1
No ,t
Nt Yo ,t
Yt
Costless Disinflation
.
Fed announces in advance that it is
going to reduce Mt
↳
prices may adjust down in anticipation
↳ reduction in Pt W/O Change init
.
Fed needs to be credible
rt
LMLMo.t.PO.tl
rot -
IS
We
Ns ( Wt , Ot )
Pt Asf
"Ats
Wo ,t
Po
,t=PoFNdlwt ,
At ,
Kt ) AD
" t
" " '
N " " " " "
"
¥N'at
Nt
to ,t
Yt

Monetary Policy
Inefficiency in New Keynesian model
.
efficient in neoclassical model L Yt = Y ft )
.
want to get to Nk outcomes in medium run quicker
Optimal Policy
.
adjustment of Mt to implement Yt =
YI
-
contraction ary L counter cyclical ) policy in response to demand Shocks
.
move Mt G Ye in Opp .
directions
.
expansionary Laccomodative ) policy in response to
supply shocks
.
move Mt E Yt in same direction
.
consistent we price stability
Fiscal Policy
.
would affect IS curve →
affect rt →
affect distribution of Output across consumption
E investment
.
long implementation tags
-
better for
long run
-
exception :
extreme cases where
monetary policy is ineffective
IS E
Supply Shocks
.
positive IS Shock →
Yet ,
but doesn't affect Yet →
positive output gap
.
reduce Mt to counteract IS Shock
.
Supply shocks ( At or Ot ) affect Yf E cause Yt to react less than Ttt
.
increase Mt L lower I to accommodate positive supply shocks L At T or O et )
.
intuition :
FF needs to adjust to implement neoclassical eqm
.
Since Pt can 't
adjust
→
adjust Mt

LM ( Met,Post )
rt LMLMo.t.R.tl
Counteracting a Positive IS Shock
r .
,
e -
ILMIMo.t.Po.tl
contraction
any
hit
.
To ,t
→
IS IS
'
Yt
wt
NS ( Wt , Ot )
Pt Asf AS
P , ,t
- o
Wo ,t
-
Po ,t=FO,t ←
→
AD
'
Ndlwt ,
At ,
Kt ) AD -
-
AD
' '
Nt Yt
Yt At Flkt ,Nt ) Ye Ye =
Yt
-I 1
No ,t
Nt Yo ,t
Yt
rt
LMLMo.t.PO.tl
Counteracting a Positive AS Shock ( Att )
→
LMLMo.t.PI.tl
expansionary rat - → LMIM2.t.PO.tl
r
,
,tI
V2 ,
t
¥Wt
NS ( Wt , Ot )
pt
ASFASF
'
As
→
→ AS
'
Wo ,t
P2 ,t= Po ,t=Fot -
Ndlwt ,
Ait
,
Kt ) 7. t
- •
'
→
Ndlwt ,
A t ,
Kt )
ADAD'
Nt Yt
y ,
Flkt ,
Nt )
ye Ye =Yt
AO.tflkt.NL)
ft"
I 1
No ,t
Nt Yo ,t
Yt
Price Stability
.
no
change in price level
.
If price level is rising
→ contraction
any
.
If price level is
falling →
expansionary

Targeting Price
Stability
rt
-
can think about price stability as
meaning that the position of the LM
ro , t
-
Curve is
endogenously chosen such that the AD curve is perfectly
horizontal at a targeted Level
IS ↳
' '
effective
"
AD curve
Yt
P
t AS
To ,
t -
A De
I
u
Yo t
=
Yo.tt It
Price Stability : IS Shock
rt
ri ,
t
ro , t
-
→
IS IS
'
Yt
P
t AS
PT ,
t -
A De
=P , ,
t
I
u
Yo t
=
Yo.tt It
=
Yi ,
t
Price Stability : AS Shock
rt
To , t
-
ri , t
-
¥Pt AS AS
'
→
To ,
t -
A De
=P ,
,
t
I I
v
Yo t
=
Yott Yi ,
t
= Y #t
' t

When is price stability not a
good goal ?
.
price stability is not a good goal conditional on Shocks to Ft
↳ shift AS curve ,
but do not change YE
Price Stability
:
Ft Shock
rt
ri , t
-
To , t
-
IS
P ASYet AS
PT , t
- T
To ,
t -
A De
=
R , t
I
Yi ,
t
Hot =
Yott Yt

Intermediate Macroeconomics

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Intermediate Macroeconomics