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Lecture 8
Short Run Output Determination:
The IS/LM/AS Framework
Mark Gertler
NYU
Intermediate Macro Theory
Spring 2015
0
Motivation
Competitive equilbrium neoclassical model
Output always at "full employment"
Money only aects nominal variables
Di cult for model to explain:
Recessions and Depressions
The eect of monetary policy on the real economy
The eects of scal policy
1
A Model of the Short Run: Preliminaries
Start with the competitive equilibrium model and introduce 3 frictions: (i) Money
(ii) Imperfect competition
(iii) Imperfect price adjustment
(i) permits introducing nominal variables and an analysis of monetary policy (iii) permits analyzing price setting behavior by rms as a prelude to introducingimperfect price adjustment
Cant model price adjustment with perfect competition since rms take pricesas given
(i), (ii) and (iii) imply: output can be below "full employment"
monetary policy can aect the real economy2
Model Ingredients
Consumption goods only. Later we add investment and government spending.
Eventually introduce nancial market frictions.
The model includes households, rms and a central bank:
The representative household consumes a nal good Ct, supplies labor Nt, holdsreal money balances Mt=Pt, saves in the form of private bonds Bt (which, inequilibrium will be in zero net supply, since everyone is the same).
Firms are monopolistic competitors and each produce a dierentiated productYt (f) using labor Nt (f). These rms set nominal prices Pt (f). f denotes rmf:
The central bank controls the money supply Mt:
3
Resource Constraints and Money Supply
Resource constraintYt = Ct (1)
Monetary policy: Central bank sets Mt = M t:Mt =M t (2)
We next derive aggregate consumption demand and money demand by households Doing so allows constructing IS/LM model to determine output and interestrates given nominal prices
Output may be below full employment
We then derive the aggregate supply side from labor demand and supply Permits deriving the gap between output and full employment output
Permits analysis of price adjustment.
4
Household Decision Problem
Goal: Derive (i) consumption demand (ii) money demand and (iii) labor supply
Maximization problem problem: Choose Ct; Bt;Mt and Nt to solve
max1
1 C1t + am
1
1 (Mt
Pt)1 an
1 + nN1+nt +
1
1 C1t+1 (3)
Ct +Mt
Pt+Bt
Pt=Wt
PtNt (4)
Ct+1 =Pt
Pt+1
Mt
Pt+ (1 + it)
Pt
Pt+1
Bt
Pt(5)
where ; n; an; am > 0.
Money in the utility function captures convenience yield.5
Unconstrained Maximzation Problem
Choose (BtPt ;MtPt; Nt) to solve
maxf 11 (
Wt
PtNt Mt
Pt BtPt)1 + am
1
1 (Mt
Pt)1 an
1 + nN1+nt
+1
1 (Pt
Pt+1
Mt
Pt+ (1 + it)
Pt
Pt+1
Bt
Pt)1g
First order condition for labor supply
Wt
PtCt = anN
nt (6)
6
Consumption and Money Demand
First order condition for BtPt :
Ct = (1 + it)
Pt
Pt+1C
t+1 (7)
First order condition for MtPt
Ct =
Pt
Pt+1C
t+1 + am(Mt=Pt)
(8)
Absent the non-pecuniary return am(Mt=Pt); the household would not holdmoney so long as it > 0 :
If am = 0 and it = 0, bonds always dominate.
7
Consumption and Money Demand (con0t)
Household rst order condition implies relation for consumption demand
Ct = (1 + it)
Pt
Pt+1C
t+1 !
(Ct )
1 = [(1 + it)Pt
Pt+1C
t+1]
1 !
Ct =1
[(1 + it)PtPt+1
]Ct+1 (9)
Consumption demand depends inversely on (1 + it) PtPt+1 and positively on Ct+1 Intuition comes from permanent income hypothesis that we studied earlier
A rise in interest rates induces an increase in saving and a decline in Ct Desire for consumption smoothing: Ct+1 "! Ct "
8
Consumption and Money Demand (con0t)
A relation for money demand follows from the rst order conditions for BtPt andMtPt:
Ct = (1 + it)
Pt
Pt+1C
t+1
Ct =
Pt
Pt+1C
t+1 + am(Mt=Pt)
Combining yields a relation for money demandMt
Pt= (
1
it+ 1)amCt
Money demand depends inversely on its opportunity cost it:
Depends positively on Ct
9
Aggregate Demand: IS Curve
Aggregate DemandYt = Ct
Ct =1
[(1 + it)PtPt+1
]Ct+1
Combining yields an IS curve
Yt =1
[(1 + it)PtPt+1
]Yt+1
Given PtPt+1 and Yt+1, IS curve is downward sloping in (Yt; it) space.
An increase in it increases the real interest rate, which reduces spending.
Yt+1 " shifts IS curve out: PtPt+1 " shifts it in.
10
it
Yt
Yt =1(
(1+i)Pt
Pt+1
) Yt+1
I
S
Figure 1: IS Curve.
1
it
Yt
I
S
I
S
Figure 2: Increase in Yt+1
2
it
Yt
I
S
I
S
Figure 3: Increase in PtPt+1
.
3
Monetary Sector: LM Curve
Monetary SectorMt
Pt= (
1
it+ 1)amYt (10)
Mt =M t
LM Curve:M t
Pt= (
1
it+ 1)amYt
Given Pt, upward sloping in (Yt; it) space
Yt "! money demand " ! it " to reduce money demand Mt "! LM Curve shifts out: Rise in real money suppy! it down to raise moneydemand
Pt #! M tPt "! LM curve shifts out.11
it
YtL
M
MPt=(1it+ 1
)amYt
Figure 4: LM Curve
4
it
YtL
M
L
M
Figure 5: Increase in M t
5
it
YtL
M
L
M
Figure 6: Increase in Pt
6
Fixed Price IS/LM Model
Sticky price assumption:Pt+i = P t+i; i = 0; 1
! IS/LM jointly determines (Yt; it)IS:
Yt =1
[(1 + it)P tP t+1
]Yt+1
LM:
M t
P t= (
1
it+ 1)amYt
12
it
YtL
MI
S
Y et
iet
Figure 7: IS/LM Model
7
Some Comparative Statics
Fixed Price IS/LM:
Yt =1
[(1 + it)P tP t+1
]Yt+1
M t
P t= (
1
it+ 1)amYt
Yt+1 " (rise in optimism)! IS curve shifts out! Yt ", it " M t " (expansionary monetary policy)! LM curve shifts out ! it # Yt " :
P tP t+1
" Increase in expected deation ! curve shifts down Yt #, it # If zero lower bound on it binds, drop in Yt increases.
Explains central bank aversion to deation.
13
it
YtL
MI
S
Y et
iet
Figure 8: Impact of Increase in Yt+1
8
it
YtL
MI
S
Y et
iet
Figure 9: Increase in M
9
it
Yt
L
MI
S
Y et
iet
Figure 10: Increase in PtPt+1
with zero lower bound on i
10
Flexible Price IS/LM
Suppose Pt adjusts so that Yt = Y t (full employment output)/ For now take Y t as given Shortly we introduce supply side to determine Y t :
Flexible price IS/LM model:
Y t =1
[(1 + it)PtPt+1
]Y t+1
M t
Pt= (
1
it+ 1)amY
t
Given expected deation, ex price IS/LM determines (Pt; it): Simple Quantity Theory Holds: M t "! Pt " proportionately: No eect on Y t :
14
it
YtL
MI
S
Y t
it
Figure 11: Flexible Price IS/LM model
11
Aggregate Supply
Supply side needed for: Deriving full employment output Y t Describing how prices adjust over time
We rst derive aggregate labor supply curve Relates real wage to aggregate employment
We then derive rm labor demand labor demand Flexible price case: rms choose price, output and employment each period
Helps determine full employment output Fixed price case: Firms choose output and employment to meet demand
So long as it is protable
15
Aggregate Labor Supply
Firm f uses the following technology to produce output Yt (f) with employmentNt(f) :
Yt (f) = AtNt (f)
Aggregating across rmsYt = AtNt (11)
Use (11) and the resource constraint (1) to eliminate Yt and Ct in the householdlabor supply curve:
Wt
Pt= anN
nt C
t (12)
= anA
tN
n+t
! Real wages vary positively with employment.
16
wP
N
N s
Figure 12: Aggregate Labor Supply
12
Aggregate Labor Demand
Monopolistically competitive rm chooses (Pt(f); Yt(f); Nt(f)) to solve
maxt =Pt (f)
PtYt (f)Wt
PtNt (f)
subject to (i) demand curve and (ii) production function:
Yt (f) =
"Pt (f)
Pt
#"Yt
Yt (f) = AtNt (f)
Two cases: Flex Price (long run); Fix Price (short run). Flex Price: Choose (Pt(f); Yt(f); Nt(f)) to maximizes prots
Fix Price: Choose (Yt(f); Nt(f)) to meet demand, so long as protable
17
Aggregate Labor Demand: Flexible Price Cases
Use constraints to eliminate Yt(f); Nt(f) ! unconstrained problem:
maxPt(f)
t =Pt (f)
Pt
"Pt (f)
Pt
#"Yt Wt
Pt
Pt(f)Pt
"Yt
At
where the rm takes WtPt ; At; and aggregate output Yt as given.
First order necessary condition (marginal revenue = marginal cost)
(1 ")"Pt (f)
Pt
#"Yt "
WtPt
At
"Pt (f)
Pt
#"1Yt = 0
18
Aggregate Labor Demand: Flexible Prices (cont)
price markup over marginal cost ! Rearranging rst order condition:
Pt (f)
Pt= (1 + )
WtPt
At
1 + =1
1 1=" Firm sets price Pt(f)Pt as a markup over marginal case Markup varies inversely with demand elasticity ":
As "!1 (perfect competition), ! 0 : i.e. price = marginal cost.
19
Flexible Price Equilbrium Employment
Pt (f)
Pt= (1 + )
WtPt
At
Since all rms are identical: Pt (f) = Pt !
1 = (1 + )
WtPt
At!
At = (1 + )Wt
Pt
! Marginal product of labor At = markup over real wage WtPt Use aggregate labor supply curve to eliminate WtPt :
At = (1 + )anA
t (N
t )
n+
Nt exible price equilibrium employment (i.e. full employment).
20
Flexible Price Equilbrium Employment and Output
Nt and Y t determined by: Labor market equilibrium
At = (1 + )anA
t (N
t )
n+
Production function
Y t = AtNt Eliminating Nt
At = (1 + )anAnt (Y
t )
n+ !
Y t = (1
(1 + )an)
1
n+A
1+n
n+t
= 0! Y t ; Nt = competitive equilbrium values Y ot ; Not > 0! Y t ; Nt < Y ot ; Not
21
WP
N
Y
N
NoN
At
N
Y
NS
AwP
Aw/P = 1 +
Figure 13: Labor Market Equilibrium: Flexible Prices. N is ht eflexible price equilibriumamount of labor, while N o is ht ecompetitive equilibrium amount.
13
Aggregate Labor Demand: Fixed Price Case
With xed prices the rm produces to meet demand so long as it is protable: Protable so long as markup t(f) = 0 (i.e. price marginal cost).
Since Pt(f) xed at P t(f); t(f) varies
P t(f)
Pt= (1 + t(f))
WtPt
At;
Symmetric equilibrium: All rms charge P t(f)! P t(f) = Pt !
1 = (1 + t)
WtPt
At!
At = (1 + t)Wt
Pt
t varies inversely with WtPt : since price xed, markup falls as marginal cost rises.
22
Aggregate Demand and the Markup: Fixed Price Case
Given Yt: Nt and t determined by Labor market equilibrium
At = (1 + t)anA
t (Nt)
n+ (13)
Production function
Yt = AtNt (14)
(13) and (14) !inverse relation between Yt and t (countercyclical markup):1
1 + t= an
Y
n+t
A1+nt
(15)
(As we show later), ination varies inversely with t Firms raise prices when markups low, and vice-versa
23
Fixed Price IS/LM/AS Model
IS Curve:Yt =
1
[(1 + it)P tP t+1
]Yt+1
LM Curve:
M
Pt= am
1 1
(1 + it)
!1Yt
AS Curve:
1
(1 + t)= an
Y
n+t
A1+nt
IS/LM determines (Yt; it): Given Yt; AS determines t t then aects ination, as we show later.
24
Flexible Price IS/LM/AS Model
[(1 + it )PtPt+1
] exible price (i.e. natural) real rate of interest
it exible price nominal rate (given PtPt+1) IS Curve:
Y t =1
f[(1 + it ) PtPt+1]gY t+1
LM Curve:
M
Pt= am
1 1
(1 + it )
!1Yt
AS Curve:
1
(1 + )= an
Yn+t
A1+nt
25
WP
N
Y
N
i
YY e
ie
NoNNe
At
NNe
Y
Ye
NS
Y
LMIS
Figure 14: Price Rigidity Case
14
General IS/LM/AS Model
IS Curve:Yt =
1
f[(1 + it) PtPt+1]gYt+1
LM Curve:
M
Pt= am
1 1
(1 + it)
!1Yt
AS Curve:
1
(1 + t)= an
Y
+nt
A1+nt
Two polar cases: Fix Price: Pt xed ! IS/LM determines Yt; it and AS determines t Flex Price: xed ! AS determines Y t and IS/LM determines Pt; it
26
Fixed Price IS/LM/AS with Output Gap
IS Curve:Yt =
1
[(1 + it)P tP t+1
]Yt+1
LM Curve:
M
Pt= am
1 1
(1 + it)
!1Yt
AS Curve (after combining AS curves for x and ex price models):
1 +
(1 + t)= (
Y tYt)+n
"Markup gap" 1+(1+t)
varies inversely with output gap
As we show later, ination varies positively with 1+(1+t)
and hence with YtYt
27
Some Comparative Statics
Yt+1 "! Yt "; it "; YtYt#; t #
M t "! Yt "; it #; YtYt"; t #
Y t # (supply shock)!Y tYt#; t #
Later we will show that ination moves inversely with t and thus inversely withY tYt
28