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The Short-Run: IS/LM
Prof. Lutz Hendricks
Econ520
February 23, 2017
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Issues
I In the growth models we studied aggregate demand wasirrelevant.
I We always assumed there is enough demand to employ allfactors / sell all output.
I Why is this appropriate for long-run analysis?
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The Short and the Long Run
Short run: supply is elastic
I only demand mattersI IS/LM model
Long run: output is on its trend growth path
I only supply mattersI capital stock adjusts
growth models
Medium run: supply depends on prices
I demand and supply matterI price setting mechanisms push output towards trendI AS/AD modelI the transition from short to long run
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Why Isn’t There One Model?
In state of the art research, there actually is one model.It has the price adjustment frictions that give rise tounemployment, business cycles, ...It has capital accumulation that matter for long-run output(growth)
It has an explicity transition path between short run and long runequilibrium
I over time, prices adjust and demand becomes less and lessimportant
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Objectives
In this section, we are concerned with the short-run IS-LM model
You will learn:
1. how to set up and interpret the IS-LM model2. what its limitations are3. how to solve for the equilibrium4. how to analyze the effects of shocks and policies
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IS-LM Model
Key assumptions:
I Output is determined by aggregate demandI There is no supply sideI Prices are fixedI Closed economy
Think: economy in recession, with lots of unemployed resources.
We relax all of these assumptions later.
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IS-LM Model
Two markets
I Goods (IS). Money (LM)I In the background there is also a bond market
Two endogenous variables
I Output (Y). Interest rate (i)
Two policy variables
I Government spending (G). Money supply (M)
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The Goods Market: IS Curve
Aggregate Demand
Start from an identity
Z = C + I + G + X− IM
Z is aggregate demand / expenditure.For now: closed economy with X− IM = 0.Add behavioral assumptions to give it content.
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Consumption function
C = C(YD) = c0 + c1YD (1)
YD = Y−T: disposable income (after taxes and transfers)c0: “autonomous consumption” (intercept)c1: marginal propensity to consume (slope)s = 1− c1: marginal propensity to save
Consumption might also depend on wealth, interest rates, expectedincomes, etc.
I these are stuffed into c0
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Investment function
I = I(Y, i) = I + b1Y−b2i (2)
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Government
I Exogenous G and T.I G is government consumptionI T is tax revenue net of transfer payments
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Goods Market Clearing
Assumption: supply is perfectly elastic.
Y = C + I + G (3)= [c0 + I + G− c1T]︸ ︷︷ ︸
Z
+ (c1 + b1)Y−b2i (4)
Z: autonomous spending / demandSolve to get the IS curve:
Y =Z−b2i
1− c1−b1(5)
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Goods Market Clearing
Y
A
45°
ZZ
Demand
Income, Y
Dem
and
Z, P
rodu
ctio
n Y
Y
Equilibrium Point:Y ! Z
Slope ! c1
AutonomousSpending
Slope ! 1Production
What happens when theinterest rate i rises?
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IS Curve
IS! (for T! > T )
IS (for taxes T )
Inte
rest
, i
Y!
Output, YY
i
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Intuition: IS Curve
Why is IS downward sloping?
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Shifting the IS CurveOnly autonomous demand Z shifts ISExample: G ↑
I Excess demand → Need higher i to reduce II New IS curve shifted up
What else shifts IS?
Clearly distinguish moving along the curve vs. shifting thecurve!
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The Fiscal Multiplier
Y =Z−b2i
1− c1−b1(6)
I Increasing government spending by $1 =⇒ increasing Y by1/(1− c1−b1).
I This holds the interest rate constant (which will not be true inequilibrium)
I Intuition:
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The Fiscal Multiplier
Y
A
BC
DE
ZZ
ZZ!!
Income, Y
Dem
and
Z, P
rodu
ctio
n Y
Y
Y!
Y!
A!
45°
$1 billion
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Saving Equals InvestmentWe can also think about goods market clearing as equating savingwith investment.Private saving:
S = YD−C = Y−T−C (7)
Public saving:SP = T−G (8)
Total saving equals investment:
I = Y−T−C + T−G (9)
This yields goods market clearing
Y = C + I + G (10)
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The Money / Bond Market: LM Curve
LM Curve
The LM curve equates supply and demand of “money.”What is “money”?
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Money Demand
How to divide wealth between “money” and bonds?
I Money: liquidity benefitI Bonds: interest benefit
Division depends on
I transactions volume (nominal income)I interest rate
Money demand can then be written as
Md = $Y×L(i) (11)
$Y is nominal income (in dollars)
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Money Demand
M
Md
(for nominal income $Y )
Md!! (for $Y! > $Y )
Money, M
Inte
rest
rat
e, i i
M !
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Money Supply
Real world: money = [currency] + [checkable deposits]
Currency: controlled by CBCheckable deposits: created by banks
For now: assume that CB controls money supply
M = Ms (12)
Money market clearing:
Ms = $YL(i) (13)
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Money Market Clearing
M
Money DemandMd
Money SupplyMs
Money, M
A
Inte
rest
rat
e, i
i
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Money Demand Increases
M
A
A!!
Md
Ms
Md!($Y ! > $Y)
Money, M
Inte
rest
rat
e, i i !
i
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Money Supply Increases
M!!
A!
A
Md
Ms!Ms
Money, M
Inte
rest
rat
e, i i
M
i!
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Open Market Operations
I The markets for money and bonds are linked.I To increase the money supply, the CB buy bonds and pays
with currency.I The price of bonds rises =⇒ the bond yield i falls.I A complication: the CB has no direct control over the supply
of bonds / the bond interest rate.I open market operations do not always work
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Reading
I Blanchard / Johnson, Macroeconomics, ch. 3-4
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