IS-LM-BP
The Basic Model of Open Economy
Macro
INTRODUCTION
• Earlier we identified a role for fiscal policy: stabilising Output near the
full capacity or “natural” level
• Clearly in the simple model of the last section the equilibrium level of
output
– (a) can be influenced by fiscal policy (changes in G and T)
– (b) is not necessarily at capacity, or full employment
• This is because the assumptions of the model are very restrictive:
– no role for money or interest rates
– prices and wages are by assumption inflexible
• This is clearly not very realistic
• We relax the first restriction and look at interest rates
• Later we will add to the model and relax many of the restrictive
assumptions
Basic Structure of Model
• Divide the economy into three markets and
study how the interact
• Goods market – Demand side
– The simple model of the last section
• Money Market
– could expand to include other assets
• Balance of Payments
– connect with rest of world
• Mundell-Flemming Model – Nobel Prize
Goods Market (IS)
• This encapsulates the simple model of the previous section
• Goods Market Equilibrium
– Aggregate Supply (AS) = Aggregate Demand (AD)
– : GDP=Income: Y
• Aggregate demand (AD)
• Equilibrium – Plans realised
– AS=AD
– Y=AD
• Assume prices fixed
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Big issue
Is it reasonable?
Is it true?
Empirical evidence that true in the Short Run
• Just review: What are the sources of
demand for produced goods?
• AD=C+I+G+X-M
– Private consumption: C(Y, r,T, Wealth)
– Private Investment: I(r,Y)
– Government Cons & Inv : G
– Exports: X(Y*,e)
– Imports: M(Y,e)
• Plans vs actual i.e. model behaviour
– Can make the model as complicated as you like
– Size and sign of effects
• Equilibrium: AD=Y
AS=AD=Y
AD
AD
Y*
Y
• Example of Change in G
– Assume all except consumption are fixed
– “exogenous”
– G increases
AD2=C+I+G2+X-M
AD
AD1=C+I+G1+X-M
Y
• Fiscal Policy and Multiplier
AD
AD2
AD1
Y1*
Y2*
Y
• Think of other “shocks” that might effect
the economy in the same way
– Fall in interest rates
– Fall in taxes
– Rise in world income
– Increase in private investment (FDI)
– A depreciation in the exchange rate (more
later)
• The effect of shock is larger than its size
– More than one for one
• Y=fn(C) and C=fn(Y)
• Example:
– Y=C+I+G+X-M
– C=a+b(Y-T) a>0 0<b<1
– Y=a+b(Y-T)+I+G+NX
Y 
1
1 b
a  I  G  NX  
b
1 b
T
Why is Multiplier>1
• Initial change in government expenditure: DG
• Implies a change in income for some group: DY1=
DG
• This leads to a increase in their consumption
DC1= bDY1= bDG
• This in turn leads to a further increase in Y
representing income for some other group DY2=
DC1= bDG
• This leads to another increase in consumption
• DC2= bDY2= b(bDG)=b2DG
• This leads to another round of income
increase
• The process continues for an infinite
number of rounds
• Total change in income
– DY= DY1 + DY2 +…+ DYn +…
– DYn=bn-1DG
– DY= DG*[1+bb2+…+bn-1+…]
– DY= DG*[1/(1-b)]
• Warning FP not a panacea
– This is very simple model
IS: Output and Interest Rates
• Split variables that can effect Y
– endogenous : r (we will explain it later)
– Exogenous: all others e.g. G, e, T
• What happens when interest rates fall?
– Output rises: consume and invest more
• Ploti a graph of all the interest rates and the
associated Y from goods market
– Locus of Goods Market Equilibrium
– IS Curve
• Reduce interest rate
• Consumption and investment rise for every
level of income
• Result is higher eqm income
AD
AD2
AD1
Y
Stability?
r
IS
Y
• Maths
Y  C  I  G  NX
C     (Y  T )
I   0  1 r   2 Y
Y 
1
1  b  2
   0  G  NX
 T 
• Aside: Savings=Investment
1 r
1  b  2
THE IS-CURVE & Eqm
• The IS-curve is the locus of all combinations of r and Y consistent with
goods-market equilibrium
r
Y > Ye
Y < Ye
IS
0
Y
What makes it Eqm?
• If not on IS curve then we are not in equilibrium
• Plans not being realised so something will change
• We assume production adjusts
– If Y<AD then production will increase
– If Y>AD then production will fall
• Note this is an assumption
• This is a very simple model of AS
– AS adjusts to meet whatever is demanded
– Prices do not adjust
– Counter intuitive to some but empirically accurate
SLOPE OF THE IS-CURVE
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Ip = Ia + b.r (b <0) also let Ia be part of Ap (similar to Ca)
Equilibrium: Ye = Ep = Ap + c(Y- T) + b.r
DYe = DAp + c DY + b.Dr
and if DAp = 0, DYe = c DY + b.Dr
Thus:
Dr/DYe = (1-c)/b
Or:
Dr/DYe = (1-c+ct+z)/b, if we assume endogenous Taxes and
Imports
This is equivalent to slope of the IS curve (+/-)  negative.
Note, the more Ip (or Consumption, etc) is responsive to changes in r, the
larger is b
This in turn implies a lower slope coefficient (flatter IS curve)
Similarly, the less responsive Ip (or C or any element of Ep) is to Dr , the
steeper is the IS-curve.
SLOPE OF THE IS-CURVE
• IS1 is more elastic: Ep relatively responsive to changes in r
• IS2 is less elastic: Ep relatively un responsive to changes in r
r
IS2
IS1
0
Y
Movements of the Curve
• Movements
– in r represent movements along the IS curve.
– Changes in other variables represent a parallel
shift in IS e.g. change in G
DY=mult*DG
AD
r
DG
IS
Y
Y
SHIFTS OF THE IS-CURVE
• Outward shift: IS1 to IS2 when DG is > 0: Fiscal expansion
r
IS1
0
IS2
Y
Money Market (LM)
• People have a demand for money
– Liquidity preference: Money vs. Bonds
– Money : cash, current accounts, demand
deposits, little or no interest
– Bonds: proxy for any asset with a return
• Exact split is ambiguous
• Why money at all? Transactions
• Demand for liquidity increases as interest
rate falls
• A change in either M or r leads to a
movement along the demand for money
curve
• An change in Y leads to a shift in the curve
– Transactions demand
M
r
d
 m 0  m1 Y  m 2 r
Md(Y2,r)
Md(Y1,r)
M
• Money supply is fixed by central bank
• More on this later
• For the moment think of open market
operations
• CB buys/sell bonds on open markets
– Any asset in principle but almost always gov
bonds
– Uses cash or cheques drawn on itself
• Buying bonds: Money supply rises
• Selling bonds: Money supply falls
• Effectively Money supply is exogenous
– i.e. not a function of r or Y
– Central bank preferences (topic 4)
r
MS
Md
M
• What is the effect of an increase in Money
supply?
– Interest rates fall
r
M
• What about an increase in GDP
– More transactions so interest rates rise
Ms/P
r
Md2/P
Md1/P
M
Money Market Equilibrium
• When y increases to Md increases. Given Ms this leads to an excess
demand for money, so r increases to r2
• For any given increase in y, by how much will r have to increase to
restore equilibrium between Ms and Md?
• The depends on how responsive Md is to changes in r
• The higher the interest-elasticity of the demand for Money, the smaller
the increase in r necessary to restore equilibrium
• As is usual equilibrium occurs if and only if all plans are consistent
– How does this work here?
LM: Output and Interest rates
• As for IS, we split variables that can effect r
– endogenous : Y
– Exogenous: M
• What happens when output fall?
– Interest rate falls: seen this already
• Plot a graph of all the interest rates and the
associated Y from money market
– Locus of Money Market Equilibrium
– LM Curve
• Reduce G
• Income falls for every level of interest rate
and money demand falls with it
• Result is lower eqm interest rate
Ms/P
LM
r
r
L2
L1
M
L ( r , Y )  m 0  m 1Y  m 2 r
M
s
 M
M  L
Y 
M  m2r  m0
m1
Y
Movements
• Movements in y represent movements along
the LM curve.
• Changes in other variables represent shift in
LM M M
s
1
s
2
LM1
r
r
LM2
Md
M
Y
SHIFTS OF THE LM-CURVE (2)
• The Central Bank (ECB, Federal Reserve, Bank of England….) is the main
agent for implementing monetary policy
• The CB can expand the Money Supply by Open Market purchases of
bonds: this adds to Banks’ reserves and enables them to expand lending,
etc.
• Similarly, Open Market bond sales can leas to a fall in Ms
• The CB can also change the rate at which it is prepared to lend to banks
(Refinancing Rate, Federal Funds rate, REPO rate,…)
• This impacts on the cost of funds to banks and therefore on the rates
which they charge borrowers. It may also influence the amount of liquid
reserve assets which banks wish to hold and therefore their willingness
to expand credit, etc.
• More about the details of monetary policy later.
SHIFTS OF THE LM-CURVE (3)
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Suppose the Central Bank expands Ms (and Ms/P as P is fixed)
This leads to excess of Ms over Md
Result: equilibrium r falls
The immediate effect is to displace the combination of (r, y) consistent
with monetary equilibrium downwards
• This corresponds to a rightwards (or downwards) shift in the LM curve
• But will the fall in r lead to an increase in Aggregate Demand and
therefore in y?
• It will, and therefore we have to turn again to the IS-curve and the
interaction between IS and LM.
IS & LM together
• Both markets are linked
– Both imply a link between Y and r
– Money: Y -> Md-> r
– Goods: r-> I-> Y
• The intersection of the two curves gives the
equilibrium
– Jointly determines Y and r
• For any policy or shock,
– work out which exogenous variable moves
– Which curve moves
– New intersection is equilibrium
IS and LM
• At E, there is both real and monetary equilibrium
• Understand the forces bringing economy to equilibrium
r
Y >AD
Md < Ms
Y < AD
Md < Ms
Y > AD
Md > Ms
E
Y < AD
Md > Ms
0
LM
IS
y