Transcript IS-LM Model 01 File

 For countries like Japan, the opposite is true; the high
private sector’s resource surplus (i.e.: S > I) and the
small budget deficit leads to relatively high TRADE
SURPLUS for Japan. In other words, Japan’s private
savings are much more than its private investment.
And these excess savings are partly used to finance
budget deficits and at the same time, to lend to other
countries which allow the rest of the world buy more
goods and services from Japan then they sell to
Japan. So internal resource surplus of Japan is
reflected on its external account as equivalent
surplus.
IS-LM Model of the Economy
 Our Simple Keynesian Model was simple in the sense that it did
not allow an interaction between the financial variables and the
output of the economy. In other words, aggregate demand
(C+I+G+X) was assumed to be not a function of financial
variables such as INTEREST RATES. But we know that in the
real world, good markets (where production and sales of goods
take place) and the FINANCIAL MARKETS (where the purchase
and sales of financial assets take place) are interdependent. In
other words, what happens in goods market (in terms of change
in Y and prices of goods) will affect the financial variables such
as stock prices, bond prices, interest rates and exchange rates.
And what happens to financial variables will affect Y through
effect on aggregate demand for goods.
 So, in this part of our lectures we extend the Simple Keynesian
Model to allow for these linkages between financial variables
and the goods market.
ECONOMY
(FINANCIAL)
ASSETS
MARKETS
R
Y
GOODS
MARKET
 In the IS-LM Model, we assume that the FINANCIAL

1.
2.
3.
SECTOR is made up of only 2 markets: MONEY
MARKET and the BOND MARKET. (In the real world,
we have additional types of asset markets such as
STOCK MARKET, GOLD MARKET and others).
So in the IS-LM Model, the economy is made up of
only 3 markets:
GOODS MARKET
MONEY MARKET
BOND MARKET
 To analyze the equilibrium of the economy
we need to focus on only two markets if we
have 3 markets. Due to famous LAW of
Economics called WALRAS’ LAW, if there are
N markets in the economy, and if N-1 of them
are in equilibrium, automatically Nth one must
also be in equilibrium. So IS-LM Model
analyses the equilibrium of the economy by
focusing on the interaction between GOODS
MARKET and the MONEY MARKET.
 In what follows, we try to introduce the basic
algebraic relationships of the goods market
and then we try to do the same for the Money
Market of the IS-LM Model (Note: We will
explain later why this model is called IS-LM
Model)
GOODS MARKET
1. Y= C + I + G + X Equilibrium condition for
2.
3.
4.
5.
the good market
C= a + b(1-t)Y
I= e - dR
d>0
G=G
X=g-mY-nR m, n>0
 As you can see the differences between the
above model (of the good market) and the
simple Keynesian model are the inclusion of
R (Interest Rate) as an additional variable as
a variable on the aggregate demand side of
the economy through INVESTMENT and NET
EXPORTS functions.
 Eq. (3): I = e - dR implies that total investment
spending is negatively affected by R. As R
↑I↓. (As the cost of borrowing from the
banks ↑, naturally firms reduce their spending
for new capital goods). e represents the
amount of investment spending which
depends on other factors such as business
optimism about the future profits, technology
and others.
 X= g-mY-nR means that Net Exports (Trade Balance) is
respectively affected both by Y and R. As Y ↑ we know that M
(Imports) will ↑leading to a fall in X. HOW ABOUT the negative
relationship between X and R? As R↑ X↓! WHY?
 As R↑ interest rates on domestic bonds ↑, this makes
domestic bonds more attractive than foreign bonds leading to
increase in relative demand for domestic bonds by domestic and
foreign portfolio investors. This leads to rising capital in flow to
the domestic economy which raises the demand for domestic
currency.
 Higher demand for domestic currency leads to appreciation of
the exchange rate making exports relatively more expensive
and imports cheaper. And this leads to deterioration of trade
balance: R ↑X↓.
 So the key insight of the new Goods Market
relationships (of the IS-LM model) is that
FINANCIAL SECTOR affects the GOODS
MARKET (REAL SECTOR of the economy)
mainly through change in INTEREST RATES.
 R↑ X↓ AD↓Y↓

I↓
HOW ABOUT THE FINANCIAL
SECTOR?
 Earlier we said that to analyze the equilibrium of the
financial sector, we need to focus only on one of the
two markets. And here we analyze how the
equilibrium in MONEY MARKET is maintained;
 Just like any other market, Money market can be
analyzed by focusing on the DEMAND and the
SUPPLY sides of the market.
 We first analyze the SUPPLY SIDE OF MONEY
MARKET.
 We assume that MONEY SUPPLY is exogenously
given to the economy by the government. And
government can change money supply (MS) any time
and in any amount it wants to!
 We define and measure Money Supply using
a “narrow measure” of money called M1. M1
is made up of currency in circulation +
Demand deposits at the banks
 So MS = C.C +D.D
 C.C = Currency in Circulation
 D.D =Demand Deposits (Checking Account)
NOTE:
 In the real world, the actual process of
bringing about a desired change in MS is not
as easy as it looks. Government can change
MS only indirectly through same policy
instruments which primarily include:
1. OPEN MARKET OPERATIONS
2. DISCOUNT RATES
3. RESERVE RATIO
 Read from your textbooks and other books how these policy
instruments can be used to alter Ms!!
 So, what is the message we should get from this description of
Ms!
1. At a given point in time Ms is EXOGENOUSLY GIVEN to the
Money Market and therefore to the ECONOMY by the policy
makers.
That is why Ms is a POLICY VARIABLE in our model.
(Additional policy variables are G and t which affect the
economy through their effects on Aggregate Demand!)
2. Government can change Ms for its policy purposes, leading to
disequilibrium in the money market which, as we will see, cause
changes in R. And changes in R will affect Y in the way
described before.
 To analyze the Money Market Equilibrium
and what happens when this equilibrium is
disturbed, we need to analyze DEMAND
SIDE OF THE MONEY MARKET (as well)
and then put the Supply and Demand Sides
together!
WHAT IS THE DEMAND FOR
MONEY?
 Md (DEMAND FOR MONEY) is simply the
total amount of Money (in the form CC+DD)
that households and the firms would like to
hold at a given point in time.
WHY DO HOUSEHOLDS (consumers) AND
THE FIRMS NEED or DEMAND MONEY?
 There are three Motives for Demand for
Money (which is actually a demand for an
asset which does not earn an interest!)
MOTIVES FOR MONEY
DEMAND
1. TRANSACTIONS MOTIVE
2. PRECAUTIONARY MOTIVE
3. SPECULATIVE MOTIVE
1. TRANSACTIONS MOTIVE
 An important percentage of the existing
demand for Money is the Transactions
Demand for Money. We need to hold money
in order to finance our transactions whose
volume is a positive function of our income (Y)
level.
 So TRANSACTIONS DEMAND for MONEY
increases as Y ↑!
2. PRECAUTIONARY MOTIVE
 We hold money also for emergency purposes
which is called precautionary motive. So
some part of our Md is due to precautionary
motive. And this PRECAUTIONARY
DEMAND FOR MONEY also positively
depends on the level of Y. As Y↑ Amount
of money demanded ↑for precautionary
reasons.
3. SPECULATIVE MOTIVE
 Some people (and firms) may hold money for
speculative reasons. In our model the other asset (in
addition to money) is the BONDS. So speculation
about the possible decline in Bond Prices in the
future may make some people hold some money to
take advantage of a possible decrease in bond prices.
Remember that low bond prices automatically imply
higher interest rates on these bonds.
 So, if the present interest rates are perceived to be
relatively low (meaning that the present bond prices
are perceived to be high) speculators will increase
their demand for money so as to be readily to buy
bonds when the bond prices fall.
 So, in our IS – LM Model SOME PART of the
DEMAND for MONEY is the SPECULATIVE
DEMAND for MONEY which is negatively
affected by R!
 As R (meaning Bond Price ), speculative
Demand for money ,
 As R speculative demand  for money.
 The above 3 motives for Money Demand
gave rise to the following mathematical
relationship between Md (Money demand)
and Y and R,
 Md = Pf (Y, R)= P (kY- hR) k > 0 , h > 0
 Md=Amount of money Demanded depends
on Y and R, and P ( Price level )
 As Y  Md 
 As R  Md 
 If P (price level for goods) , Md will automatically
increase proportionately.
 In the other words, given the values of k and h (which
measure the sensitivity of Money demand to change
in Y and R), we have a Real Demand for money;
which is the demand for money measured in units of
goods .If P (price of a unit of good) (amount of
money in units of dollar) will increase in proportion to
increase in P to keep the real demand for money
same as before.
 Read this from text books!
 Md = P (kY - hR)
MONEY DEMAND FUNCTION!
 So money demand (in nominal terms)
depends on P,Y and R.
 H1 P  Md  (proportionately)

Y  Md  (Increase depends on k)

R Md  (decrease depends on h)
MONEY MARKET
EQUILIBRIUM CONDITION
 Ms = Md = P( kY- hR )
 Ms  POLICY VARIABLE exogenously given by the




government
P  PREDETERMINED VARIABLE
P is given to the economy at the beginning of each
period by the firms, that is why it is called
Predetermined Variable!
It is determined in the beginning of each
period .Firms can unexpectedly change P if there are
some shocks to their costs of production!
Y and R are called ENDOGENOUS VARIABLES.
(They will be determined by the interaction of the
goods market and money market).
A PARTIAL EQUILIBRIUM
ANALYSIS OF MONEY MARKET
 (Partial means: We are not analyzing the
money market in a general equilibrium frame
work which includes goods market
equilibrium and their interaction with each
other. We will do this later when we fully
develop graphical IS-LM Model.
Ms
R
E0
Shift Variables
RE
Md (P, Y)
M (Quantity of Money)
M0
 Suppose government fixed Ms at M0.
 So Ms curve is vertical curve at M0, (This means that




in R has no effect on Ms. That’s why it is vertical! )
Md curve is negatively sloped!
An ↑ ın R  Md ↓ [due to lower speculative demand
for money]
↑ in P and ↑ in Y will shift the Md curve to the right. İn
other words, Md will be higher (at each interest rate)
when P↑ or Y↑! Higher P and higher Y increases the
DEMAND for money)!
Given constant Ms at M0, and given P and Y, Money
market will be in equilibrium at E0 which results in RE.
To see what happens if Ms↑ (by the government)
look at the following diagram!
R
MS0
E0
R0
MS1
A
E1
R1
Md(P0, Y0)
M0
M1
M
 When Ms ↑ from M0 to M1, Ms curve shifts to MS1,
from MS0. At the initial equilibrium interst rate (R0)
and given value of P0 and Y0, the means we have
Excess Supply of money; M1>Md0(=M0)
 M1: New Money Supply
  Excess Supply of Money People attempt to get
rid of excess money balance by buying the
alternative asset (bonds) Demand for Bonds ↑ 
Bond Prices (Bp) ↑R↓
 As R↓  Md↑ and this process continues until R↓ by
a sufficient amount which taken place at E1 (at which
point Md=M1=MS).
 So the key variable in adjustment of the money
market to emergence of any excess supply or exess
demand condition is the INTEREST RATE (R):
 A-) If we have Ms>Md (Excess Money Supply)
 R↓  Md↑ Process continues until Ms=Md !!!
 B-) If we have Ms<Md (Excess Demand for money)
 R↑Md↓The process continues until Ms=Md !!!
 Notice that:
 This adjustment mechanism is PARTIAL
because is does not tell us what will happen
to Y as R↑ or ↓. And if Y changes as a result
of change in R, this will cause additional
change in MONEY MARKET! IS-LM Model
will tell us how this happens!
 Suppose P↑ or Y↑ what happens?
R
Ms
E1
R1
R0
A
E0
Md1(P1,Y0)
Md0(P0,Y0)
M0
MdA
Y
 If P↑ from P0 to P1 Md curve will shift from Md0 to Md1.
So at the initial interest rate (R0), given a fixed Ms=M0,
thiss will mean EXCESS DEMAND for money since
the new level of Md will be given by point A (MdA).
Excess Demand for money will make people to
attempt to sell of their bonds and convert (at least
some of them) to cash to bring their money balances
to their desired level. As Bond Prices↓ R will ↑. Then
increase in R will continue until R=R1and the money
market is back in equilibrium at E1.
 NOTE:
Same analysis applies to changes in Y.
NOW WE ARE READY T INTRODUCE IS –
LM MODEL OF THE ECONOMY:
 IS represents the goods Market Equilibrium condition





of the economy.
Originally when this model was developed for a
closed economy with no public sector, goods market
equilibrium condition was given by I = S!
LM represents the Money Market Equilibrium
condition.
L Demand for money (Liquidity)
M Supply of Money
M=L
MATHEMATICAL STRUCTURE
OF THE IS –LM MODEL
 GOODS MARKET MONEY MARKET
1. Y = C + I + G + X
2. C = a + b (1-t)Y
3. I = e – dR
4. G = G
5. X = g - mY - nR
6. Ms = Md
7. Ms = M
8. Md = P (kY - hR)
 In IS - LM model for the ECONOMY to be in
EQUILIBRIUM we need to satisfy the eq. conditions
for both the Money Market and the Goods Market!
 In other words for the economy to be in equilibrium
we require:
 1. Y = C + I + G + X
and
6. Ms = Md at the
same time.
 So both GOODS M. and MONEY M. have to be in
EQUILIBRIUM for the ECONOMY to be in
equilibrium.
CLASSIFICATION OF
VARIABLES IN IS - LM MODEL
 EXOGENOUS VARIABLES  a, e, g
 So, same autonomous components of aggregate demand such as a, e,






and g are called exogenous variables.
POLICY VARIABLES  G, T, and Ms
Policy variables are also exogenous variables but we treat them
separately.
ENDOGENOUS VARIABLES  Y and R
PREDETERMINED VARIABLE: P
So, given the values of exogenous and policy variables (together with
the values of the structural parameters of the model which are the
coefficients like b, d, m, n, and h) and the value of the predetermined
variable (P), the model determine the equilibrium value of Y and R
(Endogenous variables).
EQUILIBRIUM VALUES OF Y AND R are those values of Y and R
which will emerge when GOODS MARKET and the MONEY
MARKET are in equilibrium, given the values of exogenous, policy,
and predetermined variables.
GRAPHICAL TOOLS OF IS - LM
MODEL
R
LM (Curve)
E0
R0
IS (Curve)
Y0
Y
IS CURVE
 IS curve is a negatively sloped curve in (Y-R) space showing all




the possible combinations of Y and R at which the Goods
Market will be in equilibrium. The location of IS curve depends
on the values of , G, t, a, g, e.
A given  in G, a, g, or e will shift the IS curve to the right. A
given  will shift it to the left in a parallel fashion. (No change in
slope).
A given  t() will rotate the IS curve downward (upward) by
changing its slope. (We will explain this later).
So along the IS curve, goods market is in equilibrium meaning
that the values of (Y, R) are such that Y= AD= C+I+G+X at each
point on the IS curve.
To understand why IS curve is negatively sloped look at the
following example:
R
C
RB
B
(Excess Supply of
goods)
RA
A
D
(Excess D for
goods)
(G, t, a, e, g)
YC
YA
M
 At A; YA=ADA (goods M. equilibrium). In
other words, the values of (YA,RA) are such
that the resulting values of CA, IA and XA (at
these values of YA and RA), given the values
of G, t, a, e, and g, will be such that
YA = CA + IA + G + XA.
 Suppose R  from RA to RB. At point B, Y=YA,
but R=RB!.
 At B we will have EXCESS SUPPLY of goods
in the goods market. Because R  I  X
 ADYA>ADB (Excess Supply of goods).
 For the goods market to return back to equilibrium, we need




Y=AD.
So at a HIGHER INTEREST RATE (such as RB), the only way
to return back to equilibrium is to have LOWER Y (such as YC).
So starting from a point of equilibrium on the IS curve, an  in R
will require a  in Y for the goods market to return back to
equilibrium.
Similarly you can try and see yourself that a point such as D is a
point of EXCESS DEMAND for goods market.
So in order to return back to equilibrium (after lowering interest
rate from C to D (from RB to RA) we need to have an  in Y.
(Because: lower RAD (due to  I and  X) and this
necessitates an  in Y for equilibrium.
SHIFTS IN IS CURVE
R
RA
A
B
IS1
IS0 (G, t, a, e, g)
YA
 If a, e, g, or G ↑(↓) this will lead to a parallel
rightward (leftward) shift in IS curve. Why?
After the ↑ in a or e or g or G at each interest
rate we will have a HIGHER AD than before!
(C + I + G + X = AD ↑)
 So for the goods market to be in equilibrium
we will need to have a HIGHER Y (than
before).
 If the value of t changes IS curve will rotate!
(its slope will change!
The effect of an  in t on IS curve
R
B
RB
RA
RC
A
RD
C
D
IS(t1)
YA
YD
IS(t0)
 The reason why a ∆ in t will rotate the IS curve in the
way described above is as follows:
 ∆ t affects AD through its effect on Yd (Disposable
Income) and therefore through its effect on C which
depends on Yd.
 The above rotation suggests that at low-income
levels such as YA, a given in t will require a in R
given by the distance between B and A for the goods
Market to return back to equilibrium. However if the
same  in t is taken place at a higher Y level (such as
when Y=YD), we need to have a much bigger  in R
(from RC to RD) for the goods market to return back to
equilibrium. On the other hand when Y=0, there is no
∆ in R required!
 To understand the logic of this you have to focus on the effect of
a given change in t on AD through its effect on C!
 At lower Y levels, a given in t will reduce C by a lower amount
simply because its effect on Yd (Disposable Income) will be
lower.
 Therefore the amount of excess supply that will result from a
given in t will be smaller. And therefore with a relatively smaller
 in R AD can  by enough amount to eliminate the relatively
small excess supply.
 However when Y is relatively high, same  in t will lead to
relatively larger  in Yd and therefore relatively lower  in C and
in AD. And the elimination of this relatively bigger excess supply
will require relatively bigger  in R(such as a  from RC to Rd!)
LM CURVE
R
LM (P0 M0)
Excess supply of money
C
RD
D
A
RA
B (Excess demand for Money)
YA
YB
 To understand why the LM curve is positively sloped :
Take point A. Initially we are in equilibrium in the
Money Market at A.(RA, YA) Ms = Md at A!
 Suppose Y  from YA to YB and we move to B. At B,
R=RA but Y  to YB.
  Y Md  Md> MS (Excess Demand for money).
 For the Money Market to return back to equilibrium
given a fixed P and M levels we need to have an  in
R so as to  Md back to the given MS level. And at
this higher Y level (YB) R has to  to C (RC) to  Md
to its old level so that Md=MS again.
SHIFTS IN LM CURVE
 MS  or a  in P will shift LM curve to right
(MS  or an  in P will shift LM curve to the
left!).
R
LM0 (P0 M0)
Ms↑ or ↓P
LM1 (P M0)
Y
 ANALYSIS OF THE IMPACT OF THE
SHOCKS AND POLICY CHANGES ON
SHORT-RUN EQUILIBRIUM IN IS-LM
MODEL.