sessions 17 18

Macroeconomic Analysis and Policy

Sessions:17-18

Prof. Biswa Swarup Misra

Dean, XIMB

IS-LM Model

IS-LM Model Biswa Swarup Misra

Learning Objectives

Derive the IS curve

Derive the LM curve

How equilibrium is achieved simultaneously in

the Goods market and the Money market

How equilibrium is restored when the economy

is not in equilibrium.


The IS curve

def: a graph of all combinations of r and Y that

result in goods market equilibrium

i.e. actual expenditure (output)

= planned expenditure

The equation for the IS curve is:

( ) ( )Y C Y T I r G


Y2Y1

Y2Y1

Deriving the IS curve

r I

Y

E

r

Y

E =C +I (r1 )+G

E =C +I (r2 )+G

r1

r2

E =Y

IS

I E

Y


Why the IS curve is negatively

sloped

A fall in the interest rate motivates firms to

increase investment spending, which drives up

total planned spending (E ).

To restore equilibrium in the goods market,

output (a.k.a. actual expenditure, Y )

must increase.


Deriving IS Curve from Loanable Funds Model

The IS curve can also be derived from the (hopefully now familiar) loanable funds model .

Recall, S = Y-C-G

A decrease in income from Y1 to Y2 causes a fall in national saving. The fall in saving causes a reduction in the supply of loanable funds. The interest rate must rise to restore equilibrium to the loanable funds market.

Now we can see where the IS curve gets its name:

When the loanable funds market is in equilibrium, investment = saving.

The IS curve shows all combinations of r and Y such that investment (I) equals saving (S). Hence, “IS curve.”


The IS curve and the loanable funds

model

S, I

r

I (r )r1

r2

r

YY1

r1

r2

(a) The L.F. model (b) The IS curve

Y2

S1S2

IS


Fiscal Policy and the IS curve

We can use the IS-LM model to see

how fiscal policy (G and T ) affects

aggregate demand and output.

Let’s start by using the Keynesian cross

to see how fiscal policy shifts the IS curve…


Y2Y1

Y2Y1

Shifting the IS curve: G

At any value of r,

G E Y

Y

E

r

Y

E =C +I (r1 )+G1

E =C +I (r1 )+G2

r1

E =Y

IS1

The horizontal

distance of the

IS shift equals

IS2

…so the IS curve

shifts to the right.

1

1 MPC

Y G Y


Shifting the IS curve: G

The previous slide has two purposes. First, to show which way the IS curve shifts when G changes. Second, to actually measure the distance of the shift.

We can measure either the horizontal or vertical distance of the shift. The horizontal distance of the IS curve shift is the change in Y required to restore goods market equilibrium AT THE INITIAL INTEREST RATE when G is raised.

Since the interest rate is unchanged at r1, investment will also be unchanged. This is why, in the upper panel, we write “I(r1)” in the E equation for both expenditure curves – to remind us that investment and the interest rate are not changing.


Exercise: Shifting the IS curve

Use the diagram of the Keynesian cross or

loanable funds model to show how an increase in

taxes shifts the IS curve.

In case you are not too sure, you will get a clear

picture when we derive the IS curve algebraically

and discuss what factors can shift the IS curve when

we discuss the effectiveness of fiscal and monetary

policy in session-18.(Refer: slides 42-44 in this

power point file)


The Theory of Liquidity Preference

Due to John Maynard Keynes.

A simple theory in which the interest rate

is determined by money supply and

money demand.


Money supply

The supply of

real money

balances

is fixed:

s

M P M P

M/Preal money

balances

rinterest

rate

sM P

M P


Money demand

Demand for

real money

balances:

M/Preal money

balances

rinterest

rate

sM P

M P

( )d

M P L r

L (r )


Equilibrium

The interest

rate adjusts

to equate the

supply and

demand for

money:

M/Preal money

balances

rinterest

rate

sM P

M P

( )M P L r L (r )

r1


How the Fed raises the interest rate

To increase r,

Fed reduces M

M/Preal money

balances

rinterest

rate

1M

P

L (r )

r1

r2

2M

P


CASE STUDY:

Monetary Tightening & Interest Rates

Late 1970s: > 10%

Oct 1979: Fed Chairman Paul Volcker

announces that monetary policy

would aim to reduce inflation

Aug 1979-April 1980:

Fed reduces M/P 8.0%

Jan 1983: = 3.7%

How do you think this policy change

would affect nominal interest rates?

Monetary Tightening & Rates, cont.

i < 0i > 0

8/1979: i = 10.4%

1/1983: i = 8.2%

8/1979: i = 10.4%

4/1980: i = 15.8%

flexiblesticky

Quantity theory,

Fisher effect

(Classical)

Liquidity preference

(Keynesian)

prediction

actual

outcome

The effects of a monetary tightening

on nominal interest rates

prices

model

long runshort run


Real vs. Nominal Interest Rates

Real Interest Rate = Nominal Interest Rate

- Inflation

If inflation is positive, which it generally is,

then the real interest rate is lower than the

nominal interest rate.

If we have deflation and the inflation rate is

negative, then the real interest rate will be

larger.


Nominal Interest Rates Rises or Falls

Following a Monetary Contraction?

Since prices are sticky in the short run, the Liquidity

Preference Theory predicts that both the nominal and

real interest rates will rise in the short run. And in fact,

both did. (However, the inflation rate was not zero, and

in fact it increased, so the real interest rate didn’t rise as

much as the nominal interest rate did during the period

shown.)

In the long run, the Quantity Theory of Money says that

the monetary tightening should reduce inflation. The

Fisher Effect says that the fall in should cause an

equal fall in i.


Nominal Interest Rates Rises or Falls

Following a Monetary Contraction?

By January of 1983 (which is “the long run” from the

viewpoint of 1979), inflation and nominal interest rates

had fallen.

– (However, they did not fall by equal amounts. This

doesn’t contradict the Fisher Effect, though, as other

economic changes caused movements in the real

interest rate.)

Lesson: The liquidity preference theory predicts the

movement of the nominal interest rates better in the short

run and the Fisher effects predicts the movements of the

nominal interest rates better in the medium to long run.


The LM curve

Now let’s put Y back into the money demand

function:

( , )M P L r Y

The LM curve is a graph of all combinations of

r and Y that equate the supply and demand for

real money balances.

The equation for the LM curve is:

d

M P L r Y ( , )


Deriving the LM curve

M/P

r

1M

P

L (r , Y1 )

r1

r2

r

YY1

r1

L (r , Y2 )

r2

Y2

LM

(a) The market for

real money balances(b) The LM curve


Why the LM curve is upward sloping

An increase in income raises money demand.

Since the supply of real balances is fixed, there

is now excess demand in the money market at

the initial interest rate.

The interest rate must rise to restore equilibrium

in the money market.


How M shifts the LM curve

M/P

r

1M

P

L (r , Y1 )r1

r2

r

YY1

r1

r2

LM1

(a) The market for

real money balances(b) The LM curve

2M

P

LM2


Exercise: Shifting the LM curve

Suppose a wave of credit card fraud causes

consumers to use cash more frequently in

transactions.

Use the liquidity preference model

to show how these events shift the

LM curve.


The short-run equilibrium

The short-run equilibrium is

the combination of r and Y

that simultaneously satisfies

the equilibrium conditions in

the goods & money markets:

( ) ( )Y C Y T I r G

Y

r

( , )M P L r Y

IS

LM

Equilibrium

interest

rate

Equilibrium

level of

income


The IS-LM Framework

The equilibrium levels of real GDP and the

interest rate occur at the point where the IS and

LM curves intersect

the economy is in equilibrium in both the goods

market and the money market


Figure - The IS-LM Diagram

Real GDP, Y

RealInterest

Rate, rLM curve

IS curve

Equilibriuminterest rate

Equilibriumreal GDP


Figure - Off of the IS Curve

Equilibriumreal GDP

Real interestrate, r

A relatively low realinterest rate meansthat planned expenditure> production; inventoriesare falling; production isabout to rise

I>S

A relatively high real interestrate means that planned expenditure < production; inventories are growing;production is about to fall

S>I

IS Curve


Figure - Off of the LM Curve

Equilibriumreal GDP

Real interestrate, r

At this point moneydemand Would be less

as interest rate remaining the same, a lower income level would dampen the Transactions Demandfor money

Md<Ms

At this point money demand Would be more as interest rateremaining the same, a higherincome level would increase the

Transactions Demand for moneyMd>Ms

LM Curve


Off-Equilibrium to Equilibrium in the

IS-LM framework

Please refer to the distributed material from

Shapiro (Chapter-12) to supplement the class

room discussion on how starting from a

disequilibrium position the system moves

towards the equilibrium combination of Y and r


The Big Picture

Keynesian

Cross

Theory of

Liquidity

Preference

IS

curve

LM

curve

IS-LM

model

Agg.

demand

curve

Agg.

supply

curve

Model of

Agg.

Demand

and Agg.

Supply

Explanation

of short-run

fluctuations

Effectiveness of Monetary and

Fiscal Policy in IS-LM

Framework


Learning Objectives

The algebraic derivation of IS and LM curves.

The factors which govern the slope of the IS and

LM curves

The factors which shift the IS and LM curves.

How to use the IS-LM model to analyze the

effects of shocks, fiscal policy, and monetary

policy

How to derive the aggregate demand curve from

the IS-LM model


The IS Curve

By definition, the IS curve is simply a plot in (i, Y) space

(with interest rates and GDP growth on the two axes)

comprising points where the goods market is in equili-

brium-here there is no shortage, or excess supply

(inventory) in the goods market.

Ignoring the trade sector, the condition for equilibrium in

the goods market is IS: Y=C+I+G

Substituting the expressions discussed earlier for

consumption, C = C + b*Y and capital investment, I = I0 –

f*i , we obtain:

Y = (C0+ bY) + (I0 – f*i) + G


The IS Curve

Simplifying, and solving for i, we get the IS curve:

i=A/f - Y(1-b) / f -----------------(1)

where A is simply a term for notational convenience

comprising consumer confidence C0, investor confidence

I0, and government spending, G (say G0).

On close examination, we find equation (1) to be a

straight line presented in slope-intercept form in Fig. 1

(next slide) with intercept (A/f) and slope (1- b)/f.


Figure-1

IS Curve - Graphical Depiction

Interest

Rate

GDP


Some IS Exercises

1. How will the IS curve respond to a collapse in

investor confidence?

As I0 falls, the intercept term (A/f) will fall. With

no change in the slope (b and f are held

constant), the IS undergoes a parallel drop from

ISo to IS1.

The opposite holds true: a surge in investor

confidence (perhaps due to news of an

impending tax cut, or some such uplifting

announcement or expectation) will cause the IS

to shift up from ISo to IS2, again, without any

change in slope.


2. How would the IS shift with a collapse in consumer confidence ?

The intercept term falls, dropping the IS curve from ISo toISj with no change in slope, since b and f are constants.Similarly, a surge in consumer confidence results in theIS shifting up from ISo to IS2 with no change in slope.

3. How will changes in government spending affect the IS curve?

Increases in government spending G will also increasethe intercept term (A/f), thereby shifting the IS up fromISo to IS2. Cutbacks in government spending outlays willcause the IS to shift down from ISo to 1St as G drops,decreasing the intercept component. Once again, neitherof these shifts will cause the slope of the IS to vary.

Some IS Exercises


Introducing Taxes into the IS Curve

Let t be some average tax rate prevailing in the economy under

consideration.

We now define CT as the after-tax consumption function given

by:

CT = C0 + bYD -------------(2)

Where YD is the disposable (after-tax) income defined as:

YD= Y(I- t)

Substituting this expression for after-tax income into ( 2), we

obtain the consumption function incorporating a tax rate t:

CT = C0 + bYD bY(1 - t)


Using the equilibrium condition for the goods market and

the after-tax consumption function, we obtain the

expression for the IS curve with taxes.

i = A/f- [1- b(1- t) Y] /f (3)

We can see that the intercept term Alf is exactly the

same as with the ISo curve presented earlier in

expression in (1). But the slope in expression (3), [1- b(1

- t)] / f, now includes the tax rate t.

The slope of the IS curve will be now larger with the

incorporation of the tax rate.

Introducing Taxes into the IS Curve


Some IS Exercises

4. If the tax rate were to be increased from some to = 35%. to a higher rate t1 = 43%, how would the IS be affected?

An increase in the tax rate with all other variables held constant would increase the absolute value of the slope, making the IS steeper from IS(to) to IS(t1). The intercept term, however, does not specifically incorporate the tax rate t; so, in the absence of any additional macroeconomic changes, the intercept will remain the same. The final result here will be a clockwise pivot in the IS

A tax-cut from to to some lower rate t2 (30%, perhaps) would decrease the absolute value of the slope term causing the IS to be flatter without changing the intercept term. In this case, the IS pivots counter-clockwise from IS(to) to IS(t2) with the cut in taxes.


Some IS Exercises

5. How would the IS react to increases in tax rates in aneconomy struggling to recover from a prolongedrecession? Or how would an economy, nervously eyeingan approaching slowdown, react to tax increases?

This extremely important IS exercise helps to explain partof the problem faced by the Japanese economy in the2000s. After struggling to recover from years of stagnationand collapsed equity prices, the Japanese economy wasshowing a glimmer of recovery in the mid-1990s when thegovernment, despite strong advice from policy makersworldwide, increased tax rates in 1996 in a desperateattempt to increase tax revenues. Consumer and investorconfidence, just about to stage a comeback, promptlywent into free-fall!


Some IS Exercises

The IS curve in these circumstances experiences a

"double whammy" caused by increasing taxes at a time

when the economy is exceedingly vulnerable to adverse

macroeconomic policy. The intercept term falls as fragile

consumer and investor confidence plunges, and the

slope gets steeper due to the increase in the tax rate as

discussed, with IS shifting from ISo to IS1

The opposite may also hold true. The euphoria

generated by a perfectly timed tax-cut may cause the

confidence terms to soar, lifting up the intercept, and

causing the IS to flatten.


The Slope of the IS Curve

The steepness of the IS curve depends on:

How sensitive investment spending is to changes in i

The multiplier, G

Suppose investment spending is very sensitive to i the slope, b, is large

A given change in i produces a large change in AD (large shift)

A large shift in AD produces a large change in Y

A large change in Y resulting from a given change in i IS curve is relatively flat

If investment spending is not very sensitive to i, the IS curve is relatively steep


Factors Affecting Slope of IS Curve

Slope of IS curve

Value of f Slope of IS curve

High Flat

Low Steep

Value of MPC Slope of IS curve

High Flat

Low Steep

Value of t Slope of IS curve

High Steep

Low Flat

Value of Multiplier Slope of IS curve

High Flat

Low Steep


LM Curve

Equating real money supply with money demand, we obtain the equilibrium

condition in the money market as:

M/P= kY -hi

Simplifying and solving for i, we obtain the LM curve: i = (k/h)Y - (l/h)M/P Once again, this is an equation of a straight line with slope (k/h), and negative intercept -(l/h)M/P, as presented.


LM Curve

All points on this line represent points in (i, Y)

space where the money market is in equilibrium.

The slope is positive, and will be held fixed here

since k and h are constants.

The negative intercept is an algebraic construct,

devoid of macroeconomic meaning per se but

vitally important in determining how the LM shifts

when the nominal money stock or prices

change.


LM Curve

Interest Rates LM

Y(GDP)

-(l/h)M/P


Factors that Shift the LM

What will be the effect on the LM curve of an increase in the nominal money stock, M?

The change in M by the central bank will affect theintercept term. Since this is a negative term, the increasein M would lead the intercept to become a largernegative number (for example, from -40 to -48), therebydecreasing the intercept. With no change in the slope(there is no M in the slope term), the result of anincrease in M is a parallel downward, or rightward, shiftin LM from LMo to LM1.

A decrease in money growth (decrease in M) results inan upward (leftward) shift in LM and, once again, will notaffect the slope.


Factors that Shift the LM

What will be the effect in the LM curve of an increase in

the price level P (an increase in inflation)?

An increase in the price level will cause the ratio M/P to

fall, and given the minus sign that precedes the intercept

term, we now find the intercept to be "less negative"

(increasing from say, -40 to -30). Again, with no change

in the slope, an increase in P results in an upward, or

leftward, shift in LM from LMo to LM2•

A decrease in P would cause the LM to incur a parallel

shift down (right) as the intercept term decreases


Important "Rules" for Shifting LM

(1) If the ratio (M/P) decreases due to either a

decrease in M and/or an increase in P, the LM

shifts up (to the left).

(2) If the ratio (M/P) increases due to an

increase in M and/or a decrease in P, the LM

shifts down (to the right).

Basically, if the real money supply (M/P),

increases, the LM shifts right, and vice-versa.

(3) The slope does not change in either case.

Applying the IS-LM Model


The intersection determines

the unique combination of Y and r

that satisfies equilibrium in both markets.

The LM curve represents

money market equilibrium.

Equilibrium in the IS-LM model

The IS curve represents

equilibrium in the goods

market.

( ) ( )Y C Y T I r G

( , )M P L r Y IS

Y

rLM

r1

Y1


Policy analysis with the IS-LM model

We can use the IS-LM

model to analyze the

effects of

• fiscal policy: G and/or T

• monetary policy: M

( ) ( )Y C Y T I r G

( , )M P L r Y

IS

Y

rLM

r1

Y1


causing output &

income to rise.

IS1

An increase in government purchases

1. IS curve shifts right

Y

rLM

r1

Y1

1by

1 MPCG

IS2

Y2

r2

1.2. This raises money

demand, causing the

interest rate to rise…

2.

3. …which reduces investment,

so the final increase in Y1

is smaller than 1 MPC

G

3.


IS1

1.

A tax cut

Y

rLM

r1

Y1

IS2

Y2

r2

Consumers save

(1MPC) of the tax cut,

so the initial boost in

spending is smaller for T

than for an equal G…

and the IS curve shifts by

MPC

1 MPCT

1.

2.

2.…so the effects on r

and Y are smaller for T

than for an equal G.

2.


2. …causing the

interest rate to fall

IS

Monetary policy: An increase in M

1. M > 0 shifts

the LM curve down

(or to the right)

Y

rLM1

r1

Y1 Y2

r2

LM2

3. …which increases

investment, causing

output & income to

rise.


Why Increase in M shifts the LM Curve to the Right?

The increase in M causes the interest rate to fall. [People like to

keep optimal proportions of money and bonds in their portfolios; if

money is increased, then people try to re-attain their optimal

proportions by “exchanging” some of the money for bonds: they

use some of the extra money to buy bonds. This increase in the

demand for bonds drives up the price of bonds -- and causes interest

rates to fall (since interest rates are inversely related to bond prices).

The fall in the interest rate induces an increase in investment

demand, which causes output and income to increase.

The increase in income causes money demand to increase, which

increases the interest rate (though doesn’t increase it all the way

back to its initial value; instead, this effect simply reduces the total

decrease in the interest rate).


Interaction between

monetary & fiscal policy

Model:

Monetary & fiscal policy variables

(M, G, and T ) are exogenous.

Real world:

Monetary policymakers may adjust M

in response to changes in fiscal policy,

or vice versa.

Such interaction may alter the impact of the

original policy change.


The Fed’s response to G > 0

Suppose Government increases G.

Possible RBI responses:

1. hold M constant

2. hold r constant

3. hold Y constant

In each case, the effects of the G

are different:


If Government raises G,

the IS curve shifts right.

IS1

Response 1: Hold M constant

Y

rLM1

r1

Y1

IS2

Y2

r2

If RBI holds M constant,

then LM curve doesn’t

shift.

Results:

2 1Y Y Y

2 1r r r




IS1

Response 2: Hold r constant

Y

rLM1

r1

Y1

IS2

Y2

r2

To keep r constant,

RBI increases M

to shift LM curve right.

3 1Y Y Y

0r

LM2

Y3

Results:


IS1

Response 3: Hold Y constant

Y

rLM1

r1

IS2

Y2

r2

To keep Y constant,

RBI reduces M

to shift LM curve left.

0Y

3 1r r r

LM2

Results:

Y1

r3




What is the Fed’s policy instrument?

The news media commonly report the Fed’s

policy changes as interest rate changes, as if the

Fed has direct control over market interest rates.

In fact, the Fed targets the federal funds rate –

the interest rate banks charge one another on

overnight loans.

The Fed changes the money supply and shifts

the LM curve to achieve its target.

Other short-term rates typically move with the

federal funds rate.


What is the Fed’s policy instrument?

Why does the Fed target interest rates instead of

the money supply?

Answer: They are easier to measure than the

money supply.


IS-LM and aggregate demand

So far, we’ve been using the IS-LM model to

analyze the short run, when the price level is

assumed fixed.

However, a change in P would

shift LM and therefore affect Y.

The aggregate demand curve

(introduced earlier) captures this

relationship between P and Y.


Y1Y2

Deriving the AD curve

Y

r

Y

P

IS

LM(P1)

LM(P2)

AD

P1

P2

Y2 Y1

r2

r1

Intuition for slope

of AD curve:

P (M/P )

LM shifts left

r

I

Y


Deriving the AD curve

The position of the LM curve depends on the value of

M/P. M is an exogenous policy variable. So, if P is low

(like P1 in the lower panel of the diagram), then M/P is

relatively high, so the LM curve is over toward the right in

the upper diagram. If P is high, like P2, then M/P is

relatively low, so the LM curve is more toward the left.

Because the value of P affects the position of the LM

curve, we label the LM curves in the upper panel as

LM(P1) and LM(P2).


Monetary policy and the AD curve

Y

P

IS

LM(M2/P1)

LM(M1/P1)

AD1

P1

Y1

Y1

Y2

Y2

r1

r2

The Fed can increase

aggregate demand:

M LM shifts right

AD2

Y

r

r

I

Y at each

value of P


To find out whether the AD curve shifts to the left or right,

we need to find out what happens to the value of Y

associated with any given value of P.

This is not to say that the equilibrium value of P will

remain fixed after the policy change (though, in fact, we

are assuming P is fixed in the short run). We just want to

see what happens to the AD curve.

Once we know how the AD curve shifts, we can then add

the AS curves (short- or long-run) to find out what, if

anything, happens to P (in the short- or long-run).

Monetary Policy and the AD curve


Y2

Y2

r2

Y1

Y1

r1

Fiscal Policy and the AD curve

Y

r

Y

P

IS1

LM

AD1

P1

Expansionary fiscal

policy (G and/or T )

increases agg. demand:

T C

IS shifts right

Y at each

value

of P AD2

IS2


Figure - From the IS-LM Diagram to the Aggregate Demand Curve

Session Summary

1. Keynesian cross

basic model of income determination

takes fiscal policy & investment as exogenous

fiscal policy has a multiplier effect on income.

2. IS curve

comes from Keynesian cross when planned

investment depends negatively on interest rate

shows all combinations of r and Y

that equate planned expenditure with

actual expenditure on goods & services

slide 75

Session Summary

3. Theory of Liquidity Preference

basic model of interest rate determination

takes money supply & price level as exogenous

an increase in the money supply lowers the interest

rate

4. LM curve

comes from liquidity preference theory when

money demand depends positively on income

shows all combinations of r and Y that equate

demand for real money balances with supply

slide 76


5. IS-LM model

Intersection of IS and LM curves shows the

unique point (Y, r ) that satisfies equilibrium in

both the goods and money markets.

6. Effectiveness of monetary and fiscal policy in the IS-

LM framework.

Factors governing slope of IS and LM curves

slide 77

Session Summary


Session Summary

7. AD curve

shows relation between P and the IS-LM model’s

equilibrium Y.

negative slope because

P (M/P ) r I Y

expansionary fiscal policy shifts IS curve right,

raises income, and shifts AD curve right.

expansionary monetary policy shifts LM curve right,

raises income, and shifts AD curve right.

IS or LM shocks shift the AD curve.

sessions 17 18

Documents

lm curve

lm model biswa swarup

lm model biswa swarup

curve shifts

biswa swarup misradean

familiar loanable funds

loanable funds market

y c y t i r g slide