2.3. IS-LM model (open economy ) without international capital flows

2.3. IS-LM model (open 2.3. IS-LM model (open economy) without international economy) without international

capital flowscapital flows

IS-LM model: aasumptions

Pág.2

IS-LM model

Model of income and interest rates determination

Assumptions Public sector Goods and services market –Goods sector Money market – Money sector Open economy (only goods and services flows (no capital flows) Fixed prices

Therefore, two sectors and two key relationships: For any level of output Y, the IS curve shows the real interest rate r for

which the goods market is in equilibrium … IS curve or the IS relation For any level of output Y, the LM curve shows the real interest rate r for

which the monetary sector is in equilibrium -… LM curve or the LM relation

IS-LM equilibrium … is the joint equilibrium in both commodities and financial (bonds) markets

Goods and services market and the IS curve (i)

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From the basic keynesian model, we can derive the IS curve: For any level of output Y, the IS curve shows the real interest rate r for which the goods market is in equilibrium.

We assume that firms adopt only those investment projects with a positive Net Present Value. Clearly, if the interest rate is lower, there is a greater chance that a particular project will the pass the test and the investment will be made.

Mathematically, we will assume that the investment function is linear:

being b a positive parameter which captures the sensitivity of investment to interest rates

br 0II

INVESTMENT FUNCTION

Pág.4 I

r

I=I1-br

Better expectations of investment

I0<I1

I=I0-br

Goods and services market and the IS curve (ii)

br 0II

0b

dr

dIdI

dr 11

I0I1

Pág.5 I

r

Low Sensitivity I to r (b=0)

I=I0-br

I

r

High Sensitivity I to r (b=)

I=I0-br

Goods and services market and the IS curve (iii)

TWO EXTREME CASES

WE CARRY OVER THE ASSUMPTIONS FROM THE SIMPLE KEYNESIAN MODEL AND INCLUDE THE FOLLOWING: WE ASSUME THAT FIRMS ADOPT ONLY THOSE INVESTMENT PROJECTS WITH A POSITIVE NET PRESENT VALUE. CLEARLY, IF THE INTEREST RATE IS LOWER, THERE IS A GREATER CHANCE THAT A PARTICULAR PROJECT WILL THE PASS THE TEST AND THE INVESTMENT WILL BE MADE.

Model: Substituting C, I, G and XN in the AD function:

Pág.6

mY-NX XN

GG

brII

cTRt)Y-c(1CC

Q-XGICDA

0

0

00

0

QXNX

o

G

o

I

o

C

oo mYNXGbrIcTRt)Yc(CAD

1

Goods and services market and the IS curve IS

(iv)

In compact form:

Now, any increase in the interest rate will lead a decrease in the aggregate demand, since will lead a lowe level of investment.

Pág.7

m]Yt)[c(brXNGIcTRCADA

ooooo 1

0

m]Yt)[c(brAAD 10

Goods and services market and the IS curve (v)

Y

AD 45o line

Eqiollibrium:Y = AD

E

A0-br

Y0

ADo=Ao-br+[c(1-t)-m]Y

Graphically….

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The IS curve

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•The IS curve (or relation) shows for any level of output Y, the real interest rate r for which the goods market is in equilibrium.

•Therefore, the IS consists of the set of pairs (interest rates, income levels in equilibrium) . Formally :

•IS:

• Income=spending• Investment=savings

•Remember that in equilibrium AD=Y, that is, Production=Spending=Income

AD/YY,rIS

The IS curve (ii)

Y

AD 45o line

E1

Derivation of the IS curve

A0-br1

Y0

AD1=Ao-br1+[c(1-t)-m]Y

ADo=Ao-br0+[c(1-t)-m]Y

E0

Y

r

E1r1

IS CURVE: {(Y,r) SUCH THAT Y=AD}

E0

A0-br0

r0

Y1

Y0 Y1

r1<r0

Panel a: GOODS AND SERVICES MARKET

Panel b: IS CURVE

Pág.10

Mathematically

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Then, in compact form:

)(11

1

11

1

1

0

0

0

brAmt)c(

Y

brAm]t)c(Y[

brAm]Yt)[c(Y

m]Yt)[c(brAY

ADY

:αmultiplier

o

br)α(AY 0

The IS curve: two extreme cases

Y

r

b=0

IS(A0)

Y

r

b=

IS (A0)

Investment trap

0b

dY b1dr

IS 0 b

dY b1dr

IS

IS PERFECTLY INELASTIC IS PERFECTLY ELASTIC

Pág.12

What causes shifts in the IS curve? Not only changes in A, but also in α

Y

r

IS(A0)

Y

r

IS(A1) IS(A1)

IS(A0)

A1>A0

A1<A0

INCREASE A0 DECREASE A0

Pág.13 α A0 αA1

Factors that Shift the IS CurveChanges in A0

Changes in autonomous consumer expenditureChanges in planned investment spending unrelated

to the interest rate (Autonomous investment)Changes in government spendingChanges in autonomous component of the net

exportsChanges in transfers

Changes in the multiplier (in this case not only de intercept but also the slope will be affected)Changes in taxesChanges in the marginal propensity to importChanges in the marginal propensity to consume

Pág.14

Money market and the LM curve

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For any level of output Y, the LM curve shows the real interest rate r for which the monetary sector is in equilibrium.

Then, the LM curve is defined as:

Where L is the money demand and M/P is the money supply. To this end, the money supply M/P is assumed to be exogenously determined by the central Bank: M/P=(M0/P0 )

P

M/LY,rLM

Money supply

Pág.16

•To this end, the money supply M/P is assumed to be exogenously determined by the central Bank: M/P=(M0/P0 )

The liquidity preference or demand for moneyThe demand for money – or as Keynes called it – the

liquidity preference – is a function of the level of income and the interest rate.

Three motives have been identified for holding liquid balances (money) in preference to other assets:

Transactions motive – people need money to engage in daily transactions. Thus the demand for liquidity will be some proportion of total national income.

Precautionary motive – at times major events occur that need to be resolved through transactions – for example, maintaining a cash balance to pay for engine repairs on a car. This motive also tends to vary with national income as the higher is the level of economic activity, the higher are the overall transactions.

ce will be lower.

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The liquidity preference Speculative motive – Keynes contribution, was to highlight that money is not

simply a means of exchange. People used money in times of uncertainty over movements in interest rates. They have a choice between holding money which earns no interest return or purchasing an interest-bearing asset, which has less liquidity. Keynes juxtaposed the decision to hold money or bonds. If the interest rate is expected to rise, the price of bonds falls and capital losses would be expected. So at lower interest rates more people would prefer to hold money than take a chance that they would lose should they invest in bonds. Alternatively, if the interest rate falls, the price of bonds rises and capital gains would be enjoyed. At higher interest rates, more people will form the view that rates will fall rather than rise and the liquidity preference will be lower

THEREFORE, The demand for money – or as Keynes called it – the liquidity preference – is a function of the level of income and the interest rate.

Where k , and h, are two positive parameters, which capture the sensitivity of the money demand to changes in the income level and in the interest rates, respectively.

Pág.18

Analytically

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Let us derive analytically the LM curve applying the money market equilibrium condition (demand of money = money supply).

Then the equation of the LM curve is given by:

Supply

Demand

plyMoneypreference

Liquidity

P

MkY-hr

P

ML

0

0

sup

0

01

P

MkY

hr

E0

Deriving the LM curve

L, M/P

r

L(Y0)

Y

r

L(Y1)Y1>Y0

Panel a: MONEY MARKET Panel b: THE LM CURVE

LM: {(Y,r) such that L=M/P}

M/P

E1

E0

E1

r0

r1

r0

r1

Y0 Y1Pág.20

THE LM CURVE: EXTREME CASES

Y

r

Case 1: Money demand completely insensitive to the interest rate r (h=0)

LM(M/P)0

Y

r

LM(M/P)0

Liquidity trap

0h

dY hkdr

LM

LM PERFECTLY INELASTIC

LM PERFECTLY ELASTIC

k

dY hkdr

LM

Case 2: Liquidity preference is extremely sensitive to shifts in income (Y) (k=)i

Case 1: Money demand is extremely sensitive to the interest rate (h=)Case 2: Money demand completely insensitive to cahnges in the income level Y (k=0)

0 h

dY hkdr

LM

00 k

dY hkdr

LM

Pág.21

Shifts in the LM curve

Y

r

Y

rLM(M0/P)

M1>M0

EXPANSIONARY MONETARY POLICY

CONTRACTIONARY MONETARY POLICY

LM(M1/P)

LM(M1/P)

LM(M0/P)

M1<M0

Pág.22

The equilibrium in the IS-LM model(i)

Pág.23

Tras analizar por separado la curva de equilibrio del mercado de bienes y servicios –curva IS- y la curva de equilibrio del mercado de activos –curva LM- estamos en disposición de interrelacionar ambas curvas, cosa que podemos hacer gracias a que ambas están dispuestas en el mismo plano, el plano r-Y.

De la intersección de ambas curvas de equilibrio, surgirá una combinación de tipo de interés y nivel de renta para la cual, el mercado de bienes y servicios estará en equilibrio -al pertenecer a la IS- y el mercado de activos también lo estará -al pertenecer a la LM-.

Por tanto, el par (r*, Y*) representa el equilibrio conjunto de todos los mercados existentes en la economía.

Y

rLM

Er*

Y*

IS

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The equilibrium in the IS-LM model(ii)

Deriving the equilibrium in the IS-LM model (i)

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The equilibrium will be the solution of the system of equations Para hallar de forma analítica la intersección de la IS con la LM, tan solo tendremos que hallar la solución del sistema formado por las ecuaciones de ambas curvas:

Al resolver dicho sistema, obtenemos la expresiones de la renta y el tipo de interés de equilibrio:

P

MkY

hrLM

br)α(AYIS

10

P

M

bkhA

bkh

kr

P

M

bkh

bA

bkh

hY

1*

*

0

0

Y

DA Línea 45o

E1

Puntos situados fuera de la curva IS

A0-br1

Y0

DA1=Ao-br1+[c(1-t)-m]Y

DAo=Ao-br0+[c(1-t)-m]Y

E0

Y

r

E1r1

Curva IS: {(Y,r) tales que Y=DA}

E0

A0-br0

r0

Y1

Y0 Y1

r1<r0

Puntos a la derecha de la IS (Punto A):

EXCESO DE OFERTA DE BIENES Y SERVICIOS

A

A

B

B Puntos a la izquierda de la IS (Punto B):

EXCESO DE DEMANDA DE BIENES Y SERVICIOS

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E0

Puntos situados fuera de la curva LM

L, M/P

r

L(Y0)

Y

r

L(Y1)Y1>Y0

Curva LM: {(Y,r) tales que L=M/P}

M/P

E1

E0

E1

r0

r1

r0

r1

Y0 Y1

C

D

C

D

Puntos a la izquierda de la LM (Punto C):

EXCESO DE OFERTA DE DINEROEXCESO DE DEMANDA DE BONOS

Puntos a la derecha de la LM (Punto D):

EXCESO DE DEMANDA DE DINEROEXCESO DE OFERTA DE BONOSPág.27

Y

rLM

E

IS – LM: Equilibrium and non-equilibrium points

r*

Y*

IS

EXCESS SUPPLY OF GOODS AND SERVICES

EXCESS SUPPLY OF MONEY

EXCESS SUPPLY OF GOODS AND SERVICESEXCESS DEMAND OF

MONEY

EXCESS DEMAND OF GOODS AND SERVICES

EXCESS SUPPLY OF MONEY

EXCESS DEMAND OF GOODS AND SERVICES

EXCESS DEMAND OF MONEY

Pág.28

Pág.29

Si quisiéramos saber cómo cambia el equilibrio ante un cambio en cualquiera de los parámetros del modelo, basta diferenciar las expresiones de la renta y el tipo de interés de equilibrio:

A partir de:

Si diferenciamos:

P

Md

bkhP

M

bkhddA

bkh

kA

bkh

kddr

P

Md

bkh

b

P

M

bkh

bddA

bkh

hA

bkh

hddY

11*

*

00

00

P

M

bkhA

bkh

kr

P

M

bkh

bA

bkh

hY

1*

*

0

0

Comparative Statics in the IS-LM model

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POLÍTICA FISCAL EXPANSIVA: EFECTO SOBRE LA RENTA Y EL TIPO DE INTERÉS DE UN AUMENTO DEL GASTO PÚBLICO…

Teniendo en cuenta que si se produce un aumento del gasto público, dA0=dG0

Vemos cómo tanto el tipo de interés como la renta aumentan, al aumentar el gasto público.

Gráficamente, al variar el gasto público, varía la demanda agregada y, por tanto, la curva IS se desplaza a la derecha

0

0

*

*

dGbkh

kdr

dGbkh

hdY


[1] [2]

[3] Efecto expulsión (EE)=[1]-[2]

Y

rLM (M0/P)

E0r0

Y0

IS (A0)

POLÍTICA FISCAL EXPANSIVA: EFECTO SOBRE LA RENTA Y EL TIPO DE INTERÉS DE UN AUMENTO DEL GASTO PÚBLICO…

E2

E1

Y2 Y1

r1

IS’ (A0+dG0)

dG0>0

0dGbkh

hdY LMIS

0dGdY keynesianaAspa

[1]

[2] [3]

0

2

0

dGbkh

bkEE

dGbkh

hEE

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Crowding-out effect

Podemos ver como esta política fiscal expansiva tiene un primer efecto expansivo sobre la renta que se ve parcialmente compensado por el efecto negativo que sobre la renta tiene la disminución de la inversión privada provocada por la subida de tipos. Se dice, pues, que el gasto público desplaza a la inversión privada.

0

2

0

00

dGbkh

bkdG

bkh

hEE

dGbkh

hdGEE

LMISmodeloelenrentalaenCambiobásicokeynesianomodelo

elenrentalaenCambio


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CONTRACTIONARY MONEATARY POLICY…

If the money supply decreases:

Hence:

As a result, income will decrease and the interest rate will increase.

Graphically, in the next slide, a decrease in the real money supply decreases shifts the LM curve leftward.

P

dM

P

dP

P

M

P

dM

P

dPMPdM

P

Md

2

001

00*

dMthatgivenP

dM

bkhdr

dMthatgivenP

dM

bkh

bdY


Y

rLM’ (M1/P)

E0r0

Y1

IS (A0)

CONTRACTIONARY MONETARY POLICY…

E1

Y0

r1

dM<0

LM (M0/P)

Pág.34


The effectiveness of fiscal, monetary and trade policy in stimulating economic activity

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Podemos ver cómo las pendientes de las curvas IS y LM inciden sobre la efectividad o inefectividad de una determinada política.

Por efectividad de una política entendemos el grado de acercamiento al objetivo pretendido.

Por ejemplo, una política expansiva pretende que aumente la producción y el empleo. Si como consecuencia de una política expansiva, la producción no varía diremos que tal política es completamente inefectiva.

A modo de ejemplo, veremos dos casos:

• Política fiscal expansiva cuando h

• Política monetaria expansiva cuando b

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EXPANSIONARY FISCAL POLICY

DEMANDA DE SALDOS REALES MUY SENSIBLE A CAMBIOS EN LOS TIPOS DE INTERÉS (h)

Como hemos visto, en este caso la LM es completamente elástica

Analíticamente, el efecto sobre la renta y el tipo de interés se puede calcular igual que anteriormente, pero teniendo además en cuenta que ahora h .

Para resolver la indeterminación,

0 h

LM h

k

dY

dr

00 dAdAbkh

hdY h

hbk

Lim

hbkh

hh

Limbkh

hLim

hhh1


Pág.37

EXPANSIONARY FISCAL POLICY

DEMANDA DE SALDOS REALES MUY SENSIBLE A CAMBIOS EN LOS TIPOS DE INTERÉS (h)

Por tanto,

Que como podemos observar, coincide con lo que aumentaría la renta tras una política fiscal expansiva en el modelo keynesiano básico. Diremos pues que la política en este caso es plenamente efectiva y el efecto expulsión es nulo.

Con respecto a la variación del tipo de interés:

0dAdY

00

hdAbkh

kdr


Y

r

LM (M0/P)E0

r0=r1

Y0

IS (A0)

E1

Y1

IS’ (A0+dA0)

dA0>0

EXPANSIONARY FISCAL POLICY WHEN h=

Completely effective policyCrowding out effect= null

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Pág.39


INVESTMENT HIGHLY SENSITIVE TO THE INTEREST RATE (b=)

Como hemos visto, en este caso la IS es completamente elástica

Analíticamente, el efecto sobre la renta y el tipo de interés se puede calcular igual que anteriormente, pero teniendo además en cuenta que ahora b .

Para resolver la indeterminación,

011

b

IS

IS αbdrdYdY

dr

P

dM

P

dM

bkh

bdY b

kkbh

Lim

bbkh

bb

Limbkh

bLim

bbb

1


Pág.40


INVESTMENT SPENDING HIGHLY SENSITIVE TO THE INTEREST RATE (b=)

Hence,

And the variation of the interest rate is:

Then, income level will increase while interest rate will remain constant. Monetary policy will be effective.

P

dM

kdY

1

01

b

P

dM

bkhdr


Y

rLM (M0/P)

E0r0=r1

EXPANSIONARY MONETARY POLICY WHEN b=

E1IS (A0)

dM>0

Completely effective policy

LM’ (M1/P)

Y0 Y1Pág.41


IS-LM model without IS-LM model without capital flowscapital flows

Y

rLM (M0/P)

E0

r0

Y0

IS (A0)

EFFECT OF AN INCREASE IN AUTONOMOUS CONSUMPTION….

E2

E1

Y2 Y1

r1

IS’ (A0+dC0)

dC0>0

Pág.43


Y

rLM (M0/P)

E0

r0

Y0

IS (A0)

A FAVOURABLE EFFECT ON INVESTMENT EXPECTATIONS…

E2

E1

Y2 Y1

r1

IS’ (A0+dI0)

dI0>0

Pág.44


[1] [2]

[3] CROWDING OUT=[1]-[2]

Y

rLM (M0/P)

E0r0

Y0

IS (A0)

EXPANSIONARY FISCAL POLICY (FISAL STIMULUS): AN INCREASE IN THE GOVERNMENT SPENDING…

E2

E1

Y2 Y1

r1

IS’ (A0+dG0)

dG0>0

0dGbkh

hdY LMIS

0mod dGdY elninkeynesia

[1]

[2] [3]

0

2

0

dGbkh

bkEE

dGbkh

hEE

Pág.45


[1] [2]

[3] Crowding out(EE)=[1]-[2]

Y

rLM (M0/P)

E0r0

Y0

IS (A0)

EXPANSIONARY FISCAL POLICY: INCREASE IN TRANSFERS…

E2

E1

Y2 Y1

r1

IS’ (A0+cdTR0)

dTR0>0

0dTRcbkh

hdY LMIS

0mod dTRcdY elkeynesianin

[1]

[2] [3]

0

2

0

dTRcbkh

bkEE

dTRcbkh

hEE

Pág.46


Y

rLM’ (M1/P)

E0r0

Y1

IS (A0)

CONTRACTIONARY MONETARY POLICY…

E1

Y0

r1

dM<0

LM (M0/P)

Pág.47


Y

rLM (M0/P)

E0

r0

Y0

IS (A0)

EXPANSIONARY TRADE POLICY…

E2

E1

Y2 Y1

r1

IS’ (A0+dXN0)

dXN0>0

Pág.48


Y

rLM (M0/P)

E0r0=r1

Y0=Y1

EXPANSIONARY FISCAL POLICYb=

E1

IS (A0)= IS’ (A0+dA0)

dA0>0

Pág.49

Fiscal policy completely (totally) ineffectiveCrowding out effect neutralizes discretionary fiscal policy (the expansionary effect of the fiscal stimulus is offset by the crowding out effect)


Y

r

LM (M0/P)E0

r0=r1

Y0

IS (A0)

E1

Y1

IS’ (A0+dA0)

dA0>0

EXPANSIONARY FISCAL POLICY WHEN h=

Pág.50


Ficsl policy totally effectiveCrowding out =0

Y

r

LM (M0/P)E0

r0=r1

Y0

IS (A0)

E1

Y1

IS’ (A0+dA0)

dA0>0

EXPANSIONARY FISCAL POLICY WHEN k0

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Y

rLM (M0/P)

E0

EXPANSIONARY POLICY WHEN b=0

E1

IS’ (A0+dA0)

dA0>0


IS (A0)

Y0 Y1

r0

r1

Pág.52


Y

r LM (M0/P)

E0

IS (A0)

E1

IS’ (A0+dA0)

dA0>0

EXPANSIONARY FISCAL POLICY WHEN h=0

Y0=Y1

r0

r1

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Fiscal policy completely (totally) ineffectiveCrowding out effect neutralizes discretionary fiscal policy (offset the fiscal stimulus) FULL CROWDING OUT


Y

r LM (M0/P)

E0

IS (A0)

E1

IS’ (A0+dA0)

dA0>0

EXPANSIONARY FISCAL POLICY WHEN k=

Fiscal policy completely (totally) ineffectiveCrowding out effect neutralizes discretionary fiscal policy (the expansionary effect of the fiscal stimulus is offset by the crowding out effect)FULL CROWDING OUT

Y0=Y1

r0

r1

Pág.54


Y

rLM (M0/P)

E0r0=r1

EXPANSIONARY MONETARY POLICY WHEN b

E1IS (A0)

dM>0LM’ (M1/P)

Y0 Y1Pág.55

Monetary policy completely effective


Y

r

LM (M0/P)=LM’ (M1/P)E0

r0=r1

IS (A0)

dM>0

EXPANSIONARY MONETARY POLICY WHEN h=

Y0=Y1

E1

Pág.56


Ineffective monetary policy

Y

r

LM (M0/P)E0


Y0

IS (A0)

E1

Y1

dM>0

EXPANSIONARY MONETARY POLICY WHEN k=0

LM’ (M1/P)

r0

r1

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Y

rLM (M0/P)

E0

EXPANSIONARY MONETARY POLICY WHEN b=0

E1

dM>0IS (A0)

r0

r1

LM’ (M1/P)

Y0=Y1Pág.58



Y

r LM (M0/P)

E0


IS (A0)

E1

dM>0

EXPANSIONARY MONETARY POLICY WHEN h=0


r0

r1

LM’ (M1/P)

Y0 Y1Pág.59

Y

r LM (M0/P)=LM’ (M1/P)

E0


IS (A0)

E1

dM>0

EXPANSIONARY MONETARY POLICY WHEN k=


Y0=Y1

r0=r1

Pág.60

2.3. IS-LM model (open economy ) without international capital flows

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