Ch 9Chapter 9

Ch 9Chapter 9

The IS–LM/AD–ASModel: A General Framework for Macroeconomic Analysis

Copyright © 2009 Pearson Education Canada

Introduction to the IS-LM Model

h l b d dNow, we put the labour, goods and asset markets into a single framework so we can analyze them simultaneously analyze them simultaneously This name (IS-LM) originates from its basic equilibrium conditions:equilibrium conditions:

investment, I, equals saving, S;money demanded, L, equals money supplied, M.money demanded, L, equals money supplied, M.

The model was first developed by Keynesians but can be used to represent y pboth Classical and Keynesian models.

Copyright © 2009 Pearson Education Canada 9-2

Introduction to the IS-LM Model h ( b k )The FE Line (Labour Market)

The IS Curve (Goods Market)The LM Curve (Asset Market)General Equilibrium in the IS-LMAttainment of General EquilibriumWe will analyze this economic model

hi ll (Ch 9) i ll (A 9A) d graphically (Ch 9), numerically (App 9A) and algebraically (App 9B)Ch 9 assumes a closed economy Ch 10 Ch 9 assumes a closed economy. Ch 10 relaxes this assumption


The FE Line: Equilibrium in the Labour Market

Equilibrium in the labour market is Equilibrium in the labour market is represented by full employment line, FE.

is reached after wages and prices have N is reached after wages and prices have fully adjusted so NS=ND: firms have hired N up to the point where profits are maximized

N

When the labour market is in equilibrium, output equals its full employment level,

dl f th i t t t (FE li i Y

regardless of the interest rate (FE line is vertical in the (Y, r) diagram)r has no role for full employment: only r has no role for full employment: only affects firms' long run investment decisions



Factors that Shift the FEline

F l i hift i ht ifYFrom our analysis, shifts right if:Anything shifts NS or ND curves right

Y

Beneficial supply shock (e.g. an increase in A)A i i NSAn increase in NS

An increase in the capital stockThat is, anything that affects the full employment level of output will cause the FE line to shift.


The IS Curve: Equilibrium in the Goods Marketh h f l l fThe IS curve shows for any level of

output, Y, the interest rate, r, clears the goods marketgoods market.Recall, in a closed economy, r adjusts so that Id = Sd where the saving curve slopes that I = S where the saving curve slopes up; investment curve slopes down.At all points on the IS curve I = SAt all points on the IS curve, I SIS curve slopes down because an increase in Y leads to an increase in Sd and r must in Y leads to an increase in S and r must fall to clear the goods market.


The IS Curve: Equilibrium in the Goods Market (continued)

d h h fWe can derive the IS curve using the fact that when I = S we have AD = ASS hSuppose we have:Cd = c0 + cy(1-τ)Y – crr T = τYId = ι0 – ιrr.

where the symbols “c” and “ι” are coefficients and “τ” is the income tax rate. They are all positive numbers.

Recall the goods market equilibrium Recall the goods market equilibrium condition: Y = Cd + Id + G (board)



Factors That Shift the IS CurveS f ll h ( ) hIS curve consists of all the pairs (Y,r) such

that the goods market is in equilibrium.For constant output any change in the For constant output, any change in the economy that reduces desired national saving relative to desired investment will gincrease the real interest rate that clears the goods market and, thus, shift the IS curve upwardupward.Factors that might cause Sd to fall:

An increase in Future Output or Wealth, d d

p ,shifts IS up Cd increases, Sd decreases, rincreases to clear goods market


Factors That Shift the IS Curve (continued)

i i G hif S (b d)An increase in G, shifts IS up: (board)Id=Sd = Y – Cd – G

G increases, Sd decreases, r increases to clear G increases, S decreases, r increases to clear goods market

A decrease in T, shifts IS up, only if Ricardiani l d ’t h ld equivalence doesn’t hold.

An increase in private (after-tax) disposable income, Cd increases, Sd decreases, r, , ,increases to clear goods marketFactors that cause Id to rise (for constant output ): increase in MPKf or decrease in output ): increase in MPK or decrease in the effective tax rate on capital


an


Factors That Shift the IS Curve (continued)

The shift of the IS curve can also be The shift of the IS curve can also be interpreted in terms of an alternative goods equilibrium condition: AD=ASequilibrium condition: AD=ASFor a given level of output, any change that increases the aggregate demand for goods increases the aggregate demand for goods shifts the IS curve up.

Why? An increase in AD for goods causes the quantity of goods demanded to exceed supply. GME can be restored by an increase in r which reduces Cd and Id

A increase in G with output constant will A increase in G with output constant, will shift the IS curve and interest rates up.


The Interest Rate and the Price of a Nonmonetary Asset

Before we show that the asset market Before we show that the asset market equilibrium can be represented by the LM curve, we discuss the relationship between the curve, we discuss the relationship between the price and interest rate of a NM assetGiven the promised schedule of repayments of p p ya bond or other NM asset, the higher the price of the asset, the lower is the nominal interest

t f th t P /(1+i)rate of the asset: P = coupon/(1+i)For a given rate of inflation the price of a non-monetary asset and its real interest rate are monetary asset and its real interest rate are also inversely related.


The Price of a Nonmonetary Asset (continued)

If the price of the bond were to fall because If the price of the bond were to fall, because people were selling them, then the interest rate would rise given an unchanged stream rate would rise, given an unchanged stream of payments or coupons.This is a key relationship in deriving the LM This is a key relationship in deriving the LM curve and will be used to explain how equilibrium occurs in the money market.


The Equality of Money Demanded and Supplied

The real money supply curve (MS) is a vertical The real money supply curve (MS) is a vertical line, it does not depend on the real interest rate but rather on central bank actions.The money demand curve (MD) slopes downward. With higher r the attractiveness of money as an asset decreases.Asset market equilibrium occurs at the i t ti f th MS d th MDintersection of the MS and the MD curves.When MD increases people sell nonmonetary assets their price falls and nonmonetary assets, their price falls and the interest rate increases.


The LM Curve: Asset Market EquilibriumThe LM curve is a graphical representation of the relationship between output and the real interest rate that clears the asset market.The LM curve slopes upward.u op up a dAt all points of the LM curve MD=MSMD=MS.


The LM Curve: Asset Market Equilibrium (continued)

As in the case of the IS curve, we can demonstrate the slope of the LM curve as pan equilibrium relationship, this time between real money demand and supply. Suppose that real money demand was represented by the following:

dMd/P = l0 + lyY – lr(r + πe)where the symbols “l” represent positive coefficients

E ilib i diti Md/P Ms/P (b d)Equilibrium condition: Md/P = Ms/P (board)Copyright © 2009 Pearson Education Canada 9-18


The LM Curve: Asset Market Equilibrium (continued)h l d bThe LM curve slopes upward because an

increase in Y leads to an increase in MD

and r must rise to clear the asset market (or else there would be excess MD)If Y increases, the demand for real money (M/P) increases at any given r and shifts (M/P) increases, at any given r, and shifts MD curve up.People try to sell assets for money.MS is fixed by Bank of CanadaPrice of asset falls/r increasesMoney demand decreases until MD MSMoney demand decreases until MD = MS


Factors that Shift the LM CurveFor constant output, any change that reduces real money supply relative to real

d d ill i th l money demand will increase the real interest rate that clears the asset market and cause the LM curve to shift upand cause the LM curve to shift up.Factors that might cause real money supply (MS/P) to rise: (board)supply (M /P) to rise: (board)

An increase in the nominal MS

A decrease in the price level Pp



Factors that Shift the LM Curve (continued)

Factors that might cause MD to fall:Factors that might cause MD to fall:An increase in πe, the expected inflation

As πe rises the demand for money falls (money is As πe rises, the demand for money falls (money is expected to be worth less) and people start buying NM assets.

A decrease in im (interest bank pays on money)A decrease in wealth (reduces number of A decrease in wealth (reduces number of transactions)A decrease in the risk of NM assetsA decrease in the risk of NM assetsAn increase in the liquidity of NM assets


Changes in the Real Money Demand

A change in any variable that affects real money demand, other than output or the

l i t t t ill l hift th LMreal interest rate, will also shift the LMcurve.The process works as before: any excess The process works as before: any excess demand (supply) for money causes wealth holders to sell (buy) non-monetary assetsholders to sell (buy) non monetary assets.These actions bid down (up) those asset prices and cause the real interest rate to prices and cause the real interest rate to rise (fall).



General Equilibrium in the Complete IS-LM Model

The general equilibrium of the economy:the FE line along which the labour market is

l bin equilibrium;the IS curve, along which the goods market is in equilibrium;is in equilibrium;the LM curve, along which the asset market is in equilibrium. is in equilibrium.

Labour market, Goods market and Asset market are simultaneously in equilibriumy q


General Equilibrium (continued)The general equilibrium of the economy always occurs at the intersection of the IS curve and the FE line.Adjustments of the price level cause the LM curve to shift until it passes u o u pathrough the general equilibrium point.p



A Temporary Adverse Supply ShockSuppose the productivity parameter A in Suppose the productivity parameter A in the production function drops temporarily.It reduces the MPN and shifts the labour It reduces the MPN and shifts the labour demand curve down. The labour supply curve is unaffected. curve is unaffected. Because the shock is temporary, MPKf is unaffected and accordingly the demand g yfor K remains unchanged.The FE line shifts (Y falls) left because of ( )lower N and A.


A Temporary Adverse Supply Shock (continued)A temporary adverse supply shock is a A temporary adverse supply shock is a movement along the IS curve, not a shiftof the IS curve since the shock doesn’t of the IS curve since the shock doesn t change any factor affecting Sd or Id

A temporary adverse supply shock has no A temporary adverse supply shock has no direct effect on the demand for, or the supply of money, but...It’s the LM curve that shifts until it passes through the intersection of the FE line and the IS curve.


A Temporary Adverse Supply Shock (continued)

This shift in the LM curve is caused by changes in the price level P which changes th l l M/P d th f the real money supply, M/P, and therefore the asset market equilibriumTo restore general equilibrium LM shifts left To restore general equilibrium, LM shifts left since the adverse shock causes prices to rise and thus M/P to fall and thus M/P to fall In the new general equilibrium, the real rate of interest is higher, output is lower and the of interest is higher, output is lower and the price level is higher.



Price Adjustment and the Attainment of General Eqm

We can use the IS-LM model to illustrate how the economy moves to a general

ilib i i t h th th equilibrium point where the three curves intersect.We can also use this model to show some We can also use this model to show some basic differences between the Classical and Keynesian schoolsand Keynesian schools.Consider what happens to the economy if the nominal money supply increases i.e. the nominal money supply increases i.e. the central bank decides to raise M


The Effects of a Monetary ExpansionEffects of a Monetary expansion: LM curve shifts down (P does not change right

)away)– LM: Asset market responds right away– FE: Labour market slow responseFE: Labour market, slow response– IS: Goods market response is in between;

and we move along the IS curve in the h t short run

So, short run equilibrium is where the IS-LM intersectLM intersect



The Effects of a Monetary Expansion (continued)

People rebalance portfolios: get rid of excess M balances by buying NM assets, NMprices rise r decreases prices rise, r decreases What does low r mean for Cd and Id?

– lower r means higher Cd Idlower r means higher C , I– firms are willing to temporarily produce

more to meet this demand (key assumption)At the short run equilibrium point, the demand is metdemand is met


The Effects of a Monetary Expansion (continued)h h hThe economy is at the short run

equilibrium, what's next?W h fi d P f hi h i t lik l We have fixed P so far, which is not likely to happen for a long period of timeFirms are producing more than full Firms are producing more than full employment Y right now (e.g. through overtime or reduction in inventories)overtime, or reduction in inventories).This is not sustainable; prices must adjust


The Adjustment of the Price Level

h h hFirms start charging higher pricesP starts rising, M/P is falling, and the LM

hift b kcurve shifts backThis process continues until we get back to the FE point and the GE is restoredto the FE point, and the GE is restoredClassical and Keynesians debate on how long this price adjustment takes long this price adjustment takes.


The Adjustment of the Price Level (continued)

What happened here?Ms went up, and there was a short run p,effect, but NO real long run effectP eventually rose to restore long run equilibriumReal: (r, Y, W/P) unchanged. This is referred to as monetary neutrality.Nominal: (W, P) rose proportionally to the i i i h lincrease in Ms in the long run


Attaining General Equilibrium g qwith the Equations

’ h d d d lLet’s use the IS and LM curves derived earlier to find the general equilibrium in the IS-LMmodel (board)model (board)IS curve r = αIS – βISY (eq 1)LM curve r α (1/l )(M/P) + β Y (eq 2) LM curve r = αLM – (1/lr)(M/P) + βLMY (eq 2) where: αIS = (c0 + ι0 + G)/(cr + ιr)

α = (l /l ) πe αLM = (l0/lr) – πe

βIS = (1 – (1-τ)cy)/(cr + ιr) βLM = (ly/lr)βLM ( y/ r)

“α’s” are constant terms; “β’s” are slopes.Copyright © 2009 Pearson Education Canada 9-40

Classics vs. Keynesiansll d bStill debating....

How rapidly do we reach a new GE?What are the effects of monetary policy?

There is little controversy about the fact that the price level will adjust and restore general price level will adjust and restore general equilibrium.Classics: rapid price adjustment, P rises fast, so no

i t t l ff tpersistent real effectKeynesians: slow price adjustment, Y rises and Pslow to adjust, then there are persistent real effects since labour market is not in equilibrium for an extended period.


Monetary NeutralityThere is monetary neutrality if a change in the nominal money supply changes the

i l l ti t l b t h price level proportionately but has no effect on real variables in the long run.We have already shown that this is a We have already shown that this is a feature of the model presented here.

Monetary expansion left Y r N unchangedMonetary expansion left Y, r, N unchanged

Keynesians believe in monetary neutrality in the long-run but not in the short-run.in the long run but not in the short run.


Stabilization PolicyUnexpected shifts in the IS, LM and the FEcurves are the sources of business cycles.St bili ti li i th f fi l d Stabilization policy is the use of fiscal and monetary policy to shift the position of the ISand LM curves so as to offset the effects of and LM curves so as to offset the effects of such shocks.

Classics believe there is no need for stabilization fpolicies (economy is self-correcting)

Keynesians advocate stabilization polices to avoid suffering the consequences of a prolonged suffering the consequences of a prolonged disequilibrium.


The AD-AS ModelThe AD-AS and the IS-LM models are equivalent and express the same basic macroeconomic theoryEach version can be used to focus on either r or P.IS-LM: relates (Y, r)

– more useful for saving, investmentAS-AD: relates (Y, P)AS AD: relates (Y, P)

– more useful for inflationCopyright © 2009 Pearson Education Canada 9-44

The Aggregate Demand CurveThe aggregate demand (AD) curve shows the relation between the aggregate

tit f d d d d (Cd+Id+G) quantity of goods demanded (Cd+Id+G) and the general price level, P.The AD curve slopes downward because The AD curve slopes downward because an increase in the price level will shift the LM curve up and to the leftLM curve up and to the left.


The Aggregate Demand Curve (continued)

ll h h fRecall what happens if P goes up in IS-LM– M/P falls, so LM shifts left

IS LM ilib i i t l Y– IS-LM says new equilibrium is at a lower Y– So P rises, Y falls– If we plot these equilibrium points we get the ADIf we plot these equilibrium points, we get the AD

curve

So, the reduction in the real money supply , y pp ywill raise the real interest rate which reduces the demand for goods by h h ld /f h lhouseholds/firms, thus lowers aggregate demand.Copyright © 2009 Pearson Education Canada 9-46


The Aggregate Demand Curve (continued)

Recall the expression for the IS and LM Recall the expression for the IS and LM curves. We can use these expressions to derive the AD curve:derive the AD curve:

r = αIS – βISY (1/l )(M/P) + β Yr = αLM – (1/lr)(M/P) + βLMY

To get the AD curve we set each equal to eliminate r, which then gives us an expression in P and Y:Y = [αIS - αLM + (1/lr)(M/P)]/(βIS + βLM)


Factors That Shift the ADCurve

From this expression, we can see that Y is a decreasing function of PFor a constant price level:

any factor that changes the aggregate any factor that changes the aggregate demand for output will cause the AD curve to shift;any factor that causes the intersection of the IS and the LM curves to shift will cause the AD to shift.



The Aggregate Supply Curve

The aggregate supply (AS) curve shows the The aggregate supply (AS) curve shows the relation between the price level and the aggregate amount of output that firms aggregate amount of output that firms supply.The prices remain fixed in the short run and The prices remain fixed in the short run and prices adjust to clear all the markets in the long-run, thus:

SRAS: price level fixed for any Y (horizontal line)LRAS: labour market clears (FE) and we are at f ll l t ( ti l li )full employment (vertical line)



The Aggregate Supply Curve (continued)From the expression for the IS and LM curves. We can use these expressions to d i th AS derive the AS curves:

SRAS: P= and AD curve determine SR equilibrium:

Pequilibrium:

Y = [αIS - αLM + (1/lr)(M/ )]/(βIS + βLM)P

LRAS: Y= and AD curve determine LR equilibrium (solving for LR price level):

Y

P = M/{lr[αLM - αIS + (βIS + βLM) ]}Copyright © 2009 Pearson Education Canada 9-53

Y

Factors That Shift the AS CurveLRAS shifts due to

– anything that affects FE output (or anything that affects FE output (or shifts the FE curve)

SRAS shifts iffi h h i i i h h – firms change their prices in the short run

– shifts up if costs rise in the short runCopyright © 2009 Pearson Education Canada 9-54

Equilibrium in the AD-ASModel

Long-run equilibrium is the same as general equilibrium because in long-g q grun equilibrium, all markets clear.In general equilibrium or long-run In general equilibrium, or long run equilibrium, AD, SRAS, and LRAScurves intersect at a common pointcurves intersect at a common point.



Monetary Neutrality in the AD-AS Model

Consider an increase in M when the Consider an increase in M when the economy is in LR equilibrium. This shifts the AD curve up and to the right (board)AD curve up and to the right. (board)In the short run the price level remains fixed and SRAS does not change.and SRAS does not change.In the long run the price level rises, the SRAS shifts up to the point where the ADp pand the LRAS curves intersect.We conclude that money is neutral in the ylong-run.



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