The Aggregate Demand Schedule

Pedro Serodio

July 20, 2016

Learning objectives

I To understand:

I An essential part of the tool-kit. How the quantity theory ofmoney, IS-LM and IS-MP models give rise to the AggregateDemand curve.

I The potential importance of wealth effects and forward-looking behaviour for Aggregate Demand.

I How various assumptions about expectations, the workings ofthe labour market, and price-setting affect the shape of theAggregate Supply curve and give rise to different empiricalpredictions and policy prescriptions.options.

Outline

I Derivation of AD curve in the IS-LM, quantity theory andIS-MP models.

I The slope of the AD curve.

I Wealth effects.

The AD schedule

I The AD curve shows combinations of the price level and realoutput (for the IS-LM and quantity theory models) andbetween inflation and real output gap for the IS-MP model.

I In any of these

1. Actual and planned expenditure on real output are equal;2. The price level (inflation) and real output (output gap)

correspond to an equilibrium in the money market (oroperation of the monetary rule).

I The AD curve plots the price level (inflation rate) at whichthe IS and LM (MP) curves intersect, for all levels of outputgap (the output gap).

The AD schedule

I Taking the expression for equilibrium output in the IS-LMmodel, we have that:

y∗ =h

(1− c)h + dk(a− ct + b + g) +

d

(1− c)h + dk(m − p)

I Differentiating p with respect to y , we get:

∂p

∂y= −(1− c)h + dk

d

Which gives us the slope of the aggregate demand schedule in(p, y) space.

The AD schedule

I In the IS-MP framework, the equilibrium level of output isgiven by:

y∗ =1

1− c − dφy(a− ct + b + g) +

+d

1− c − dφy(r + φy y − φππ)

I Differentiating π with respect to y , we get:

∂π

∂y= −(1− c) + dφy

dφπ

Which gives us the slope of the aggregate demand schedule in(π, y) space.

The AD schedule

The equation of exchange and the aggregate demand schedule.

I The equation of exchange is a useful identity that holds in anymonetary economy and is a useful starting point for a numberof important theories:

MV ≡ PY ,

where M is total amount of money, V the velocity oftransactions, P the aggregate price level and Y the level ofoutput.

I Here, we focus on the implicit relationship it has for the shapeof the aggregate demand schedule.

I Solving the equation for P, we have:

P =MsV (i)

Y

The AD schedule

I Taking logs, we have:

p = m + ηi − y

I Notice that this is simply an alternative formulation for alinear money demand function:

(m − p)d = y − ηi

I Under this specification, the aggregate demand schedule willagain be a negative function of the price level and, therefore,the aggregate demand schedule will be downward sloping.

Aggregate Demand

r

y

IS

MP0

MP1

A

B

π

y

AD

A

B

I The AD curve has a negative slopein (p, y) space ∂p

∂y < 0. as long as:

1. The real rate rises when outputincreases because the moneysupply falls.

2. A rise in the real interest rate isassociated with a fall in realoutput. These effects can beshown in r − y space, as here, orin a combination of r − π andr − y spaces.

Aggregate Demand

r

y

IS0

IS1

MP0

π

y

AD0

AD1

I The AD curve will be flatter in(p, y) space:

1. The larger is the MPC;2. The larger is the responsiveness

of consumption and investmentto the real interest rate Cr , Ir (din the expression above) (shownleft).

3. The less monetary policyresponds to output fluctuations(the lower is φy );

4. The more monetary policyresponds to inflation fluctuations(the larger is φπ);

Criticism

The MP model improves on the LM model by more accuratelycapturing policy and response to inflation. It is possible to criticisethe basic IS curve:

1. The interest rate relevant for spending might differ from thepolicy target rate.

2. Wealth effects are absent, though they can be added to themodel (we’ll discuss these ahead).

3. A third objection is that the IS curve remains ’Keynesian’ innature. It is ’static’ and not explicitly microfounded. Analternative, microfounded, Dynamic IS curve (DIS) has beendeveloped, and is currently used in modern New Keynesianmodels, which we’ll cover in when we discuss the NewKeynesian model.

Aggregate Demand

r

y

IS0

IS1

LM0

π

y

AD0

AD1

I A special case of the aggregatedemand schedule occurs when theinterest sensitivity of bothinvestment and consumption to theinterest rate is zero.

I We know that the slope of theaggregate demand schedule isgiven by:

∂p

∂y= −(1− c)h + dk

d

I Taking the limit as d → 0, it isclear that:

limd→0

∂p

∂y= −∞

Aggregate Demand

I If the planned expenditure function (here, plannedconsumption and investment) is interest-inelasticCr = 0, Ir = 0, where Cr is the interest elasticity ofconsumption and Ir interest elasticity of investment), thenmonetary policy is ’ineffective’: it cannot alter output,although it can affect the price level.

I If AS is also inflation-inelastic, an AD-AS equilibrium mightnot exist. In that case, if the AD curve lies to the left of theAS curve, the level of output is demand- determined.Furthermore, the excess supply could not be eliminated bydisinflation or falling prices.

The Pigou effect

A response of consumption to real wealth can be captured fairlyeasily by simply making consumption respond directly to wealth.

I This effect is named the Pigou effect, after Cambridgeeconomist Arthur C. Pigou.

I Pigou suggested real wealth could be modelled asA = M/P + (PB/P)B , but Ricardian Equivalence (Barro:government bonds are not net wealth) would suggest justincluding real money balances. The Pigou effect is also knownas the real balance effect.

I How does the Pigou effect operate?

I A reduction in the price level raises consumers’ net real wealthat any given income level.

I Reducing saving (since there is less need to accumulate wealthto fund future consumption) and

I Increasing current consumption demand.

The Pigou effect

I Going back the planned expenditure function introducedearlier, we can see that consumption depends partly on theamount of assets owned by the households. Recall that:

Y = C

(Y − T , r ,

M

P+

Pb

PB

), where 0 < CA < 1

I Real balances, MS/P, affect the position of the IS curve.I A rise in real balances shifts the IS schedule outwards, for any

given level of the real interest rate.I The Pigou effect is probably best known for its implications

concerning the effect of deflation - and the consequences forthe possibility of a liquidity trap.

I If the Pigou effect operates, a reduction in the price level cancause a direct increase in AD.

I Direct effect: It occurs even without a reduction in theinterest rate.

The Pigou effect

I Deflation is more expansionary. The AD curve is flatter thanit otherwise would be.

I In a liquidity trap (not shown here), the Pigou effect actscontrary to the negative impact of deflation via theautonomous rise in the real interest rate p and viaexpectations of future lower prices.

I In practice, real money balances are a small fraction of realwealth. The marginal propensity to consume out of realwealth is estimated to be about CA = 0.1, whereas that out ofdisposable income is around CY = 0.8. Thus the size of thePigou effect is likely to be small.

The Pigou effect

I The type of money supply increase relevant here is ahelicopter drop. Ricardian Equivalence states that governmentbonds are not net wealth, implying that an increase in themoney supply due to central bank bond purchase would alsoincrease net wealth. But: Does Ricardian Equivalence hold? Ifnot, bond-money swaps have less/no effect on net wealth.

I If their nominal value (asset price) remained unaltered, thereal value of other forms of wealth would also rise followingdeflation, which could boost consumption through a wealtheffect. However, price deflation - particularly in a liquidity trap- is often accompanied by falls in asset prices (so no increasein real wealth from that source).

The Tobin-Fisher effect

I The Tobin-Fisher effect is also known as the redistributioneffect, or the debt-deflation effect.

I An unexpected reduction in the price level (deflation) cancause a direct decrease in AD, if it changes the distribution ofwealth from high-spending borrowers to low-spending lenders.

The Tobin-Fisher effect: Intuition

I Debt contracts are usually set in nominal terms, i.e. theyspecify interest (and capital) payments in money value.

I Suppose that there is a reduction in the price level that wasnot anticipated by either creditors or debtors at the time ofsigning the debt contract.

I Moreover, suppose that the nominal debt contract is neitherindexed to the price level, nor can be renegotiated by theparties.

The Tobin-Fisher effect: Intuition

I Borrowers (e.g. people with mortgages, entrepreneurs,farmers) see that the real value of their debt has increased,which implies that lenders (banks, savers) receive morepayments in real terms.

I In other words, there is a redistribution from debtors tocreditors.

I If debtors have a higher marginal propensity to spend thancreditors, this redistribution effect causes a reduction in AD:creditors spend a smaller fraction of their additional income,and debtors are forced to cut back consumption andinvestment to reduce/repay their debts.

I Eventually, debtors can become insolvent (e.g. firms can shutdown plants).

The Tobin-Fisher effect: Intuition

r

y

IS0

IS1

LM0

LM1

A

B

C

π

y

AD0AD1

A

B

C

The Tobin-Fisher wealth redistributioneffect counteracts monetary policy

I The AD curve is steeper than itotherwise would be.

I In a liquidity trap (not shownhere), the Tobin-Fisher effect addsto the negative impact of deflationvia the autonomous rise in the realinterest rate and via expectationsof future lower prices.

Summary and Look Forward

I We have defined the AD curve.

I We have seen what determines its slope.

I You should also make sure that you can pinpoint everythingthat will shift the AD curve.

I The simple AD model can be extended to capture financialfrictions, confidence and wealth effects, which all affect the IScurve. - These are important to capture accurately responsesto financial crises, monetary expansion and deflation.

I We will see ahead that the static IS curve can be replacedwith a dynamic version.

I Next: We summarise what the AS curve looks like undervarious assumptions about wage-setting, price-setting andexpectations.