Macroeconomic Theory II

AEB 7240
Instructor: James L. Seale, Jr.
Food and Resource Economics
University of Florida
Spring Term

Stevenson et al., Chapter 2

Aggregate Supply

AS
P AS
p P P
p p

AS

AD’
AD’
AD’
AD AD AD

Y Y Y
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Classical Model

We start with the production function qi = q(N i , K i ) q N  0 , q NN  0

where i = 1, . . . , n firms, N is labor, and K is capital.

We assume perfect competition and profit maximization.

 i = P q(Ni, Ki ) − WNi − RKi

where R = retail price of capital, and W = wages. We basically assume K is fixed in the

short-run.

W
First order conditions include q N = , that is,
P

the marginal productivity of labor = real wages.

In terms of labor demand, N id = N d 

W
So if , Nd  .
P

Labor supply for utility maximizing household under a budget constraint is

W  W 
N Sj = N S   dN S d    0
P P

so it is upward sloping. (Keynes essentially assumes it is horizontal.)

So in labor market, we have

W 
Nd = Nd  
P 
W 
Ns = Ns  
P 
Nd = Ns

W
so labor market clears at full employment, N*, and at equilibrium real wage, *.
P

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Thus, for fixed capital, there is a production function that relates output to N (labor
K

given K).

W/P NS
q _
q = q(N(W/P), K )
q*
(W/P)*

Nd

_
N* N*
N/K

Thus, labor market determines labor employed, which determines output. In this model,

N * determines q * (N *) , and the aggregate supply is vertical at q * (N *) .

AS
P

AS

q* (N*) q

“Classical “Aggregate Supply

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The properties of model when combining aggregate demand with supply are:

W 
Nd = Nd  , K  1
P 

W 
Ns = Ns   2
P

Nd = Ns 3

(
q = q N, K ) 4

y = q 5

y = e (y , r ) 6

l (y , r) =
M
7
P

*
W 
The system is recursive. Equations 1, 2, and 3 determine jointly N * and   , which
P

then via short-run production function determines q*, which determines y*. With y*

determined in the equilibrium of aggregate demand and supply, IS determines the real

interest rate while LM (money market) determines the price (which has no effect on

output (i.e. vertical aggregate supply)).

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The “Classical” Model.

IS

W/P*
W/P q, y
q* = y*
NS

N*

Nd
_
q=q(N,K)
iii N iv

W * 
Graphically, quadrant iii determines labor market  , N *  . Given N*, the production
P 

function determines q* = y* in quadrant iv. To bring aggregate y* into equilibrium with

aggregate supply requires the equilibrium real interest rate (in quadrant i). A flexible

price ensures through LM that IS - LM yields appropriate r*. Quadrant ii summarizes

factor prices.

The model incorporates three major classical properties:

1. Classical dichotomy — system is separated into real and nominal (money)

sectors. Role of money supply is to determine price level. Real side determines

labor employment and output.

2. If we differentiate the LM equation, setting dy = dr = 0 , we get

1 M
l y dy + lr dr = dM − 2 dP = 0
P P
dM dP
=
M P

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Thus, any change in money changes price in the same proportion. This is the

traditional quantity theory of money.

3. Neutrality of money. Changes in money change all nominal variables in the

same proportion but do not change real variables.

In the classical world, prices adjust to clear markets. In the case where q  q * ,

*
W W
this implies  . This causes W to fall as workers attempt to return to employment.
P P

This leads to a reduction in output price due to fixed proportion to costs and perfect

competition which leads to an increase in real money balances (for given stock of

nominal money) shifting LM to right (Keynes effect) until full employment is reached.

r
The “Keynes” effect. LM1
E1
r1 LM2
r* E*

IS
(W/P)1 (W/P)*
W/P y, q
y1 y*
Ns N1
s

N* q* = y*
Ns
_
Nd q = q(N,K)
N

Keynes suggests this might not happen for several reasons. lr =  (liquidity trap) and

er = 0 .

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Liquidity trap. r LM1

r1
LM2
r*

IS
(W/P)1 (W/P)*
W/P y, q
y1 y*
Ns N1

N* q* = y*
Ns
_
Nd
N q = q(N,K)

Because of liquidity trap, cannot shift LM to point of equilibrium r* (i.e., full

employment) since lr =  . If shift IS, it also does not change r. The only way to get

back to N* and q* is to shift IS out.

Interest-inelastic IS curve. r IS

LM
r*
r1

(W/P)1 (W/P)*
W/P y, q
y1 y*
Ns N1

N* q* = y*

Ns
_
Nd
N q = q(N,,K)

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The real economy is interest insensitive when er is low. This results in a steeply sloped

IS curve. Although an increase in money supply will shift LM out and change the

interest rate, r, this has little effect on aggregate demand or on output. Thus, shifts in LM

alone cannot get us to equilibrium output, y*. These two situations are anomalies and

difficult to believe.

The Keynes effect is a term used in economics to describe a situation where a change

in interest rates affects expenditure more than it affects savings. As prices fall, a

given nominal amount of money will become a larger real amount. As a result, the

interest rate will fall and investment demanded rises. [1] This means that insufficient

demand in the product market cannot exist forever.

There are two cases in which the Keynes effect does not occur: in the liquidity trap (when

the LM curve is horizontal), or when expenditure is inelastic with respect to interest rates

(when the IS curve is vertical). The Patinkin-Pigou real balance effect suggests that due

to wealth effects of changes in price level, insufficient demand cannot persist even in the

two cases above.

________________________________________________________________________

Pigou Effect

This effect is due to a wealth effect. The postulate is that aggregate consumption

expenditure depends on wealth as well as real income. Patinkin added the wealth effect

of money (real balance effect) into neoclassical economics. Now there can be a trade off

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between consumption at Ct and Ct +1 . This trade off depends on r, and the budget

Pt + 1
constraint slope is − .
Pt (1+ r )

A’
ct
A

c2 E’

c1 E
E”

B B’ ct+1

Let AB be the initial budget wealth constraint. If Pt and Pt +1 fall in equal measure,

given existing stock of nominal wealth, Vo , there will be an increase in value of real

wealth causing the budget constraint to shift out, and we generally consume more in both

periods (unless Ct is an aggregate of inferior goods). The decrease in prices shifts out

LM, and it also shifts out IS due to the effect of increased expenditures on output. Now,

the economy, in the long run, cannot settle into unemployment either due to the liquidity

trap or due to an interest inelastic IS since, as Pt and Pt +1 decrease, IS shifts

automatically to the right. Basically, the Pigou effect causes expenditure to respond to

price level changes thus ensuring a downward sloping aggregate demand curve. This

combined with a vertical aggregate supply curve ensures that the economy ends up at full

employment.

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“Pigou” Effect r IS1 IS2 LM1

LM2
r1

IS
(W/P)1 (W/P)*
W/P y, q
y1 y*
Ns N
1

N* q* = y*

_
Nd q = q(N,K)
N

Some Doubts about Neoclassical Synthesis

1. The analysis is comparative statics and not dynamic as Keynes intended. Also, unlike

Keynes, there is no use of expectations. If after a price decrease, people expect prices

to fall further, they may postpone consumption until the next period and not increase

expenditures as suggested by the Pigou effect. Thus, it is possible for a price

decrease to shift IS to the left if expectation of a further price decrease occurs. (Later,

we shall see that the Monetarist and New Classical Schools include expectations in

their versions of the model).

2. Problem of what constitutes wealth: outside versus inside money argument.

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3. Ignoring distributional effects of wealth could lead to serious shortcomings for the

neoclassical synthesis.

4. The magnitude of wealth effects is an empirical question, one that has not been

satisfactorily answered.

5. Wealth effects weaken classical model’s properties.

a. Classical dichotomy of economy does not hold as shown by Patinkin’s real

balance effect.

b. When non-money financial assets are introduced, such as bonds with fixed

nominal value, the strict quantity theory and neutrality of money no longer hold.

However, as Barro argues, government bonds, at least, may not be considered

wealth.

c. If labor supply decisions are based on wealth and have distributional effects on

this decision, the classical model will no longer be recursive since aggregate

supply becomes dependent on monetary conditions via wealth effects.

Important Questions

1. Is government intervention necessary?

2. Does government intervention work, that is, increase income?

3. Should the government intervene in the economy?

4. Is government intervention stabilizing or destabilizing?

5. Is the private sector inherently unstable necessitate government intervention for

stabilization, or is the private sector inherently stable and government intervention

destabilizing?

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6. What role does expectations play in the effectiveness of government intervention

in the economy?

Neoclassical synthesis: Conclusions

In the strict classical model, Keynes’ main proposition of an unemployment

equilibrium is not sustainable. However, given the special cases proposed by Keynes (i.

e., liquidity trap or interest inelastic IS curve), wealth effects are vital to ensure self-

stabilization back to a full-employment equilibrium, and wealth effects weaken the

propositions of the classical model.

Keynesians lost the intellectual debate but still argued that pragmatically their

analysis is important because an economy may not adjust rapidly enough and government

intervention could speed up the process back to full employment. This would be

particularly so if the interest sensitivity of the demand for money is high while that of

expenditure is low and wealth effects are weak. Further, Keynesians did not believe

prices are flexible but that they adjust slowly.

Milton Friedman, a Monetarist, argued that often, by the time the effects of

government spending or monetary policy worked its way through the economy (he

presumed about 18 months), the economy would already be recovering and the

intervention effects could cause adverse overheating (over stimulation) of the economy

and be destabilizing.

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Keynesian Fixed-Wage Model

There are two versions, one with fixed nominal wage, and the other with money illusion.

Keynes directly invokes both assumptions.

Keynes suggests that workers resists cuts in nominal wages even in times of

recession. If this is the case, the market clearing condition of labor supply equals labor

demand must be dropped. The market would clear only by accident. Essentially, the

labor supply equation becomes redundant when unemployment exists in that labor in the

market is determined by labor demand only; the labor supply curve is horizontal.

Accordingly, the aggregate supply curve is upward sloping until full employment is

reached. This is because the real wage varies inversely with the price level so that the

demand-driven employment rises with the price level until full employment is reached.

NOTE: This model fixes nominal wage and not the price level. If P increases, labor

demand increases because real wages fall. (If P , then N d  because W P  . )

W0
P
(ii) W1
AS' AS'' (i)
P2

P3
AS
W1 P0 AD2
W0
W0 W0 = W1 W0 P1 AD0
P2 AS AD1
P1 P0 P3
y2 y1 y0
W Nd Ns2 q, y
P Nd
1

N0
Ns1 _
(iii) Ns (iv)
Nd q = q(N, K)
2
The Keynesian Fixed-Wage Model N .

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In the figure above, assume that wage is fixed at W0. When the price level equals

P0 , the labor market is in equilibrium as well as the money and goods markets. If

aggregate demand falls from AD0 to AD1, the price level falls to P1, real wages rise to

W0/P1, employment falls to N1d , and output falls to y1. Thus, the fall in aggregate demand

decreases the price level as well as output. Unemployment is N1s - N1d of which N 0 -

N1d is considered involuntary, or demand deficient, because government could eliminate

this amount by expanding aggregate demand back to AD0 through fiscal spending. This

model runs into problems at employment levels above full employment. At that point,

aggregate supply is either backward bending or vertical. Suppose aggregate demand

increases to AD2 such that the price is now P2 , and the real wage is W0/P2. Now there is

excess demand of labor and actual employment is determined by labor supply, N 2s . If

the wage remains at W0, then the aggregate supply curve bends backwards. However, the

prediction that both output and employment will be less than at full employment when

aggregate demand is expanded past the point of full employment is counterintuitive. To

get around this problem, it is generally assumed that workers have a wage-floor only if

employment is less than at full-employment. After that, workers will allow upward

flexibility in the money wage. So, if aggregate demand shifts to AD2, workers bid up the

wage to W1 so that W0/P0 = W1/P3, and we restore full employment and get a vertical

aggregate supply curve. However, this causes an unexplained asymmetry in the behavior

of workers.

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W Ns (P0)
Nd 0
P
Ns (P1)
1

(W/P)o

(W/P)1

No N1 N
Money Illusion in the Labor Market

By further assuming money illusion, we can get an upward sloping aggregate supply

curve both below and beyond the full employment equilibrium. Workers now respond to

money wages, not real wages. So if the price level increases and thus decreases the real

wage, workers do not respond correctly (i.e., to real wages) but will supply the more

labor onto the market than before the price increase because the labor supply curve will

now shift outward so that, for every real wage, workers will supply more labor than

previously. However, since the labor supply curve shifts outward, the new intersection of

labor supply and demand curves is at a lower real wage so that more labor is employed at

the same nominal wage but lower real wage. Note: Any employment problems can

simply be corrected by government caused shifts in aggregate demand.

A problem with the model is that money wage is exogenous. This begs the question of

how the current wage came into being, under what circumstances will it change, and by

how much? The Keynesians did not have answers for these questions. Further, if in the

long run markets adjust, then nominal wage will fall causing prices to fall until we get the

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classical equilibrium through the Keynes and Pigou effects. (Question: Why would prices

fall if nominal wage fell?)

Reinterpretation of Keynesian Non-Market-Clearing Models

The classical world has markets that cleared according to Walras Law. Basically, in an n

good economy, if n-1 goods markets are in equilibrium, then the nth market is assured

mathematically to be in equilibrium (i.e., Walras Law). The Keynesian model contradicts

Walras Law because it can have equilibrium in all markets except the labor market. For

example, as we saw above, it is possible to be at the point where aggregate supply equals

aggregate demand, which insinuates that all goods market clear, but there exists excess

supply of labor.

Note that the figure below represents the classical case where all markets clear

and we have full employment equilibrium.

AS W
P P Ns
Nd
AD

W
P0 P 0

y* y N0 N
(a) (b)

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In the Keynesian model, we can have a shift in aggregate demand from AD to AD’ so

that price falls from P0 to P1. Since we assume that W is fixed, we have an increase in

real wages so that we now have an excess supply of labor. However, the aggregate

supply curve equals the aggregate demand curve at Y1 suggesting all goods markets are

in equilibrium. Thus, this model contradicts Walras’ Law.

P AS W
AD
P Nd Ns
AD' Excess supply
W of labor
P 0 P 1

P W
1
P 0

y 1 y* y Nd N0 Ns 1 N

(a) (b)

Critique of “Disequilibrium” models

The fixed-money wage Keynesian model is a special case of “general disequilibrium”

models shown below. In the former, prices are flexible and money wage is fixed, while

in the latter both prices and wage are fixed.

A. In the fixed-money wage model, Walras’ law does not hold when aggregate

demand falls because the labor supply is out of equilibrium while all goods

markets are in equilibrium.

B. The fixed-money-wage model with money illusion gives us an upward sloping

supply curve both below and above the full-employment level. The

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“disequilibrium” model does not. If aggregate demand increases above the full

employment point, households will not supply more labor because the wage has

not changed, nor has the price. Since household do not supply more labor,

notional labor supply falls short of the firms’ effective demand for labor.

Employment cannot increase so that output cannot increase. To restore the result

that output increases when aggregate demand increases above the point of full

employment, one needs to reintroduce the assumption of money illusion.

AD'
P W
AD P
Ns

Nd
Ns’
P* W*
P

y* y
1 y N* N 1 N
(a) (b)

C. One of biggest problems of these models is why disequilibrium persists in the

long run. Sticky prices and wages can be utilized to obtain a short-run

disequilibrium, but why would prices and wages remain sticky? Once these

adjust, then the Keynes and Pigou effects would force the economy back into the

classical full-employment equilibrium.

D. These models have little to say about the effects of inflation or stagflation.

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A Simple Model of General Disequilibrium

Consider a model where neither money wage nor prices adjust. If aggregate demand

shifts from AD to AD’ with price remaining unchanged, we are at point E in figure i.

That corresponds to E’ in figure ii, which is a point off the notional labor demand and

labor supply curves. Essentially, ABC becomes the effective labor demand curve in this

model. Note that at this juncture, output has fallen to y1 and labor to N1. The utility at

point E, U1, is less than the utility at full employment, U2.

Given that income has fall to y1, households now will spend cy1 where c is the marginal

propensity to spend. Since c < 1, this means in the next period, consumption and thus

income will fall to y2=cy1. Now the effective labor demand is AB’C’. The final

equilibrium will be stable since c<1.

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W
AD
P A B' B
N
P AD'C
s
D
AD’' E
(ii) W0 E' P0 (i)
P
Nd
C' C F
N2 N1 N0 N y2 y1 y*
y
y y
y = f(N)
y0
(iii) y1 (iv)
y2
45°
N2 N1 N0 N y
U2 S
U1 U0
y=WN
P y*

(v) y1 E’’ A Model of “General Disequilibrium”

N2 N1 N0 N

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