Lecture III Keynesian Model
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Keynes’ General Theory, by all accounts, is difficult to
understand
For this reason, Keynes’ ideas have come down to us
filtered through the eyes of those that either were there
when the ideas were being worked out or by later
writers that have more or less guessed at what the
“great master” had in mind
In this way, Keynes is very much like Jesus Christ, whose
words and meaning have come to us through the
“apostles”; although in the case of Keynes, we do have
his actual writings to fall back on
What Keynes was proposing
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He was trying to work out a new way of looking at the
economy that could explain the existence of widespread
unemployment when so many people were willing to
work for wages well below the market wage
He referred to this phenomenon as “involuntary”
unemployment
The classical view was that this cannot occur; the wage
rate will simply fall to the equilibrium wage and all
markets, including the labor market, will be in
equilibrium
Thus general equilibrium at full employment is
maintained
The idea of “effective” demand
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Keynes begins with the notion that aggregate demand
for the goods and services in the economy can be
decomposed into two parts: a part that depends on the
level of output and a second part that is exogenous
Thus, D = D1(Y) + D2
We can think of these two as D1(Y) = C and D2 = I,
which is exogenous to Y
Unlike classical theory, Keynes does not really look upon
investment demand as depending strongly on the
interest rate, although that will not be a major problem
to his model
Keynes on investment
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It is critical to his theory to understand how he felt about
the decision to invest or not
He viewed investment decisions by firms and
entrepreneurs as dependent on their “animal spirits”,
that is, once businesses are frightened off from the
market, perhaps due to continued losses sustained by
themselves and other investors, it may be next to
impossible to convince them to return
As a sidebar, much of the discussions we here today
about what to do after the financial crisis, concerns the
“credibility” of central banks actions; more on this later
IS-LM model
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John Hicks in Mr. Keynes and the “Classics” first
introduced the IS-LM analysis
Some of Keynes’ contemporaries argued that
Keynes never used such models; however,
writings of Keynes discovered after his death did
find the he worked on such equations
The IS curve is the locus of points in i-Y space at
which the product market is in equilibrium while
the LM curve does the same for the loanable
funds market
The IS curve
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Keynes starts with the premise that expenditures E =
output Y = C + I in a closed economy with no or limited
government
C depends primarily on Y, but let’s suppose some saving
is generated through a rise in I, so C = c(i,Y) which
implies that S = s(i,Y) where Si and SY > 0.
Investment depends only on I and Ii < 0
Equilibrium requires that S = I or I – S = 0; furthermore,
for it to be maintained, the change in I – S must = 0, so
d(I – S) = Ii di – (Si di + SY dY) = 0
Solving for di/dY, we get di/dy = SY dY/(Ii di – SY dY) <
0; thus, the IS curve is down-sloping
The LM curve
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The demand for money depends on both Y and i, where
people hold more money to finance transactions at
higher levels of Y and economize on money holdings as i
rises
The supply of money is either fixed or rises with i say as
financial institutions reduce excess reserves as the return
on loans increases
Again, we need Demand for money L to equal M, the
money supply and along the LM curve, d(L – M) = 0
So, Li di + LY dY – Mi di = 0 and solver for di/dY we get
di/dY = LY/(Mi – Li) > 0
Graph of IS and LM curves
IS LM Curves
0.45
LM
IS
0.4
0.35
0.3
r
0.25
0.2
0.15
0.1
0.05
Y
00
60
00
55
00
50
00
45
00
40
00
35
00
30
00
25
00
20
00
15
00
10
0
50
0
0
IS-LM in equation form
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E = A + cY – ai = Y, so (1 – c)Y = A – ai
Real money demand M/P = mY – bi = Ms/P for monetary
equilibrium
Thus, i = [mY – Ms/P]/b; substituting into first equation we get
(1 – c)Y = A – a[mY – Ms/P]/b
Solving for Y we get [1 – c + (a/b)m] Y = A + (a/b)(Ms/P)/b and
Y = A/[1 – (c – m(a/b))] + Ms/P[1/[m + (b/a)(1-c)]
Keynes assumed both consumption and investment were relatively
insensitive to i (that is, a is small) and demand for money was very
sensitive to i when rates are close to 0 (that is, b is large)
These two imply that changes in the money supply have very little
influence on aggregate supply while the Keynesian multiplier is close
to 1/(1-c)
The Keynesian consol example
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A consol is a perpetuity bond that pays a fixed amount each period, say a
year
S = ∑1/(1+r)n, n = 1, ∞ = 1/(1+r) + 1/(1+r)2 + … + 1/(1+r)n + …
(1+r)S = 1 + S => (1+r)S – S = rS = 1 and S = 1/r
So I pay $20 for this console
If the rate falls to 4%, I make $5, or 20% return for a 1% drop in interest
rates; if r goes up to 6%, on the other hand, the price falls to $16.67 and I
lose $3.33 or 16.67%
What if the interest rate is near 0%? The rate can hardly fall, so the next
move in interest rates must be upward; that is, I can only lose money (or
stay the same) if I buy a consol now
But I can earn the same return by simply hoarding my cash
This Keynes referred to as the zero-bound or the liquidity trap
The Keynesian Model in
Undergraduate Economics
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Let Y = C + I = a + cY + I, a and I are exogenously determined
Then at equilibrium Ye = [1/(1–c)](a + I), and 1/(1-c) = k, the
Keynesian multiplier
Now suppose Ye < Yp, potential, or full-employment, output
Keynes argued that government should fill the expenditure gap,
which he referred to as the recessionary gap.
Now Y = a + cY + I + G, and we assume the government
expenditures do not affect a, c, or I.
Then solving for Ye gives Ye = k(a + I + G) which is greater than
the previous equilibrium output
So if kG = (Yp – Ye), so the recessionary gap is g = 1/k(Yp – Ye)
Example 1
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Y = C + I = 400 + .6Y + 1000 = 1400 + .6Y and
solving for Y gives [1/(1-c)] (a +I0) = (1/.4)(1400)
= 2.5*1400 = 3500, and k = 2.5
Keynesian Cross Diagram
5000
4500
4000
We see that AD = AS at the equilibrium AS of 3500
3500
AD
3000
AD
45-degree
2500
2000
1500
1000
500
0
0
500
1000
1500
2000
2500
AS
3000
3500
4000
4500
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Now if I declines to 900, AD will decline by
k*d(AD) = - 250, so AD = 3250
This is shown on the Keynesian cross diagram
below
To restore the equilibrium level of AD to the
desired 3500 we need add G = 100 and we will
be back to the original AD curve
Keynesian Cross Diagram
5000
4500
When I = 1000, we see that AD = AS at the equilibrium AS of 3500
4000
3500
AD
45-degree
I = 900
3000
AD
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2500
2000
1500
Aggregate demand for I = 900; AD = AS at AS = 3250
1000
500
0
0
500
1000
1500
2000
2500
AS
3000
3500
4000
4500
What about budget deficits?
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David Ricardo considered the case of debt financing of
government expenditures and conjectured that, if the
public perceived the increase in debt as a future tax
liability, it might elect to save more, even and equal
amount to the debt, as a way to pay the future liability
Apparently, Ricardo rejected the idea of such foresight of
the public, but the notion, called the Ricardian
Equivalence Theorem, still bears his name
But let’s suppose we decide to finance the expenditures
with lump-sum tax today
Then Y = a + c(Y – T) + I + G, T = G is a lump-sum tax
Lump-sum tax multiplier
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Now our model is Y = a + c(Y – T) + I0 + G, where
T=G
Then solving for Ye we get Ye = [1/(1-c)](a – cT + I0
+ G) = [1/(1-c)] (a + I0 + G – cG) = [1/(1-c)][a + I0 +
(1-c)G] = [1/(1-c)] (a + I0) + G, since T = G
Thus, the “balanced budget multiplier” is 1; if the
government spends an amount just equal to Yp –
Ye equilibrium is restored at full employment
Income Tax financing
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Since taxes are collected from individuals and not the country
as a whole (since passage of the 16th amendment in 1909), a
more realistic model is
Y = a + c(Y – tY) + I + G, tY = G
Then Y(1 – c + tc) = Y(1 – c(1 – t)) = a + I + G, so Ye = 1/[1 –
c(1-t)] (a + I + G) and k* = 1/(1-c(1-t)) is smaller than before
Thus the recessionary gap has increased to 1/k*( Yp – Ye)
In our earlier example, suppose t = .2, then k* = 1/(1 - .6(1 .2)) = 1/.52 or around 2
It appears we now need to increase G to 250/2 = 125
Uh-oh!
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When we substitute the numbers back, they
don’t work; Y = 2(a + I + G) = 2(400 + 900 +
125) = 2850
The reason is we collect too much in taxes;
.2*2850 = 570, but we only need 125
So let’s let the model tell us the optimal tax rate
t*; t*Y = G, which we also need to solve for
The second equation is (1-c(1-t*))Y = a+I+G;
so (1-.6(1-t*))3500 = 400+900+G = 1300+G
Optimal t* and G
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We get 3500 = (1/(.4+.6t*))(1300+G); but G = 3500t*
So we solve for t* in the following equation 3500 =
1/(.4+.6t*) (1300+3500t*)
Dividing both sides by 3500, we get
1=1/(.4+.6t*)(1300/3500+t*) so
.4+.6t* = 1300/3500 +t* => .4t* = .4-13/35
t* = 1-13/14 = 1/14
G = t*(3500) = 3500/14 = 250!
The same answer as we got with a lump-sum tax
Thus, the balanced budget multiplier is again 1; is this
just a coincidence? Let’s see.
Solving using algebra
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Yp = a + c(Yp –t*Yp) + I + G; G = t*Yp
So Yp = a + c(Yp –t*Yp) + I + t*Yp
(1-c)Yp = a – ct*Yp + I + t*Yp = (a + I) + t*Yp(1-c)
Thus, Yp = (a + I)/(1-c) + t*Yp = (a + I)/(1-c) + G
That is, Y changes 1 for 1 with G; the multiplier on G financed
using the optimal tax is still 1
In general, however, a proportionate tax does reduce the
multiplier to 1/(1 – c(1 – t))
What about an open economy?
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With trade the equation becomes Y = a + c(Y – T)
+ I + X – M, where X = exports and M = imports
While exports are generally considered as
determined externally to our economy, imports
should grow with Y
In fact, it is often the case that fast growing
economies are great exporters; just think about
China
This issue will be covered later when we discuss
the monetary approach to the balance of payments
The general model
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Y = a + c(Y – t0 – t1Y) + I + G + X – M0 – mY
Then Y – cY + ct1Y + mY = (1-c(1-t1)+m) = a
+I+G+X
In the literature, the right-hand side variables
are called injections; savings, taxes and
imports are referred to as leakages
At equilibrium, injections must equal leakages
How does the degree of openness affect
the slope and location of the IS curve?
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The more open an open is economy the less
“bang for the buck”, that is the additional
leakage from imports increases the slope so that
a monetary change – a movement along the IS
curve – will have less affect on Y and more on I
The addition of export demand, say from greater
world output, the further to the right the IS
curve will lie
IS-LM Exercises
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Exercise 1: Draw a set of IS-LM curves
What is the effect of an increase in
Government spending?
What happens to equilibrium i and Y?
Now, how can the Fed reduce crowding
out?
What now happens to equilibrium i and Y?
What happens to the budget deficit?
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Exercise 2: Draw a set of IS-LM curves
What is the effect of an increase in central
bank credit to lending institutions?
What happens to equilibrium i and Y?
What happens to the budget deficit?
What happens to equilibrium i and Y?
The real wealth effects of deficits
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One issue with deficits financed by bond creation is the public
perception of their increased bond holdings
At one end is the Ricardian Equivalence, which believes that
these holdings are viewed as both wealth and as a liability at
its limit one for one
At the other end of the spectrum is the belief that the public
sees these bonds only as wealth and therefore will spend even
more than the Keynesian model predicts (although this effect
was never included in the model; we could show this as C = a
+ cY + gB, where B is the stock of government bonds held by
the public)
Since some of the expansion in the economy is financed by
increased tax revenues, the amount needed to be financed
through bonds is reduced and if a portion of the bonds held
increases private spending through the wealth effect, the
negative impact of the deficits can be reduced, making the
Keynesian argument even stronger
Arguments for and against the
wealth effect of government bonds
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To the extent that future generations may be impacted
by the tax liability, the negative Ricardian effect is
reduced
Barro argues, however, that the fact that people
bequeath wealth to their heirs indicates that they care
about the higher tax liabilities they are leaving them
But some don’t care; either they have no heirs or they
figure the next generation will be so much better off that
they can pay the taxes themselves
Plus the government can borrow more cheaply than the
private sector, so the burden is reduced
“Normal Case” with flexible wages and prices and no liquidity trap
LM o
r
LM 1
SL
W /P
(W /P )o
(W /P )f
DL
IS
Y
L
45deg
Y
Y
Yo
Yf
Y
Lo
Lf
L
W ith flex ib le w ag es an d p rices an d th e in terest rate w ell ab o v e its lo w er b o u n d
th e eco n o m y ad ju sts to fu ll-em p lo ym en t eq u ilib riu m v ia m o n etary p o licy alo n e
Flexible wage and prices; liquidity trap (inflexible r)
LM o
r
LM 1
SL
W /P
DL
IS
L
Y
45deg
Y
Y
Y
L
P u sh in g o u t th e L M cu rv e d o es n o t lo w er th e in terest, w h ich is alread y at
its lo w er b o u n d .
“Almost” in a liquidity trap
LM o
r
LM 1
SL
W /P
(W /P )o
Lower bound r
(W /P )f
DL
IS
Y
L
45deg
Y
Y
Yo
Y1 < Yf
Y
Lo
L1 < Lf
L
W ith flex ib le w ag es an d p rices an d th e in terest rate clo se to its lo w er b o u n d
th e eco n o m y ad ju sts to less th an fu ll-em p lo ym en t eq u ilib riu m v ia m o n etary p o licy alo n e
The Pigou Effect
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Arthur Pigou, a contemporary and (kind of) a
friend of Keynes, argued that the price declines
will increase the real wealth of the public and
thereby increase their expenditures
Critiques are compelling: effect can be too slow;
the fall in prices have negative effect on
business optimism; increased bankruptcies
reduce investment; postponement of
consumption awaiting further price declines; etc.
The Keynes-Pigou Debate
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Pigou may have won the intellectual debate, showing that the
economy, given enough time and flexible wages and prices,
would return to full employment on its own
On the policy side, however, concerns about the speed of
adjustment (“In the long run we’re all dead”) led most
western economies to adopt Keynesian style fiscal policies
Even today, this is the most often used model by most
politicians and their staffs
Central banks, on the other hand, have begun to use the
alternative DSGE model for their analyses
This incorporates more of the elements of rational
expectations and take into account the Lucas Critique by
allowing parameters of their models to adjust and by
disaggregating the economy into several sectors
Even these models, however, are limited as to the amount of
disaggregation they employ
Open Economy & the Balance of Payments
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Let’s look at the BP line where BOP = 0
As Y increases a country wants to import more
As i increases, more capital flows inward
Thus as Y increases i must also increase to
maintain balance, so BP is positively sloped
The slope depends on the interest elasticity of
capital flows and the income elasticity of imports;
the more the interest elasticity of capital flows,
the smaller the adjustment in I needed to
balance flows, so the flatter the BP curve; the
greater the income elasticity of imports the
greater the interest rate change needed to
balance payments, so the steeper the BP line
Stimulative fiscal policy under a
fixed exchange rate
LM
BP
B
C
A
IS '
IS
Y
S ta rtin g fro m a n in itia l p o in t o f trip le in te rs e c tio n o f th e IS , L M a n d B P c u rve s .
If th e L M c u rve is s te e p e r th a n th e B P c u rve , th e n a p o s itive fis c a l s tim u lu s
in c re a s e s th e in te re s t ra te b y m o re th a n e n o u g h to c o m p e n s a te fo r th e
h ig h e r in c o m e a n d a B O P s u rp lu s re s u lts . T h e a d d itio n a l in flo w s o f c a p ita l
m a y p u s h d o w n th e in te re s t ra te . U n d e r fix e d e x c h a n g e ra te s , c a p ita l in flo w s
in c re a s e th e m o n e y s u p p ly a n d , a s s u m in g n o s te riliza tio n o f th e s e flo w s ,
p u s h e s o u t th e L M c u rve to a n e w trip le in te rs e c tio n a t p o in t C .
BP steeper than LM
BP
LM
B
C
A
IS '
IS
Y
If th e L M c u rve is fla tte r th a n th e B P c u rve , th e n a p o s itive fis c a l s tim u lu s
in c re a s e s th e in te re s t ra te b y le s s th a n e n o u g h to c o m p e n s a te fo r th e
h ig h e r in c o m e a n d a B O P d e fic it re s u lts . T h e o u tflo w o f c a p ita l d e c re a s e s
th e m o n e y s u p p ly a n d a n d p u lls in w a rd th e L M c u rve to a n e w trip le
in te rs e c tio n a t p o in t C .
Keynesian model and the Phillips Curve
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Keynes worked in real values since inflation was
not an issue in times of depression; if anything,
prices fell
But Keynesians had to address the issue of what
happened as the economy approached full
employment
Let us look at the “stripped down” version of the
aggregate supply-aggregate demand diagram
P ric e
AD'
Y = AS
AD
In th e o rig in a l ve rs io n , th e e c o n o m y is in o n e o f tw o s ta te s : fu ll e m p lo ym e n t
o r le s s th a n fu ll e m p lo ym e n t. In th e la tte r c a s e , th e e c o n o m y fa c e s n o p ric e
in c re a s e s u n til it a tta in s fu ll e m p lo ym e n t, a fte r w h ic h a n y s h ift in A D is m e t
w ith h ig h e r p ric e s a n d n o a d d itio n a l o u tp u t
P ric e
AD"
AD'
AD
AS
In th e re vis e d ve rs io n , th e re is a n in te rm e d ia te ra n g e in w h ic h p ric e s ris e
w ith a g g re g a te d e m a n d a n d s u p p ly. T h is ra n g e c o rre s p o n d s p e rfe c tly to th e
P h illip s C u rve . A s A S in c re a s e s in re s p o n s e to th e o u tw a rd s h ift in d e m a n d ,
p ric e s ris e a s Y in c re a s e s , ie u n e m p lo ym e n t d e c re a s e s . T h is is th e P h illip s
C u rve . S o th e p u b lic a tio n o f P h illip s ' a rtic le g a ve a s to ry fo r K e yn e s ia n s
to te ll.
The Phillips Controversy
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So the idea of a permanent and stable tradeoff
relationship between inflation and
unemployment provided additional armor
against attacks from those that would worry
about the hyper-inflationary danger of
permanent deficits or monetary stimulus
In fact, a thorough reading of Phillips himself
shows that he did not intend for the empirical
results to be inerpreted by policy makers as an
excuse to inflate the economy so as to reduce
unemployment
Stagflation and the end of the
Phillips Curve
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The events that occurred starting in 1970 demonstrated
that the critics were correct after all; continued attempts
to stimulate the economy in the face of real supply side
shocks took its toll and inflation hit double digits with
little effect on the unemployment rate
This period became known as stagflation, and was only
ended with the recession of 1981-83 caused by Paul
Volcker
During this recession unemployment hit 10% for the first
time since the Great Depression
Now we are once again experiencing such high rate of
unemployment
The vertical long-run Phillips Curve
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The events in that began at the time of stagflation led
most economists to abandon the conventional view and
to adopt Friedman view that there is no long-run Phillips
Curve
Friedman viewed the relationship as a short-term fix that
would eventually lead to expectations of inflation that
would nullify the short-term benefits
Later he adopted the rational expectations view that
even the short run Phillips Curve tradeoff would
disappear in favor of a vertical Phillips Curve at the
permanent natural rate of unemployment