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The Classical Model versus the Keynesian Model of Income and
Interest Rate Determination
Classical
Keynesian
goods market
I(r) = S(r)
or I(r) = Y - C(r)
I(r) = S(Y)
or I(r) = Y - C(Y)
money market
M = kPY
M = kPY + L(r)
production function
Y = Y(N, K )
Y = Y(N, K)
labour market
D(
W
W
)  S( )
P
P
W
W
D
S
N (P)N (P)
Three major differences:
(1) no induced consumption
induced consumption
(consumption as a
(positive “feedback”
residual decision after
between C and Y)
saving)
reflecting behaviour of different income groups?
feedback CYBERNETICS
(2) no multiplier effect
multiplier effect
important implications for autonomous expenditure
including G
(3) “classical dichotomy ”
between the goods and
the money markets
interaction between the
goods and the money
markets
*Read Brian Morgan, chapter 2.
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National Income Determination and the Wealth Effect: the IS-LM
Model
The IS-LM model is a behavioural model with an identity and separate
functions for key variables, some of which are endogenous (determined
within the model) while others are exogenous (not determined by the
model and therefore assumed to be independent).
IS
(1) IS curve: the equilibrium locus of the goods market, tracing out the
relationship between income Y and interest rate r.
YC+I+G
(identity)
C = c0 + c(Y – T)
T = t0 + tY
(endogenous)
(endogenous)
G= G
(exogenous)
I = i0 – fr
(endogenous)
By substitution
Y = c0 + c[Y – (t0 + tY)] + i0 – fr + G

  G  Y[1  c(1  t)]
r = c 0 ct 0 i 0
f
Y=
(IS curve without wealth effect)
f
1
(c 0  ct 0  i 0  G) r
1  c(1  t)
1 - c(1 - t)
(IS curve without wealth effect)
Multiplier:
1
1

1  c(1  t) 1 - c  ct
When tax is imposed lump-sum, i.e. T = to:
Y=C+I+G
= c0 + c(Y – t0) + i0 – fr + G
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
  G  Y(1  c)
r = c 0 ct 0 i 0
f
Y=
f
1
(c 0  ct 0  i 0  G) r
1 c
1- c
Multiplier:
1
1
, which is greater than
. So lump-sum tax
1 c
1 - c  ct
produces a larger multiplier.
(2) Wealth augmented consumption function:
C = co + c (Y – T) + jW
working out: r =
Y=
1
1  c(1  t)
(c0  ct0  i0  G  jW) Y
f
f
1
f
(c0  ct0  i0  G  jW)r
1 c(1 t)
1 c(1 t)
(IS curve with wealth effect)
LM
(2) LM curve: the equilibrium locus of the money market, tracing
out the relationship between income Y and interest rate r.
Neglecting the price and the Pigou (price) Effect
Ms  Md
(identity—equilibrium condition)
Md = hY – lr + gW
(endogenous)
Ms = M
(exogenous)
1
l
h
l
r=  M Y
(LM curve without wealth effect)
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Y=
1
l
M r
h
h
(LM curve without wealth effect)
Adding the wealth effect to the money demand
Function:
Md = hY – lr + gW
r=
1
g
h
W M Y
l
l
l
(LM curve with wealth effect)
Y=
1
g
l
M W r
h
h
h
(LM curve with wealth effect)
LM
Pigou Effect
Wealth Effect
IS
LM’
Wealth
Effect
IS’
Saving the inadequacy
of Keynesian effect in
face of wage rigidity
IS-LM equilibrium with wealth effect
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1  c(1  t)
1
g
h
(c 0  ct 0  i 0  G  jW) Y= W  M  Y
f
f
l
l
l
 h 1  c(1  t) 
1
1
g

Y
=
(
G
W)
M
W




j

c ct 0 i 0
l

f
f 0
l
l


hf  l[1  c(1  t)]
1
1
g
Y = (c 0  ct 0  i 0  G  jW)  M - W
lf
f
l
l
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Y=
1
lf
(c  ct 0  i 0  G  jW) +
hf  l[1  c(1  t)] f 0
lf
1
lf
g
MW
hf  l[1  c(1  t)] l
hf  l[1  c(1  t)] l
Y* =
l
(c  ct 0  i 0  G  jW) hf  l[1  c(1  t)] 0
f
f
gW +
M
hf  l[1  c(1  t)]
hf  l[1  c(1  t)]
LM’’
LM’
LM
IS’
IS
Y*’’ Y* Y*’
The relative effectiveness of fiscal versus monetary policy (i.e. the
relative size of the fiscal multiplier versus the monetary multiplier)

depends on the size of l  f ?
Repeat: the multiplier is a kind of damped positive feedback.
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