© Pilot Publishing Company Ltd. 2005 Chapter 6 Income Determination II --- The IS-LM Model.
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Transcript of © Pilot Publishing Company Ltd. 2005 Chapter 6 Income Determination II --- The IS-LM Model.
© Pilot Publishing Company Ltd. 2005
• Assumptions of the IS-LM Model• What is the IS curve?
• Graphical derivation of the IS curve
• Slope of the IS curve
• Shift of the IS curve • What is the LM curve?
• Graphical derivation of the LM curve
• Slope of the LM curve
Contents:
© Pilot Publishing Company Ltd. 2005
• Shift of the LM curve
• Equilibrium in both the goods market and money market
• Change in equilibrium caused by an autonomous change in injection or withdrawal
• Change in equilibrium caused by an autonomous change in money demandor money supply
Contents:
© Pilot Publishing Company Ltd. 2005
Assumptions of the IS-LM model:
1. Yf is a constant.
2. An unemployment of resources.-- The model is to find out determinants of the equilibrium GNP and ways to eliminate unemployment.
3. GNP = GDP = Y.
4. Price level is kept constant.-- Nominal variables = real variables and nominal r = real r.
© Pilot Publishing Company Ltd. 2005
Keynesian models
Keynesian model
Markets involved Endogenous variables
Y-E model (elementary Keynesian
model)
• Goods market Y
IS-LM model • Goods market• Money market
Y and r
AD-AS model • Goods market• Money market• Factor market
Y, r and P
© Pilot Publishing Company Ltd. 2005
IS Curve is a line relating real national income (Y) to real interest rate (r) at which the goods market is in equilibrium (i.e., with Y = E or J = W).
What is the IS Curve?
© Pilot Publishing Company Ltd. 2005
r
Y
W
J0
Quadrant II (NW quadrant)
Quadrant III (SW quadrant)
Quadrant IV (SE quadrant)
Four-quadrant diagram
Quadrant I (NE quadrant)
© Pilot Publishing Company Ltd. 2005
r
J
J=I+G+X
r
JInjection function: J = I + G + X
Quadrant II (NW quadrant)
G and X are autonomous.
Thus, J is negatively related to r.
0
I is negatively related to r.
© Pilot Publishing Company Ltd. 2005
W
W=S+T+M
Y
W
Withdrawal function W = S + T + M
S, T and M are positively related to Y
Thus, W is positively related to Y
Quadrant IV (SE quadrant)
Y
0
© Pilot Publishing Company Ltd. 2005
J1
J=W
45o
W
J
W1 (= J1)
Quadrant III (SW quadrant)
0
J and W of points on the 45° line are equal. Hence they represent equilibrium in the goods market, where J = W.
© Pilot Publishing Company Ltd. 2005
45o
r
Y
W
J0
Ar0
J0
W0
Y0
B
IS
When interest rate = r0 injection = J0
Corresponding national income = Y0
Equilibrium in goods market
To achieve equilibrium: J0
= W0
© Pilot Publishing Company Ltd. 2005
IS
Y1
r1
r
YY0
r0
0
Initial goods market equil.: (Y0, r0)Downward slopingDownward sloping 1. If r ( r0 to r1) J ( J0 to J1)
So at point Z, J > W
2. To restore equil., Y should (Y0 to Y1) to raise W until W = J again.
Z r & Y are negatively related.
© Pilot Publishing Company Ltd. 2005
r
Y0IS0
A (Y0,r0)
B (Y1,r0)
Assumption: An autonomous in J or in W (not caused by changes in r or Y)
IS1
J > W
If r remains constant, Y has to Y has to to Y to Y11 until W & equates with J again.
IS curve shifts rightward to restore equilibrium.
© Pilot Publishing Company Ltd. 2005
Assumption: An autonomous in J or in W (not caused by changes in r or Y)
J > W
If Y remains constant, r has to r has to to r to r11 until J & equates with W again.
IS curve shifts upward to restore equilibrium.
r
Y0IS0
IS1
C (Y0,r1)
A (Y0,r0)
© Pilot Publishing Company Ltd. 2005
IS2
r
Y0
IS0
A (Y0,r0)
E (Y0, r2)
D (Y2, r0)
J < W
IS curve shifts leftward or downward to restore equilibrium.
Assumption: An autonomous in J or in W (not caused by changes in r or Y)
© Pilot Publishing Company Ltd. 2005
Q6.2: Derive from four-quadrant diagrams the change in the IS curve, (a) when there is an autonomous rise in J. (b) when there is an autonomous fall in J. (c) when there is an autonomous rise in W. (d) when there is an autonomous fall in W.
© Pilot Publishing Company Ltd. 2005
Result Possible causes
Rightward (upward) shift of the IS curve
Leftward (downward) shift of the IS curve
Q6.3: Fill in the following table.
W autonomously
J autonomously
W autonomously
J autonomously
© Pilot Publishing Company Ltd. 2005
What is the LM Curve?
LM curve is a line relating real national income (Y) to real interest rate (r) at which the money market is in equilibrium [i.e.,with real money demand (Md) or real liquidity preference (L) = real money supply (Ms)].
© Pilot Publishing Company Ltd. 2005
Transactions demand for money:
d is the change in Mt resulting from a unit change in income.
Income & Mt are positively related & so d > 0.
Mt = dY
Income elasticity of transactions demand for money
© Pilot Publishing Company Ltd. 2005
Asset demand for money:
e is the change in Ma resulting from a unit change in r e < 0
Ma = e r + Ma*
Interest elasticity of asset demand for money
Autonomous asset demand for money
Ma* is the autonomous asset demand for money
Ma* > 0
© Pilot Publishing Company Ltd. 2005
Money supply function
P
M1Ms
P
M1Ms
M1 is the sum of legal tender in public circulation
and demand deposits
M1 is the sum of legal tender in public circulation
and demand deposits
General price levelGeneral price level
© Pilot Publishing Company Ltd. 2005
r
Y
Mt
Ma
0
Quadrant II (NW quadrant)
Quadrant III(SW quadrant)
Quadrant IV (SE quadrant)
Four-quadrant diagram
Quadrant I (NE quadrant)
© Pilot Publishing Company Ltd. 2005
r
Ma
r
Ma
Ma = er + Ma*
0
Asset demand for money
Ma is negatively related to r
Quadrant II (NW quadrant)
© Pilot Publishing Company Ltd. 2005
Y
Mt
Y
Mt
Mt = dY
Transactions demand for money
Mt is positively related to Y
Quadrant IV (SE quadrant)
© Pilot Publishing Company Ltd. 2005
M1/P = Ms = Ma+Mt
Ma
Mt
45o
M1/P
M1/P
Equil. Condition: (Md=Ms )
MaMt
= M1/P - Ma
Mt
Quadrant III (SW quadrant)
If Mt = M1/P - Ma, then Mt + Ma = Md = M1/P = Ms
© Pilot Publishing Company Ltd. 2005
r
Y
Mt
Ma
0
45o
LM
Ma0
Mt0
Y0
r0
When interest rate = r0 assets demand = Ma0
In Equilibrium: Mt0 = Ms – Ma0
Ma0 + Mt0 = Ms
Corresponding national income = Y0
A
B
Equilibrium in money market
© Pilot Publishing Company Ltd. 2005
Assume initial money market equil.: (Y0, r0)
If Y (Y0 to Y1) Mt ( Mt0 to Mt1)
At point Z, Md > Ms
To restore equilibrium, r should ( r0 to r1 ) such that Ma & Mt + Ma equates with Ms again.
r & Y are positively relatedr0
Y0
r
YY1
r1
0
Upward sloping
Upward sloping
LM
Z
© Pilot Publishing Company Ltd. 2005
B (Y1,r0)
r
Y0
A (Y0,r0)
LM0
LM1
Assumption: An autonomous in Md or in Ms
(not caused by changes in r or Y)
Md > Ms
If r remains constant, Y has to to Y1 such that Mt and Md = Ms again.
LM curve shifts leftward to restore equilibrium.
© Pilot Publishing Company Ltd. 2005
Assumption: An autonomous in Md or in Ms
(not caused by changes in r or Y)
Md > Ms
If Y remains constant, r has to to r1 such that Ma and Md = Ms again.
LM curve shifts upward to restore equilibrium
C (Y0,r1)
r
Y0
A (Y0,r0)
LM0
LM1
© Pilot Publishing Company Ltd. 2005
r
Y0
A(Y0,r0)
LM0
LM2
E (Y0,r2)
D (Y2,r0)
Md < Ms
LM curve shifts rightward or downward
Assumption: An autonomous in Md or in Ms
(not caused by changes in r or Y)
© Pilot Publishing Company Ltd. 2005
Q6.4: Derive from four-quadrant diagrams, the change in the LM curve(a) when there is an autonomous rise in Ma.
(b) when there is an autonomous fall in Ma.
(c) when there is an autonomous rise in Mt.
(d) when there is an autonomous fall in Mt.
(e) when there is an autonomous rise in Ms.
(f) when there is an autonomous fall in Ms.
© Pilot Publishing Company Ltd. 2005
Result Possible causes
Rightward (downward) shift of the LM curve
Leftward (upward) shift of the LM curve
Q6.5: Fill in the following table.
Md autonomously
Ms autonomously
Md autonomously
Ms autonomously
© Pilot Publishing Company Ltd. 2005
r
Y0
IS
A(J = W)
B(J < W)
Goods market equilibrium and the IS curve
There is an unintended inventory investment. Firms cut production & Y.
Pt. B lies above pt. A. At pt. B, r J At pt. B, J < W
© Pilot Publishing Company Ltd. 2005
r
Y0
IS
A(J = W)
C(J > W)
There is an unintended inventory disinvestment. Firms raise production & Y.
Goods market equilibrium and the IS curve
Pt. C lies below pt. A. At pt. C, r J
At pt. C, J > W
© Pilot Publishing Company Ltd. 2005
r
Y0
Money market equilibrium and the LM curve
LM
B (Md < Ms)
A (Md=Ms)
Pt. B lies above pt. A. At pt. B, r Ma
At pt. B, Md < Ms
Pt. B lies above pt. A. At pt. B, r Ma
At pt. B, Md < Ms
With excess money balance, people buy bonds to earn interest.
Bond price r
© Pilot Publishing Company Ltd. 2005
C( Md > Ms)
Pt. C lies below pt. A. At pt. C, r Ma At pt. C, Md > Ms
Pt. C lies below pt. A. At pt. C, r Ma At pt. C, Md > Ms
With excess money demand, people sell bonds for liquidity.
r
Y0
LM
A (Md=Ms)
Money market equilibrium and the LM curve
Bond price r
© Pilot Publishing Company Ltd. 2005
Adjustment towards twin equilibrium
1. Whenever a point is not on the IS curve, Y will change until it reaches the IS curve.
2. Whenever a point is not on the LM curve, r will change until it reaches the LM curve.
© Pilot Publishing Company Ltd. 2005
r
Y0
LM
IS
J<W YMd<Ms r
J>W YMd>Ms r
J>W YMd<Ms r
J<W YMd>Ms r
Adjustment towards twin equilibrium
© Pilot Publishing Company Ltd. 2005
Change in Equilibrium Caused by
an Autonomous Change in Injection or Withdrawal
© Pilot Publishing Company Ltd. 2005Crowding-out effect
r
Y0
LM0
IS1
IS0
r1
r0
Y1Y0 Y’}
Transmission mechanism:Autonomous J or W
As J > W Y W & Mt
Md > Ms r Ma & J
Until both markets r
estore equil.
IS curve shifts rightward
© Pilot Publishing Company Ltd. 2005
Q6.6:
When J < W, both income and interest rate fall. Describe the transmission mechanism.
© Pilot Publishing Company Ltd. 2005
Change in Equilibrium Caused by
an Autonomous Change in Money Demand or Money Supply
© Pilot Publishing Company Ltd. 2005
Transmission Mechanism:
Y1
r1
LM1
r
Y0IS0
LM0
r0
Y0
As Md > Ms r Ma & J
Autonomous Md or Ms
LM curve shifts leftward
J < W Y W & Mt
Until both markets r
estore equil.
© Pilot Publishing Company Ltd. 2005
Q6.7:When Md < Ms, income rises and interest rate falls. Describe the transmission mechanism.
© Pilot Publishing Company Ltd. 2005
Q6.8:(a) Suppose there exist an autonomous increase in J and an autonomous increase in Ms. Predict the change in Y and r with the aid of an IS-LM diagram.
(b) Suppose there exist an autonomous increase in W and an autonomous increase in Ms. Predict the change in Y and r with the aid of an IS-LM diagram.
© Pilot Publishing Company Ltd. 2005
Mathematical derivation of the IS-LM equilibrium
In a four sector economy, E = C + I + G + X – M
1. Mathematical derivation of the IS curve
where C = cYd+C*;
Yd= Y-tY-T*+qY+Q*;
I = br+I*+iY;
G= G*;
X = X*;
M = mY+M*
© Pilot Publishing Company Ltd. 2005
Mathematical derivation of equil. income & multiplier
Y = cYd+C* +br+I*+iY + G* +X*-mY-M*
Y = c(Y-tY-T*+qY+Q*)+C* +br+I*+iY +G*+X*-mY-M*
(1–c-i+ct-cq+m)•Y = C*+ I*+ G*+ X*-M*-cT*+cQ* +br
1. Mathematical derivation of the IS curve
Equation of IS curve: Y = E = C+I+G+X-M
bcQ*)*cT*M*X*G*I*(C
Yb
mcq-cti-c-1
r =
(1)
© Pilot Publishing Company Ltd. 2005
Given Md = Mt + Ma; Ms = M1/P
where Mt = dY & Ma = er + Ma*
dY + er +Ma* = M1/P
er = -dY + (M1/P – Ma*)
2. Mathematical derivation of the LM curve
Equation of a LM curve: Md = Mt + Ma = Ms
e
Ma*)(M1/PY
e
d r = (2)
© Pilot Publishing Company Ltd. 2005
b
cQ*)*cT*M*X*G*I*(CY
b
mcq-cti-c-1
Sub. equation (1) into (2), the equil. income can be found.
e
Ma*)(M1/PY
e
d
e
Ma*)-(M1/P
b
*AY
e
dY
b
mcq-cti-c-1
e
Ma*)-(M1/P
b
*AY
be
bdm)ecq-cti-c-(1
Ma*)P
M1(
dm)e/bcq-cti-c-(1
1*A
bd/em)cq-cti-c-(1
1Y
=A*
© Pilot Publishing Company Ltd. 2005
IS-LM multiplier
Note: As b<0, d>0 and e<0 bd/e>0 IS-LM multiplier is smaller than Y-E multiplier, because
When there is a rise in autonomous E, Y With money market, Y Mt & disturb money market
As Md > Ms, r and crowds out private investment
Overall in equilibrium income is smaller.
ebdm)cq-cti-c-(1
1