Quantity Theory of Money
Velocity
PY
V=
M
Equation of Exchange
MV=PY
Quantity Theory of Money
1. Irving Fisher’s view: V is fairly constant
2. Equation of exchange no longer identity
3. Nominal income, PY, determined by M
4. Classicals assume Y is determined by real factors, not monetary
5. P determined by M
Quantity Theory of Money Demand
1
M=
 PY
V
Md = k  PY
Implication: interest rates not important to Md
1
Change in Velocity
from Year to Year: 1915–2002
Cambridge Approach
Is velocity constant?
1.Classicals thought V constant because
didn’t have good data
2.After Great Depression, economists
realized velocity far from constant
Keynes’s Liquidity Preference
Theory
3 Motives
1. Transactions motive—related to Y
2. Precautionary motive—constant
3. Speculative motive
A. related to W and Y
B. negatively related to i
Liquidity Preference
Md
= f(i, Y)
P
–+
Keynes’s Liquidity Preference
Theory
Implication: Velocity not constant
P
1
d =
M
f(i,Y)
Multiply both sides by Y and substitute in M = Md
PY
Y
V =
=
M
f(i,Y)
1. i , f(i,Y) , V 
2. Change in expectations of future i or change f(i,Y) results
in a change in V
Determination of Output
Keynesian IS-LM Model assumes price level is fixed
Aggregate Demand
Yad = C + I + G + NX
Equilibrium
Y = Yad
Consumption Function
C = a + (mpc  YD)
Investment
1. Fixed investment
2. Inventory investment
Only planned investment is included in Yad
6
Consumption
Function
7
Keynesian Cross Diagram
Assume G = 0, NX = 0, T = 0
Yad = C + I = 200 + .5Y + 300 =
500 + .5Y
Equilibrium:
1. When Y > Y*, Iu > 0  Y  to
Y*
2. When Y < Y*, Iu < 0  Y  to
Y*
8
Expenditure Multiplier
Analysis of Figure 3:
Expenditure Multiplier
I = + 100  Y/I = 200/100 = 2
1
Y = (a + I) 
1 – mpc
A = a + I = autonomous spending
Conclusions:
1. Expenditure multiplier = Y/A = 1/(1 – mpc)
whether change in A is due to change in a or I
2. Animal spirits change A
The Great Depression
and the Collapse of Investment
Role of Government
Analysis of Figure 5:
Role of Government
G = + 400,  T = + 400
1. With no G and T, Yd = C + I = 500 + mpc Y = 500 + .5Y, Y1 = 1000
2. With G, Y= C + I + G = 900 + .5Y, Y2 = 1800
3. With G and T, Yd = 900 + mpc  Y – mpc T = 700 + .5Y, Y3 = 1400
Conclusions:
1. G  Y ; T  Y 
2. G = T = + 400, Y  400
Role of International Trade
NX = +100,
Y/NX = 200/100 = 2
= 1/(1 – mpc) = 1/(1 – .5)
Summary:
Factors that
Affect Y
IS
Curve
IS curve
1. i  I  NX ,
Yad , Y 
Points 1, 2, 3 in
figure
2. Right of IS: Y >
Yad  Y  to IS
Left of IS: Y <
Yad  Y  to IS
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Relation of Liquidity Preference
Framework to Loanable Funds
Keynes’s Major Assumption
Two Categories of Assets in Wealth
Money
Bonds
1. Thus:
2. Budget Constraint:
3. Therefore:
Ms + Bs = Wealth
Bd + Md = Wealth
Ms + Bs = Bd + Md
4. Subtracting Md and Bs from both sides:
Ms – Md = Bd – Bs
Money Market Equilibrium
5. Occurs when Md = Ms
6. Then Md – Ms = 0 which implies that Bd – Bs = 0, so that Bd = Bs and
bond market is also in equilibrium
1. Equating supply and demand for bonds
as in loanable funds framework is
equivalent to equating supply and
demand for money as in liquidity
preference framework
2. Two frameworks are closely linked, but
differ in practice because liquidity
preference assumes only two assets,
money and bonds, and ignores effects
from changes in expected returns on real
assets
Liquidity Preference Analysis
Derivation of Demand Curve
1. Keynes assumed money has i = 0
e
2. As i , relative RET on money  (equivalently, opportunity cost of money
d
)  M 
3. Demand curve for money has usual downward slope
Derivation of Supply curve
s
1. Assume that central bank controls M and it is a fixed amount
s
2. M curve is vertical line
Market Equilibrium
d
s
1. Occurs when M = M , at i* = 15%
s
d
2. If i = 25%, M > M (excess supply): Price of bonds , i  to i* = 15%
d
s
3. If i =5%, M > M (excess demand): Price of bonds , i to i* = 15%
Money
Market
Equilibrium
Rise in Income or the Price Level
1. Income , Md , Md
shifts out to right
2. Ms unchanged
3 i* rises from i1 to i2
Rise in Money Supply
1. Ms , Ms shifts out
to right
2. Md unchanged
3. i* falls from i1 to i2
Factors
that Shift
Money
Demand
and
Supply
Curves
LM Curve
LM curve
1. Y , Md , i  Points 1, 2, 3 in figure
2. Right of LM: excess Md, i  to LM
Left of LM : excess Ms, i  to
LM
24
ISLM
Model
Point E, equilibrium
where Y = Yad (IS) and
Md = M s (LM )
At other points like A, B,
C, D, one of two
markets is not in
equilibrium and arrows
mark movement towards
point E
Shift in
the IS
Curve
1. C : at given iA, Yad , Y
  IS shifts right
2. Same reasoning when I
, G , NX , T 
Shift in the LM Curve from a Rise in Ms
1. Ms : at given YA, i  in panel (b) and (a)  LM shifts to the right
Shift in the LM Curve from a Rise in M
1. M d : at given YA, i  in panel (b) and (a)  LM shifts to the left
d
s
Response to an Increase in M
1. M s : i , LM shifts
right  Y  i 
Response to Expansionary Fiscal Policy
1. G  or T : Yad , IS
shifts right  Y  i 
Summary:
Factors
that Shift
IS and
LM
Curves
Effectiveness
of Monetary
and Fiscal
Policy
d
d
s
1. M is unrelated to i  i , M = M at
same Y  LM vertical
2. Panel (a): G , IS shifts right  i , Y
stays same (complete crowding out)
s
d
3. Panel (b): M , Y so M , LM shifts
right  i  Y 
d
Conclusion: Less interest sensitive is M ,
more effective is monetary policy relative
to fiscal policy
32