Transcript Document

Chapter 22
The Demand
for Money
Quantity Theory of Money
Velocity
V = (P × Y) / M
Equation of Exchange M  V = P  Y
(an identity)
Quantity Theory of Money
1. Irving Fisher (1911): V is fairly constant in the short run
(determined by the institutional and technological features).
2. Nominal income, PY, determined by M
3. Classicals assume Y fairly constant (flexible p and w, and full
employment)
4. P determined by M
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Quantity Theory of Money
Quantity Theory of Money Demand
M = (1/V)  PY
Md = k  PY
Implication: interest rates not important to Md
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22-3
Change in Velocity
from Year to Year: 1915–2002
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22-4
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
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22-5
Keynes’s Liquidity Preference Theory
3 Motives
Transactions motive—related to Y
- Since money is a medium of exchange it can be used to carry out
everyday transactions. Keynes believed that these transactions were
proportional to income.
2.
Precautionary motive—related to Y
- People hold money as a cushion against an unexpected need. This
motive is determined primarily by the level of transactions that they
expect to make in the future and that these transactions are
proportional to income.
3.
Speculative motive
- Since money is also a store of value, Keynes called this reason for
holding money the speculative motive. Keynes divided the assets that
can be used to store wealth into two categories: money (that pays no
interest rate) and bonds (that pays positive interest rates).
- Money demand is negatively related to i
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22-6
Keynes’s Liquidity Preference Theory
Liquidity Preference (real money balances)
Md
= f(i, Y)
P
–+
Keynes’s conclusion that the demand for money is related to
income and interest rates is a major departure from Fisher’s
view of money demand.
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22-7
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, change f(i,Y) and V
changes
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22-8
Baumol-Tobin Model
of Transactions Demand
Assumptions
1. Income of $1000 each month
2. 2 assets: money and bonds
If keep all income in cash
1. Yearly income = $12,000
2. Average money balances = $1000/2
3. Velocity = $12,000/$500 = 24
Keep only 1/2 payment in cash
1. Yearly income = $12,000
2. Average money balances = $500/2 = $250
3. Velocity = $12,000/$250 = 48
Trade-off of keeping less cash
1. Income gain = i $500/2
2. Increased transactions costs
Conclusion: Higher is i and income gain from holding bonds, less likely
to hold cash: Therefore i , Md 
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22-9
Cash Balance in Baumol-Tobin Model
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22-10
Baumol-Tobin Model
• Suppose that the cost of a banking transaction
(trip) is b and that the interest rate is i.
•
• Total cost = Forgone interest + cost of trips
•
iY
TC 
 bn
2n
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Baumol-Tobin Model
• The optimal value of n, denoted n* can be
calculated as follows:
iY
TC 
 bn
2n
Min
n
• FOC:
TC iY
 2 b  0
n
2n
• n can be solved as:
iY
n 
2b

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22-12
Baumol-Tobin Model
• Therefore, the optimal money demand is:
Y
L 

2n
t
Y
bY

2i
iY
2
2b
• The model predicts that the demand for money will increase in less
than proportion to the volume of transactions (income), that is, there
are economies of scale in money holding for the individual. Also,
demand for money depends on interest rate.
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22-13
Baumol-Tobin Model
• Take logarithm:
1
(ln b  ln Y  ln 2  ln i)
2
1
1
1
 (ln b  ln 2)  ln Y  ln i
2
2
2
ln Lt 
• Income elasticity of money demand:  ln Lt /  ln Y  1/ 2
• or, increasing returns to the scale
t
• Note: classical model, L  kY,income elasticity is 1.
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Precautionary and Speculative Md
Precautionary Demand
Similar tradeoff to Baumol-Tobin framework
1. Benefits of precautionary balances
2. Opportunity cost of interest foregone
Conclusion:
i , opportunity cost , hold less precautionary balances, Md 
Speculative Demand
Problems with Keynes’s framework:
Hold all bonds or all money: no diversification
Tobin Model:
1. People want high Re, but low risk
2. As i , hold more bonds and less M, but still diversify and hold M
Problem with Tobin model: No speculative demand because T-bills have
no risk (like money) but have higher return
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Friedman’s Modern Quantity Theory
(1956)
• The demand for money must be influenced by the
same factors that influence the demand fro any
asset.
• The demand for money therefore should be a
function of the resources available to individuals
(their wealth) and the expected returns on other
assets relative to the expected return on money.
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22-16
Friedman’s Modern Quantity Theory
d
e
Theory of asset demand: M function of wealth (YP) and relative R of other
assets
Md
P
e
= f(YP, rb – rm, re – rm,  – rm)
+
–
–
–
Differences from Keynesian Theories
1. Other assets besides money and bonds: equities and real goods
2. Real goods as alternative asset to money implies M has direct effects
on spending
3. rm not constant: rb , rm , rb – rm unchanged, so Md unchanged: i.e.,
interest rates have little effect on Md
4. Md is a stable function
Implication of 3:
Md
Y
= f(YP)  V =
P
f(YP)
Since relationship of Y and YP predictable, 4 implies V is predictable: Get Qtheory view that change in M leads to predictable changes in nominal income,
PY
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Friedman’s Modern Quantity Theory
• Even though velocity is no longer assumed to be
constant, the money supply continues to be the
primary determinant of nominal incomes in the
quantity theory of money.
• In Keynesian liquidity preference function, i and V
are procyclical, while in Friedman’s quantity
theory, income (Y) and V are procyclical.
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22-18
Empirical Evidence on Money Demand
Interest Sensitivity of Money Demand
Is sensitive, but no liquidity trap
Stability of Money Demand
1. M1 demand stable till 1973, unstable after
2. Most likely source of instability is financial
innovation
3. Cast doubts on money targets
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22-19