Download Velocity of Money

CHAPTER
30
Demand for Money &
Equilibrium of Money Market
Economics
PRINCIPLES OF
N. Gregory Mankiw
© 2009 South-Western, a part of Cengage Learning, all rights reserved
The Demand for Money
The Opportunity Cost of Holding Money
 Short-term interest rates are the interest rates
on financial assets that mature within six months
or less.
 Long-term interest rates are interest rates on
financial assets that mature a number of years in
the future.
The Demand for Money
Interest Rates and the Opportunity Cost of
Holding Money
Other determinants of money demand
 Real GDP (+)
 Price Level (+)
 Technology
 Institutions
Money demand function
 MD = P *m(Y, R)
 Y = Real GDP
 R = Nominal Interest Rate
 m(Y,R) = Real Money Demand
 P* m(Y,R) = (Nominal) Money Demand
 MD = P *m(Y, r+π)
 r = Real interest rate
 π = inflation rate
 MD decreases with R, or with r and π.
The Money Demand Curve
Interest
rate,
R
Money demand
Quantity of
money
The Money Demand Curve
Price
Level,
P
MD = P *m(Y, R)
Money demand
Quantity of
money
Money Supply, Money Demand, and
Equilibrium Price
Price
Money Supply
Level,
P
MD = P *m(Y, R)
Equilibrium
Price
A
Quantity fixed
By Central Bank
Quantity
of money
The effects of money injection
Price
Level,
P
MS1
MS2
1. An increase
in money supply
MD = P *m(Y, R)
2. An
increase in
price level
A
M1
M2
Quantity
of money
The Classical Dichotomy and Monetary
Neutrality
 Nominal variables are variables measured in
monetary units.
 Real variables are variables measured in
physical units.
The Classical Dichotomy and Monetary
Neutrality
 According to the classical dichotomy, different
forces influence real and nominal variables.
 Changes in the money supply affect nominal
variables but not real variables.
 The irrelevance of monetary changes for real
variables is called monetary neutrality.
 The consensus among economists: money is
neutral in the long run, but not in the short run.
Velocity of Money
 The velocity of money refers to the speed at
which the typical dollar bill travels around the
economy from wallet to wallet.
V = (P  Y)/M
 V = velocity
P = the price level
Y = the quantity of output
M = the quantity of money
 A simple example:
 The quantity of money is fixed at M=$20
 May 1: Alf paid $20 to Ben for a pizza
 May 10: Ben paid $10 to Chris for donuts
 May 31: Ben paid $10 to Alf for a sushi
 Nominal value of transactions in May = $40.
Each dollar is used twice on average.
 A simple example:
 P x Y = $1000 = nominal GDP per year ≒
nominal value of transactions
 M = $50 = quantity of money
 (P x Y)/M = 20 = each dollar must be used for 20
times per year
Quantity Theory of Money
• Rewriting the equation gives the quantity
equation:
MV=PY
• The quantity equation relates the quantity of
money (M) to the nominal value of output
(P  Y).
 The velocity is relatively stable over time
 Because velocity is stable, changes in the
quantity of money (M) causes proportional
changes in nominal output (PY)
 Y is primarily determined by real factors, not
money. Thus, changes in PY caused by changes
in M are reflected by changes in P.
 Therefore, changes in M leads only to changes in
P.
 From MV = PY, we can derive
%ΔM + %ΔV = %ΔP + %ΔY
 Money Growth + Velocity Growth
= Inflation + Output Growth
(1) M t 1Vt 1  Pt 1Yt 1
(2) M tVt  PtYt
M t 1 Vt 1 Pt 1 Yt 1
(3)

M t Vt
Pt Yt
M t 1  M t M t 1
Pt 1  Pt Pt 1
(4)  m 

 1,  

1
Mt
Mt
Pt
Pt
(5) (1   m )(1   v )  (1   )(1   y )
(6)  m   v   m v  1     y   y  1
(7 )  m   v     y
The Quantity Theory of Money – Irving Fisher
 Suppose now money supply increases.
 assume that %ΔV = 0 and %ΔY = 0.
 doubling the quantity of money doubles the price
level.
 Inflation is a monetary phenomenon (Milton
Friedman).
20-18
Nominal GDP, the Quantity of Money, and the
Velocity of Money
Indexes
(1960 = 100)
2,000
Nominal GDP
1,500
M2
1,000
500
Velocity
0
1960
1965
1970
1975
1980
1985
1990
1995
2000
Copyright © 2004 South-Western
International Evidence of Monetary Neutrality
 The figure on the next slide shows the annual
percentage increases in the money supply and
average annual increases in the aggregate price.
 The scatter of points clearly lies close to a 45degree line, showing a more or less proportional
relationship between money and the aggregate
price level.
 The data support the concept of monetary
neutrality in the long run.
The Long-Run Relationship Between Money and Inflation
The Inflation Tax
 When the government raises revenue by printing
money, it is said to levy an inflation tax.
 If the annual inflation rate is 5%, one dollar will
buy $1 worth of goods and services this year, but
it would require $1.05 to buy the same goods or
services the next year; this has the same effect
as a 5% annual tax on cash holdings.
 An inflation tax is like a tax on everyone who
holds money, as it reduces the value of the
money held by the public.
 The inflation ends when the government
institutes fiscal reforms such as cuts in
government spending.
Hyperinflation
 Informal definition: 50 percent monthly inflation
 In 1923, Germany’s money was worth
so little that children used stacks
of banknotes as building blocks
or built kites with them.
Money and Prices During Four Hyperinflations
(a) Austria
(b) Hungary
Index
(Jan. 1921 = 100)
Index
(July 1921 = 100)
100,000
100,000
Price level
Price level
10,000
10,000
Money supply
1,000
100
Money supply
1,000
1921
1922
1923
1924
1925
100
1921
1922
1923
1924
Copyright © 2004 South-Western
1925
Money and Prices During Four Hyperinflations
(c) Germany
(d) Poland
Index
(Jan. 1921 = 100)
100,000,000,000,000
1,000,000,000,000
10,000,000,000
100,000,000
1,000,000
10,000
100
1
Index
(Jan. 1921 = 100)
10,000,000
Price level
Money
supply
Price level
1,000,000
Money
supply
100,000
10,000
1,000
1921
1922
1923
1924
1925
100
1921
1922
1923
1924
Copyright © 2004 South-Western
1925
Taiwan’s hyperinflation, 1945--1949
Consumer Price Index, Taiwan, 1937--1997
Zimbabwe’s Inflation
 Zimbabwe’s money supply growth was matched by
almost simultaneous surges in its inflation rate. Why did
Zimbabwe’s government pursue policies that led to
runaway inflation?
 The reason boils down to political instability, which in
turn had its roots in Zimbabwe’s history.
 Robert Mugabe, Zimbabwe’s president, tried to solidify
his position by seizing farms and turning them over to
his political supporters. But because this seizure
disrupted production, the result was to undermine the
country’s economy and its tax base. It became
impossible for the country’s government to balance its
budget either by raising taxes or by cutting spending.
Money Supply Growth and Inflation in
Zimbabwe
Consumer Prices in Zimbabwe, 1999-2008
The banknote with the greatest number of
zeros shown
Zimbabwe 100 trillion dollar bill
The worst monthly inflation rate = 7.96e+10%
(November, 2008)
The banknote with the highest denomination
Hungary 100 million b-pengo issued in 1946
Billion in long scale = trillion (1e+12)
100 million b. in long scale = 100 million trillion = 1e+20
Worst monthly inflation rate = 4.19e+16%
Hyperinflation
 By giving away its independence, the central
bank work in concert with the treasury. The
treasury issues debt, and the central bank
monetizes the debt by creating money and
buying the public debt.
The Vicious Circle of Hyperinflation
Government Spending ↑
Money growth rate ↑
Inflation rate ↑
The purchasing power of money ↓
Real seignorage (鑄幣稅) ↓
Government accelerate money growth to finance
its spending
To Stop Hyperinflation…
 Cutting down government spending
 Monetary reform
 Independent central bank
 New money
 More reserves (e.g. gold, foreign assets)
 Restore the credibility of fiat money
 Hyperinflation can be stopped very quickly once
the credibility is restored.
THE COSTS OF INFLATION
 A Fall in Purchasing Power?
 Inflation does not in itself reduce people’s real
purchasing power.
 In particular, during a period of inflation,
wages also rise. Sometimes wages rise faster
than prices, and sometimes prices rise faster
than wages.
THE COSTS OF INFLATION
 Shoeleather costs
 Menu costs
 Relative price variability
 Tax distortions
 Confusion and inconvenience
 Arbitrary redistribution of wealth
Shoeleather Costs
 Shoeleather costs are the resources wasted
when inflation encourages people to reduce their
money holdings.
 Inflation reduces the real value of money, so
people have an incentive to minimize their cash
holdings.
Shoeleather Costs
 Less cash requires more frequent trips to the
bank to withdraw money from interest-bearing
accounts.
 The actual cost of reducing your money holdings
is the time and convenience you must sacrifice to
keep less money on hand.
 Also, extra trips to the bank take time away from
productive activities.
Menu Costs
 Menu costs are the costs of adjusting prices.
 During inflationary times, it is necessary to
update price lists and other posted prices.
 This is a resource-consuming process that takes
away from other productive activities.
Inflation-Induced Tax Distortion
 The income tax treats the nominal interest
earned on savings as income, even though part
of the nominal interest rate merely compensates
for inflation.
 The after-tax real interest rate falls, making
saving less attractive.
A
B
4%
4%
(2) Inflation Rate
0
8
(3) Nominal Interest Rate = (1) + (2)
4
12
(4) Reduced Interest Due to 25% tax rate =
0.25*(3)
1
3
(5) After-tax Nominal Interest Rate = 0.75*(3)
3
9
(6) After-tax Real Interest Rate = (3) – (2)
3
1
(1) Real Interest Rate
 The difference in the after-tax real rate between
A and B is 2 percent, equal to the product of
inflation rate and tax rate (8%*0.25)
Relative-Price Variability and the
Misallocation of Resources
 Inflation distorts relative prices.
 Consumer decisions are distorted, and markets
are less able to allocate resources to their best
use.
 例如: 「什麼都漲，就是工資不漲」=>
勞動力的相對價格被扭曲。
Confusion and Inconvenience
 When the Fed increases the money supply and
creates inflation, it erodes the real value of the
unit of account.
 Inflation causes dollars at different times to have
different real values.
 Therefore, with rising prices, it is more difficult to
compare real revenues, costs, and profits over
time.
A Special Cost of Unexpected Inflation:
Arbitrary Redistribution of Wealth
 Unexpected inflation redistributes wealth among
the population in a way that has nothing to do
with either merit or need.
 These redistributions occur because many loans
in the economy are specified in terms of the unit
of account—money.