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Money and Inflation
He realised well that the abundance of money makes
everything dear, but he did not analyse how that takes
place. The great difficulty of this analysis consists in
discovering by what path and in what proportion the
increase of money raises the price of things.
RICHARD CANTILLON (died 1734),
Essai sur la nature du commerce en général, II, 6.
Money and Inflation





Price = amount of money required to buy a good.
Inflation rate = ΔP/P = the percentage increase in
the average level of prices (e.g. π = 5 % p.a.).
Deflation = decrease in the average level of prices.
(e.g. π = - 1 % p.a.)
Disinflation = decrease in the inflation rate
(e.g. π1 = 5 % → π2 = 3 %)
Price level stability: π = 0 % p.a.
Price of beer in the Czech Republic
CPI in the Czech Republic
150
140
130
120
110
100
90
80
70
60
50
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I.11
I.10
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I.08
I.07
I.06
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I.02
I.01
I.00
I.99
I.98
I.97
I.96
I.95
I.94
I.93
Price level has more than
doubled since 1993
12,0%
10,0%
Inflation rate, Czech Republic
8,0%
6,0%
4,0%
2,0%
0,0%
1996
1997
1998 1999
2000
2001 2002
2003
2004 2005
2006
2007 2008
2009
2010
Inflation rate in the Czech Republic
8,00%
7,00%
6,00%
5,00%
4,00%
3,00%
2,00%
1,00%
I.15
I.14
I.13
I.12
I.11
I.10
I.09
I.08
I.07
I.06
I.05
I.04
I.03
I.02
-1,00%
I.01
0,00%
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VII.12
I.12
VII.11
I.11
VII.10
I.10
VII.09
I.09
VII.08
I.08
VII.07
I.07
VII.06
I.06
VII.05
I.05
VII.04
110
I.04
120
VII.03
140
I.03
150
VII.02
I.02
VII.01
I.01
VII.00
I.00
Food and rents in the CR
Food and nonalcoholic beverages
130
Housing, water,
electricity, gas and
other fuels
100
90
80
70
Average inflation rate 2000 - 2013
U.S. inflation rate
(% per year)
25
20
15
10
5
0
-5
-10
-15
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
The Quantity Theory of Money




o

Stock


How does the quantity of money affect the economy?
QTM - the quantity of money in the economy is related
to the number of dollars exchanged in transactions.
Suppose that the supply of money in the economy is
$10. In the first half of the year, 5 bottles of beer are
sold each for $2. The owners of money then buy 1 lb.
of ham for $10.
The total value of transactions over the year:
$2×5 + $10×1 = $20
M Velocity
= $10, of
socirculation
each unit of M was transacted twice/year.
$10 × 2 = $2×5 + $10×1
M × V = ∑piqi
Flow
The Quantity Theory of Money
Fisher (1911): The Purchasing Power of Money:
Let us begin with the money side. If the number of dollars in a country is
5,000,000, and their velocity of circulation is twenty times per year, then the
total amount of money changing hands (for goods) per year is 5,000,000
times twenty, or $100,000,000. This is the money side of the equation of
exchange…
200,000,000 loaves of bread at $ .10 a loaf,
10,000,000 tons of coal at 5.00 a ton, and
30,000,000 yards of cloth at 1.00 a yard.
The value of these transactions is evidently $100,000,000, i.e. $20,000,000
worth of bread plus $50,000,000 worth of coal plus $30,000,000 worth of
cloth. The equation of exchange therefore (remember that the money side
consisted of $5,000,000 exchanged 20 times) is as follows:—
$5,000,000 × 20 times a year
= 200,000,000 loaves × $ .10 a loaf
+10,000,000 tons × 5.00 a ton
+30,000,000 yards × 1.00 a yard.
The Quantity Theory of Money

If we aggregate over the entire economy (and over
all transactions), we may write:
M × VT = P × T IDENTITY





T … the total number of transactions during some
period of time
P … price of a typical transaction
PT … number of dollars exchanged in a year
M … quantity of money
VT … transactions velocity of money
The
rate at which money circulates in the economy
The Quantity Theory of Money







Number of transactions T is difficult to measure so it
is replaced by the total output in the economy Y.
Assume that Y is proportional to T: T = aY
M × VT = P × T
M × VT = P × aY
M × VT/a = P × Y
M × VY = P × Y
VY …Income velocity of money
Number
of times a dollar bill enters someone’s
income in a given period of time.
The Quantity Theory of Money



V can be viewed as a ratio of nominal GDP (PY),
to the quantity of money (M): V = PY/M
Assume that V is constant and exogenousV V
M×V=P×Y
If V is constant, a change in the quantity of
money (M) must cause a proportionate change
in nominal GDP (PY).
U.S. Nominal GDP, M2, and Velocity
1960–2011
3,000
1960=100
2,500
Velocity is fairly
stable over the
long run.
Nominal GDP
2,000
M2
1,500
1,000
500
Velocity
0
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
The Quantity Theory of Money
Recall that in the classical model:

Y*=F(Kfixed,Lfixed)

M×V=P×Y
Classical Dichotomy
Fixed
 M  P
The quantity theory implies that the price
level is proportional to the money supply.
MONEY IS NEUTRAL
-Does not affect Y
-Does not affect relative prices
ACTIVE LEARNING
1
Exercise
One good: corn.
The economy has enough labor, capital, and
land to produce Y = 800 bushels of corn.
V is constant.
In 2008, MS = $2000, P = $5/bushel.
Compute nominal GDP and velocity in 2008.
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
1
Answers
Given: Y = 800, V is constant,
MS = $2000 and P = $5 in 2005.
Compute nominal GDP and velocity in 2008.
Nominal GDP = P x Y = $5 x 800 = $4000
$4000
PxY
= 2
=
V =
$2000
M
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
The Quantity Theory of Money

M×V=P×Y

See the BB:

%ΔM + %ΔV = %ΔP + %ΔY
%ΔV = 0 by assumption
%ΔY depends on the growth of K,L and A. All
constant by assumption => %ΔY = 0
Hence, the growth in the money supply (%ΔM)
determines the rate of inflation (%ΔP = π).



ACTIVE LEARNING
2
Exercise
One good: corn. The economy has enough labor,
capital, and land to produce Y = 800 bushels of corn.
V is constant. In 2008, MS = $2000, P = $5/bushel.
For 2009, the Fed increases MS by 5%, to $2100.
a. Compute the 2009 values of nominal GDP and P.
Compute the inflation rate for 2008–2009.
b. Suppose tech. progress causes Y to increase to
824 in 2009. Compute 2008–2009 inflation rate.
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
2
Answers
Given: Y = 800, V is constant,
MS = $2000 and P = $5 in 2008.
For 2009, the Fed increases MS by 5%, to $2100.
a. Compute the 2009 values of nominal GDP and P.
Compute the inflation rate for 2008–2009.
Nominal GDP = P x Y = M x V (Quantity Eq’n)
= $2100 x 2 = $4200
P = P x Y = $4200 = $5.25
800
Y
$5.25 – 5.00
Inflation rate =
= 5% (same as MS!)
5.00
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
2
Answers
Given: Y = 800, V is constant,
MS = $2000 and P = $5 in 2005.
For 2009, the Fed increases MS by 5%, to $2100.
b. Suppose tech. progress causes Y to increase 3%
in 2009, to 824. Compute 2008–2009 inflation rate.
First, use Quantity Eq’n to compute P in 2009:
$4200
MxV
P =
= $5.10
=
824
Y
$5.10 – 5.00
Inflation rate =
= 2%
5.00
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
U.S. inflation and money growth,
1960-2006
15%
12%
Over the long run, the inflation and
money growth rates move together,
M2 growth
as the quantity
theory rate
predicts.
9%
6%
3%
0%
1960 1965
inflation
rate
1970 1975
1980 1985
1990 1995
2000 2005
slide 23
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M2
I.03
160
I.02
CPI
I.01
180
I.00
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I.98
I.97
I.96
I.95
I.94
I.93
Money and prices in the CR
240
220
200
140
120
100
80
60
40
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I.12
I.11
I.10
I.09
I.08
I.07
I.06
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20,0%
I.02
I.01
I.00
I.99
I.98
I.97
I.96
I.95
I.94
Money and prices in the CR
25,0%
Inflation
Money growth
15,0%
10,0%
5,0%
0,0%
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I.11
I.10
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I.08
I.07
I.06
I.05
I.04
Inflation
I.03
I.02
I.01
I.00
I.99
I.98
I.97
I.96
I.95
I.94
Money and prices (MA-12)
25,0%
20,0%
15,0%
Money growth
10,0%
5,0%
0,0%
International data on inflation and
HW (p.88) Seigniorage:
money
growthThe Revenue From Printing Money
Turkey
100
Ecuador
Inflation rate
Indonesia
Belarus
(percent,
logarithmic scale)
10
1
Argentina
U.S.
Singapore
Switzerland
0.1
Milton Friedman:
“Inflation 10
1
is always and everywhere a
monetary phenomenon.’’
100
Money Supply Growth
(percent, logarithmic scale)
The Consumer Price Index
(CPI)

measures the typical consumer’s cost
of living

the basis of cost of living adjustments
(COLAs) in many contracts
How the CPI Is Calculated
1.
2.
3.
Fix the “basket.”
The Bureau of Labor Statistics (BLS)
surveys consumers to determine what’s in
the typical consumer’s “shopping basket.”
Find the prices.
The BLS collects data on the prices of all
the goods in the basket.
Compute the basket’s cost.
Use the prices to compute the total cost of
the basket.
How the CPI Is Calculated
4.
Choose a base year and compute the index.
The CPI in any year equals
100 x
cost of basket in current year
cost of basket in base year
5. Compute the inflation rate.
The percentage change in the CPI from the
preceding period.
Inflation
=
rate
CPI this year – CPI last year
CPI last year
x 100%






2010 Price of Apples = $0.50
2010 Quantity of Apples = 4
As if quantity
(basket) was
2010 Price of Oranges = $1.00fixed
2010 Quantity of Oranges = 3
2015 Price of Apples = $1.00 (i.e. increase by
100%)
2015 Price of Oranges = $3.00 (i.e. increase by
200%)
1 4  3  3
13
CPI 2015 
 100 
 100 
0.5  4  1  3
5
 2.6  100  260






2010 Price of Apples = $0.50
2010 Quantity of Apples = 4
2010 Price of Oranges = $1.00
2010 Quantity of Oranges = 3
… weight_apples in the base year = 2/6 = 40%
… weight_oranges in the base year = 3/6 =
60%
EXAMPLE
basket: {4 pizzas, 10 lattes}
year
price of
pizza
price of
latte
2013
$10
$2.00
$10 x 4 + $2 x 10
2014
$11
$2.50
$11 x 4 + $2.5 x 10 = $69
2015
$12
$3.00
$12 x 4 + $3 x 10
cost of basket
= $60
= $78
Compute CPI in each year
Inflation rate:
2013: 100 x ($60/$60) = 100
115 – 100
x 100%
15% =
100
130 – 115
x 100%
13% =
115
2014: 100 x ($69/$60) = 115
2015: 100 x ($78/$60) = 130
What’s in the CPI’s Basket in
the U.S.?
4% 3%
Housing
6%
Transportation
6%
Food & Beverages
43%
6%
Medical care
Recreation
Education and
communication
Apparel
15%
17%
Other
7%
6%
FOOD AND NON-ALCOHOLIC
BEVERAGES
17%
CPI CR
1%
ALCOHOLIC BEVERAGES AND
TOBACCO
CLOTHING AND FOOTWEAR
9%
HOUSING, WATER, ELECTRICITY, GAS
AND OTHER FUELS
9%
3%
FURNISHINGS, HOUSEHOLD
EQUIPMENT AND ROUTINE
MAINTENANCE OF THE HOUSE
HEALTH
TRANSPORT
3%
COMMUNICATION
10%
RECREATION AND CULTURE
EDUCATION
2%
RESTAURANTS AND HOTELS
6%
27%
MISCELLANEOUS GOODS AND
SERVICES
CPI
CPI 2015 
papple, 2015  qapple, 2010  porange, 2015  qorange, 2010
papple, 2010  qapple, 2010  porange, 2010  qorange, 2010
papple, 2015


papple, 2010
papple, 2010  qapple, 2010 
porange, 2015
porange, 2010

 porange, 2010  qorange, 2010
papple, 2010  qapple, 2010  porange, 2010  qorange, 2010
papple, 2015
papple, 2010
 weight apple 
porange, 2015
porange, 2010
 weight orange
Problems with the CPI:
Substitution Bias




Over time, some prices rise faster than
others.
Consumers substitute toward goods that
become relatively cheaper, mitigating the
effects of price increases.
The CPI misses this substitution because
it uses a fixed basket of goods.
Thus, the CPI overstates increases in the
cost of living.
Prices of food and rents in the CR
150
Food and nonalcoholic beverages
140
130
Housing, water,
electricity, gas and
other fuels
120
110
100
90
80
I.13
VII.12
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VII.11
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VII.10
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I.00
70
Problems with the CPI:
Introduction of New Goods

The introduction of new goods increases
variety, allows consumers to find products
that more closely meet their needs.

In effect, dollars become more valuable.

The CPI misses this effect because it uses
a fixed basket of goods.

Thus, the CPI overstates increases in the
cost of living.
Problems with the CPI:
Unmeasured Quality Change



Improvements in the quality of goods in
the basket increase the value of each
dollar.
The BLS tries to account for quality
changes
but probably misses some, as quality is
hard to measure.
Thus, the CPI overstates increases in the
cost of living.
Problems with the CPI



Each of these problems causes the CPI to
overstate cost of living increases.
The BLS has made technical adjustments,
but the CPI probably still overstates inflation
by about 0.5 percent per year.
This is important because Social Security
payments and many contracts have COLAs tied
to the CPI.
The GDP Deflator


The GDP deflator is a measure of the
overall level of prices.
nominal GDP
Definition:
GDP deflator = 100 x
real GDP
 One way to measure the economy’s inflation
rate is to compute the percentage increase in
the GDP deflator from one year to the next.
EXAMPLE:
Pizza
year
2013
2014
2015
P
$10
$11
$12
Latte
Q
400
500
600
P
$2.00
$2.50
$3.00
Compute nominal GDP in each year:
2013:
$10 x 400 +
$2 x 1000
Increase:
= $6,000
2014:
$11 x 500 + $2.50 x 1100
= $8,250
2015:
$12 x 600 +
= $10,800
$3 x 1200
Q
1000
1100
1200
37.5%
30.9%
EXAMPLE:
Pizza
Latte
year
P
Q
P
Q
2013
$10
400
$2.00
1000
2014
$11
500
$2.50
1100
2015
$12
600
$3.00
1200
Compute real GDP in each year,
using 2013 as the base year:
Increase:
2013:
$10 x 400 + $2 x 1000
= $6,000
2014:
$10 x 500 + $2 x 1100
= $7,200
2015:
$10 x 600 + $2 x 1200
= $8,400
20.0%
16.7%
EXAMPLE:
year
2013
Nominal
GDP
$6000
Real
GDP
$6000
2014
$8250
$7200
2015
$10,800
$8400
In each year,

nominal GDP is measured using the (then)
current prices.

real GDP is measured using constant prices from
the base year (2013 in this example).
EXAMPLE:
year
2013
Nominal
GDP
$6000
2014
$8250
2015

$10,800
37.5%
30.9%
Real
GDP
$6000
$7200
$8400
20.0%
16.7%
The change in nominal GDP reflects both prices
and quantities.
 The change in real GDP is the amount that
GDP would change if prices were constant
(i.e., if zero inflation).
Hence, real GDP is corrected for inflation.
EXAMPLE:
year
2013
2014
2015
Nominal
GDP
$6000
$8250
$10,800
Real
GDP
$6000
$7200
$8400
GDP
Deflator
100.0
114.6
128.6
14.6%
12.2%
Compute the GDP deflator in each year:
2013:
100 x (6000/6000) =
100.0
2014:
100 x (8250/7200) =
114.6
2015:
100 x (10,800/8400) =
128.6
Two Measures of Inflation, 1950–2010
15
Percent per year
10
5
0
-5
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
CPI
GDP deflator
Contrasting the CPI and GDP Deflator
Imported consumer goods:
included in CPI
excluded from GDP deflator
Capital goods:
 excluded from CPI
 included in GDP deflator
(if produced domestically)
The basket:
 CPI uses fixed basket
 GDP deflator uses basket of
currently produced goods & services
This matters if different prices are
changing by different amounts.
Contrasting the CPI and GDP Deflator
n

n
CPIt 
p
i 1
n
p
i 1
i ,t qi ,base
i ,base

i 1
pi ,t
p i ,baseqi ,base
p i ,base
n
p
qi ,base
i 1
i ,base
n
GDPnom
DEFLt 
GD Pr eal
p
i 1
i ,t qi ,t
i ,base
In textbook: Index … × 100
qi ,base
n
p
i 1
n
Laspeyres
index
qi ,t

p
i 1
n

i 1
i ,t qi ,t
pi ,t qi ,t
pi ,t
p i ,base
Paasche
index
Contrasting the CPI and GDP
Deflator

Weights in the current year may not be
known (every month).
ACTIVE LEARNING
3
CPI vs. GDP deflator
In each scenario, determine the effects on
the
CPI and the GDP deflator.
A. Starbucks raises the price of Frappuccinos.
B. Caterpillar raises the price of the industrial
tractors it manufactures at its Illinois factory.
C. Armani raises the price of the Italian jeans it
sells in the U.S.
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
3
Answers
A. Starbucks raises the price of Frappuccinos.
The CPI and GDP deflator both rise.
B. Caterpillar raises the price of the industrial tractors it
manufactures at its Illinois factory.
The GDP deflator rises, the CPI does not.
C. Armani raises the price of the Italian jeans it sells in the
U.S.
The CPI rises, the GDP deflator does
not.
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Correcting Variables for Inflation








Wnom 2000 = 13,219 CZK
Wnom 2013 = 25,078 CZK
CPI2000 = 100 (e.g. price of beer = 9 CZK)
CPI2013 = 137 (e.g. price of beer = 12 CZK)
In 2000, one can buy 13,219 / 9 = 1,497 bottles
In 2013, one can buy 25,078 / 12 = 2,090 bottles
2,090 / 1,497 = 1.4
One can buy 40% more bottles
Real wage in theory


Wreal = Wnominal / P
P … price level measured by e.g. CPI
10,00%
growth in Wnom
growth in Wreal
8,77%
8,00%
7,97%
7,80%
7,22%
6,10%
6,00%
5,84%
5,70%
4,00%
6,55%
6,31%
5,03%
4,00%
3,90%
4,30%
3,40%
3,33%
3,00%
2,30%
2,00%
1,40%
2,23%
2,48%
2,50%
0,70%
0,60%
0,04%
0,00%
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
-0,80% -1,40%
-2,00%
Correcting Variables for Inflation:
Very important! Real vs. Nominal Interest
Rates
The nominal interest rate:

the interest rate not corrected for inflation
The real interest rate:
 corrected for inflation
Real interest rate
= (nominal interest rate) – (inflation rate)
Inflation and interest rates






o
Suppose you deposit $100 in a bank account that
pays i=8 % interest annually. Assume that the price
of beer this year is P1=$2.
Next year, you withdraw your savings and the
accumulated interest: $100×(1+i)= $108
Assume that the price of beer next year is P2=$2.04
Are you 8 percent richer than you were when you
made the deposit a year earlier?
In the first year, you could buy: $100/$2 = 50 bottles
In the second year, you can buy: $108/$2.04 = 53
bottles.
=> You can buy 53/50-1 = 0.06 = 6% more
What is the
inflation rate in
this economy?
Inflation and interest rates
100  (1  i )
P2
1  0.06 
100
P1
r … real interest rate
(1  i )
1  0.06 
P2
1
P1
1  0.06 
(1  i )
P2
P1
1 r 
(1  i )
1 
P2
1  
P1
Inflation and interest rates




Nominal interest rate, i … the interest rate
that the bank pays:
is not adjusted for inflation
Real interest rate, r … the interest rate that
reflects the true increase in the purchasing
power (6% in our example):
is adjusted for inflation.
Inflation and interest rates
1 r 
(1  i )
1 
(1  r)  (1   )  (1  i )
1 r     r  1 i
i  r 
Fisher equation
If we neglect π×r = 0.02 × 0.06 = 0.0012
r  i
Correcting Variables for Inflation:
Real vs. Nominal Interest Rates
Example 1:

Deposit $1,000 for one year in 2015.

Nominal interest rate is 20%.

P2015 = 2; P2016 = 2.1

What is the real interest rate?
Correcting Variables for Inflation:
Real vs. Nominal Interest Rates

Can the real interest rate be zero or even
negative?

Can the nominal interest rate be zero or
even negative?

Can the real interest rate exceed the
nominal interest rate?
Real and Nominal Interest Rates in the U.S.,
1950–2010
Fisher equation and the Fisher effect




i = r+π
r is determined by S = I (Classical model)
π is determined by the money growth (QTM)
The one-for-one relation between the
inflation rate and the nominal interest rate is
called the Fisher effect.
Inflation and nominal interest
rates in the U.S., 1955-2006
percent
per year
15
nominal
interest rate
10
5
0
inflation rate
-5
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Inflation and nominal interest
rates across countries
Nominal 100
Interest Rate
Romania
(percent,
logarithmic scale)
Zimbabwe
Brazil
10
Bulgaria
Israel
U.S.
Germany
Switzerland
1
0.1
1
10
100
1000
Inflation Rate
(percent, logarithmic scale)
Two Real Interest Rates: Ex Ante
and Ex Post



o


o

o
When a borrower and lender agree on a nominal interest rate,
they do not know what the inflation rate over the term of the loan
will be.
Suppose that they expect πe= 3 %. If the agreed r is 4 %, then:
i = r + πe = 7 %
If the realised inflation differs, e.g. π = 5 %, then the ex post real
interest rate will be:
Who lost and who
rex post = 7 % - 5 % = 2 %
gained when π > πe ?
Hence, we must distinguish between two concepts of the real
interest rate:
The real interest rate the borrower and lender expect when the
loan is made:
… ex ante real interest rate = i – πe = 4 %
and the real interest rate actually realized:
… ex post real interest rate = i – π = 2 %
Two Real Interest Rates: Ex Ante
and Ex Post

Because the nominal interest rate agreed by lender and
borrower can adjust only to expected inflation (not to the
realized inflation), the Fisher effect is more precisely
written as:
i = r + πe


The ex ante real interest rate r is determined by
equilibrium in the market for goods and services (or I=S).
The nominal interest rate i moves one-for-one with
changes in expected inflation πe.
The Costs of Inflation

Shoeleather costs: the resources
wasted when inflation encourages
people to reduce their money holdings


Includes the time and transactions costs
of more frequent bank withdrawals
Menu costs: the costs of changing
prices

Printing new menus, mailing new
catalogs, etc.
The Costs of Inflation


Misallocation of resources from relativeprice variability: Firms don’t all raise
prices at the same time, so relative prices
can vary…
which distorts the allocation of resources.
Confusion & inconvenience: Inflation
changes the yardstick we use to measure
transactions.
Complicates long-range planning and the
comparison of dollar amounts over time.
The Costs of Inflation

Tax distortions:
Inflation makes nominal income grow
faster than real income.
Taxes are based on nominal income,
and some are not adjusted for inflation.
So, inflation causes people to pay
more taxes even when their real
incomes don’t increase.
ACTIVE LEARNING
3
Tax distortions
You deposit $1000 in the bank for one year.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
a. In which case does the real value of your deposit
grow the most?
Assume the tax rate is 25%.
b. In which case do you pay the most taxes?
c. Compute the after-tax nominal interest rate,
then subtract inflation to get the
after-tax real interest rate for both cases.
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permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
3
Answers
Deposit = $1000.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
a. In which case does the real value of your
deposit grow the most?
In both cases, the real interest rate is 10%,
so the real value of the deposit grows 10%
(before taxes).
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permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
3
Answers
Deposit = $1000. Tax rate = 25%.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
b. In which case do you pay the most taxes?
CASE 1: interest income = $100,
so you pay $25 in taxes.
CASE 2: interest income = $200,
so you pay $50 in taxes.
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permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
3
Answers
Deposit = $1000. Tax rate = 25%.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
c. Compute the after-tax nominal interest rate,
then subtract inflation to get the
after-tax real interest rate for both cases.
CASE 1:
nominal = 0.75 x 10% = 7.5%
real
= 7.5% – 0% = 7.5%
CASE 2:
nominal = 0.75 x 20% = 15%
real
= 15% – 10% = 5%
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permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
ACTIVE LEARNING
3
Summary and lessons
Deposit = $1000. Tax rate = 25%.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
Inflation…
 raises nominal interest rates (Fisher effect)
but not real interest rates
 increases savers’ tax burdens
 lowers the after-tax real interest rate
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
A Special Cost of Unexpected Inflation

Arbitrary redistributions of wealth
Higher-than-expected inflation transfers
purchasing power from creditors to debtors:
Debtors get to repay their debt with dollars that
aren’t worth as much.
Lower-than-expected inflation transfers
purchasing power from debtors to creditors.
High inflation is more variable and less
predictable than low inflation.
So, these arbitrary redistributions are frequent
when inflation is high.
The Costs of Inflation


All these costs are quite high for
economies experiencing hyperinflation.
For economies with low inflation (< 10%
per year),
these costs are probably much smaller,
though their exact size is open to debate.
Exercise:
Suppose V is constant, M is growing 5% per year,
Y is growing 2% per year, and r = 4.
a. Solve for i.
b. If the central bank increases the money growth rate by
2 percentage points per year, find i.
c. Suppose the growth rate of Y falls to 1% per year.
 What will happen to  ?
 What must the central bank do if it wishes to
keep  constant?