Chapter 6: Money and Inflation in the Long Run
Learning Objectives
After reading this chapter, you should be able to:
6.1 Define money and discuss its four functions (pages x – x)
6.2 Explain the quantity theory of money and use it to explain inflation (pages x – x)
6.3 Discuss the relationship between money growth, inflation, and nominal interest rates (pages x
– x)
6.4 Explain the costs of inflation (pages x – x)
6.5 Explain the causes of hyperinflation (pages x – x)
[Chapter-opening vignette starts]
A Future Challenge for Monetary Policy
The world economy experienced a severe shock to its financial markets during the 2007-2009
time period. The value of many financial assets such as mortgage backed securities decreased,
which hurt the financial institutions that owned those securities. As a result, financial institutions
became much more reluctant to make loans to households and firms which contributed to the
world wide economic downturn. To combat this downturn, central banks such as the Bank of
England in the United Kingdom and the Federal Reserve in the United States took steps to
protect the financial system and stimulate the economy in the short run. These steps included
reducing short-term nominal interest rates to almost zero as well as developing new policy tools
to help the financial system respond to the financial crisis.
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These central bank policies increased the ability of banks to make new loans which
helped reduce the severity of global economic downturn. However, as the global economy
recovered in 2009 and 2010, global liquidity and the increased ability of banks to make new
loans increases the risk of inflation. Central banks now face the problem of unwinding their
policies to stimulate the economy before inflation develops.
Source: Guha, Krishna. “Big Economies’ Central Bankers Face Delicate Balancing Act,”
Financial Times, October 6, 2009 p.5. Hall, Kevin. “Bernanke unveils plan to unwind Fed’s
Massive Asset Purchases,” McClatchy – Tribune Business News, February 10, 2010.
An Inside Look [or An Inside Look at Policy] on page xx explores …
[Chapter-opening vignette ends]
Big Questions in Macroeconomics
In this chapter, we will also answer one of the Big Questions that we introduced in Chapter 1:
Big question # 3: Why do the nominal interest rate and the inflation rate rise with the
growth rate of the money supply in the long run?
As you read this chapter, see if you can answer these questions. You can check your answers
against those we provide at the end of the chapter.
Continued on page xx
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[Transition statement begins]
In Chapter 5, we learned that total factor productivity (TFP) growth is the ultimate source of both
labor productivity growth and the growth of the standard of living. In the previous chapters, we
focused on potential real GDP and potential real GDP per worker hour. These are real variables
because they represent quantities. In this chapter, we focus on the behavior of nominal variables
such as the price level, inflation, and the nominal interest rate. As you will see, the key to
understanding these nominal variables is to understand the money supply. The money supply is
the total amount of paper money and coins held by the non-bank public plus deposits. In Chapter
7, we explore why in the long run the price level and money supply do not affect real GDP.
(MD: Money Supply The total amount of paper money and coins held by the non-bank public
plus deposits.)
[Transition statement ends]
6.1 Define Money and Discuss its Four Functions
Central banks, such as the Federal Reserve in the United States, have the responsibility of
controlling inflation. As we will see in this chapter, in the long run the inflation rate is
determined by the growth rate of the money supply. Therefore, we begin this chapter by
discussing how central banks measure the money supply. In Chapter 3, we learned that “liquid”
refers to the ease with which someone can exchange assets for cash, other assets, or goods and
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services. Money is the most liquid of all assets. In the United States, dollar bills are money
because you can use them to buy food at a grocery store and a haircut at a salon.
The Functions of Money
For an asset to function as money, the asset must fulfill four functions: it must store value,
provide a unit of account, serve as a medium of exchange, and serve as deferred payment.
A store of value is an asset that transfers purchasing power from the present to the future. For
example, suppose you want to purchase a plasma TV next year that now costs $1,000. If you
had $1,000 in your pocket today, then you could simply hold the $1,000 in cash for the year and
then purchase the plasma TV. However, there are many other assets that can store the $1,000
purchasing power for a year. You could put the $1,000 into a savings account, a certificate of
deposit, purchase stocks, purchase bonds, or buy gold. After the year, you could then sell one of
these alternative assets to purchase the plasma TV.
(MD: Store of Value An asset that transfers purchasing power from the present to the future;
one of the functions of money.)
The unit of account is the provision of a way of measuring the value of goods and
services For example, when you purchase the plasma TV the price of the TV is quoted in terms
of dollars rather thanshares of Microsoft stock or ounces of gold. Having an agreed upon unit of
account makes an economy more efficient. When all costs and revenues are recorded as dollars,
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firms can determine which activities to expand and which to contract to earn a profit, while
investors learn which firms are the most profitable.
(MD: Unit of Account The provision of a way of measuring the value of goods and services;
one of the functions of money.)
What is the benefit of storing your wealth in money rather than one of the many other
assets, such as stocks or gold? Because money is the most liquid of all assets, it acts as a
medium of exchange to settle transactions for goods and services. When you go into the store
to purchase the $1,000 plasma TV, you have to provide the store with $1,000 of money. You do
not give the store shares of Microsoft stock, Treasury securities, ounces of gold or other asset.
Why not? It is much easier if everyone agrees to use the same asset as the medium of exchange.
For example, suppose you had $1,000 of Microsoft stock that you wanted to use to purchase the
plasma TV. You go to the store and discover that the store wants $1,000 worth of Treasury
securities. Then you have to go exchange your Microsoft stock for Treasury securities. This
takes time. You also have to pay your stock broker for the service of selling the Microsoft stock
and purchasing Treasury securities. Therefore, having a single asset serve as the medium of
exchange makes market transactions much easier and less expensive. As a result, the economy is
more efficient.
(MD: Medium of Exchange An asset used to settle transactions for goods and services; one of
the functions of money.)
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Money acts as a medium of exchange to facilitate transactions at a point in time, but also
as a standard of deferred payment to facilitate transactions over time. For example, if you
purchase a $1,000 plasma TV today the store may allow you several months to pay that amount.
For an asset, such as money, to fulfill this function, the value of the asset must be stable over
time or changes in its value must be predictable.
(MD: Standard of Deferred Payment An asset that is accepted as credit to facilitate
exchange over time; one of the functions of money.)
Commodity Money versus Fiat Money
To be considered money, an asset must fulfill the four functions that we described above.
Because the function of a medium of exchange is so important, we will examine that further. To
serve as a medium of exchange, an asset must have the following five characteristics:

The asset must be acceptable (that is, usable) to most people.

The asset should be of standardized quality so that any two units are identical.

The asset should be durable so its value is not lost due to spoilage.

The asset should be valuable relative to its weight so that amounts large enough to be
useful in trade can be easily transported.

The asset should be divisible because different goods are valued differently.
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There are two types of assets with these five characteristics: commodity money and fiat
money. Commodity money is a physical good (particularly precious metals) that is used as the
medium of exchange. Throughout history gold has been a common form of commodity money.
However, the value of gold depends on its purity. If someone mixed gold with a metal of lesser
value, then that person could make a profit by deceiving other individuals into accepting impure
gold as payment for goods and services. Therefore, a time-consuming process may be needed to
verify the purity of the gold. In addition, the supply of gold fluctuates with unpredictable
discoveries of gold and changes in the technology of extracting gold from existing mines,
leading to large fluctuations in the stock of money.
(MD: Commodity Money Physical goods (particularly precious metals) that are used as the
medium of exchange.)
Large quantities of gold can be heavy to carry, which is another disadvantage. However,
gold does not have to circulate for it to serve as money. From 1882 to 1933, gold certificates
circulated in the United States as money. The certificates looked much like modern dollar bills,
except the certificates indicated that the U.S. Treasury held an amount of gold equal to the face
value of the certificate. In addition, the certificates entitled the holder to go to the U.S. Treasury
and exchange it for gold. So, the U.S. government could issue certificates only up to the amount
of gold it actually held. Confidence that the U.S. government held all the gold that it claimed
allowed the gold certificates to function as money.
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Fiat money is also a potential medium of exchange. Fiat money is money authorized by
central banks — such as the Federal Reserve in the United States — that does not have to be
exchanged by the central bank for gold or some other commodity money. Fiat money is valuable
only because it is accepted as a medium of exchange and has no intrinsic value. Fiat money is
not backed by anything of value such as gold or silver, but people accept it for two reasons.
First, fiat currency is legal tender. If you look at a U.S. dollar, you will see the words “This note
is legal tender for all debts, public and private.” This expression means that the federal
government requires that cash or checks denominated in dollars be used in payment of taxes and
that dollars must be accepted in private payments of debt. Second, households and firms have
confidence that if they accept paper dollars in exchange for goods and services then the dollars
will not lose much value during the time they hold them. Without this confidence, dollar bills
would not serve as a medium of exchange or fulfill the other functions of money. Hence, the
confidence individuals have in the willingness of others to accept a dollar bill is the only real
limit on the government’s ability to create money.
(MD: Fiat Money Money authorized by central banks and that does not have to be exchanged
by the central bank for gold or some other commodity money.)
How is Money Measured?
We know that money is the most liquid of all assets. But how does the Federal Reserve and
other central banks measure money, and which assets should they count to determine the
quantity of money circulating in the economy? There is no single correct answer to this
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question. Any asset can eventually be sold and converted into another asset or a good or service.
Because all assets are liquid to some degree, whether an asset counts as money depends on what
“most liquid” means. The narrowest possible definition would include just the assets that serve
as a medium of exchange such as currency, checking account deposits, traveler’s checks, and
accounts linked to debit cards. However, many other assets are almost as liquid as currency and
checking account deposits. For example, it is relatively easy to transfer funds from a savings
account to a checking account or to withdraw cash from a savings account using an ATM.
Although they are not as liquid as currency or checking accounts, assets such as savings should
be included as a medium of exchange and count as money.
The narrowest definition of the money supply includes just currency that immediately
serves as a medium of exchange. However, currency is not the only asset that serves as a
medium of exchange. For example, you can go into most stores and purchase goods and services
with a check, a traveler’s check, or debit card. Not every store will accept these forms of
payment so these assets are not as liquid as currency, but they are almost as liquid as currency.
Checking accounts (and debit cards; prepaid or linked to a checking account) and traveler’s
checks are examples of demand deposits, accounts held in banks that people can use as
currency.
(MD: Demand Deposit Accounts held in banks, such as checking accounts, traveler’s
checks, or accounts linked to debit cards, that people can use as currency.)
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Table 6.2 shows the definitions of the money supply. M1 is the narrowest definition of the
money supply that includes currency and demand deposits such aschecking accounts. Checking
account deposits are not the only close substitute for currency as a medium of exchange. You
can withdraw currency from a savings account at most ATMs or transfer funds from a savings
account to a checking account, so savings accounts are almost as liquid as currency and checking
accounts. To a limited extent, individuals can also write checks against their money market
mutual funds, so these are also almost as liquid as checking accounts. In addition, smalldenomination time deposits (less than $100,000) of specific maturity, such as a 3-month
certificate of deposit, are also close substitutes for savings accounts. M2 is a broad measure of
the money supply that includes the components of M1 plus savings accounts, small
denomination deposits (under $100,000), balances in money market deposit accounts in banks,
and non-institutional money market fund shares.)
MD: M1 The narrowest definition of the money supply that includes currency, demand deposits,
and other checking accounts.)
(MD: M2 A broad measure of the money supply that includes the components of M1 plus
savings accounts, small denomination deposits (under $100,000), balances in money market
deposit accounts in banks, and non-institutional money market fund shares.)
Table 6-2 Components of the Money Supply
Measure of the Money
Supply
Assets Included
10
Amount in August 2010
(billions of dollars)
M1
Currency
Demand Deposits
M2
All the Assets Included in
M1
Savings Accounts
Small-Denomination
Time Deposits
Money Market Mutual
Funds
Other Short-Term
Deposits
Source: Federal Reserve…
Figure 6-1 shows the different components of the money supply for the United States.
Figure 6-1 M1 and M2 in the United States, 1959-2009
SOURCE: Board of Governors of the Federal Reserve System
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Caption:
Currency, checking accounts, and savings accounts have been around for the entire time period
depicted in the figure. However, financial innovation has led to new assets like small-time
deposits, such as certificates of deposit in the 1960s, and money market deposit accounts in the
1970s. In addition, savings accounts become more desirable relative to currency and checking
accounts due to the ease with which individuals can transfer funds from interest-bearing savings
accounts to either cash or checking accounts using either the internet or automated teller
machines.
End Caption
Currency, checking accounts, and savings accounts have been around for the entire time period
depicted in the figure. However, financial innovation has led to new assets like small-time
deposits, such as certificates of deposit in the 1960s, and money market deposit accounts in the
1970s. In addition, savings accounts become more desirable relative to currency and checking
accounts due to the ease with which individuals can transfer funds from interest-bearing savings
accounts to either cash or checking accounts using either the internet or automated teller
machines.
Which measure of the money supply should you use?
The correct measure of the money supply to use depends on the purpose. M1 was the
most common measure of the money supply until the early 1980s when substitutes to checking
accounts emerged and the relationship between M1 and nominal GDP became unstable; that is
M1 had less predictive power for nominal GDP. Since the 1980s, M2 has become the more
common measure of the money supply. However, further financial market innovation has made
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M2 a less reliable measure of the money supply as the relationship between M2 and nominal
GDP has become unstable. Figure 6-2
Figure 6-2 Growth Rates of M1 and M2 in the United States, 1960-2009
SOURCE: Board of Governors of the Federal Reserve System
Caption: M1 and M2 have similar growth rates much of the time, but significant differences can
emerge for short periods of time. The two measures of the money supply move broadly together
over long periods of time. However, some significant differences have occurred during certain
periods. For example, while the growth rate of M1 rose during the 1970s and mid-1990s, the
growth rate of the broader measure M2 actually decreased. Therefore, different measures of the
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money supply can give a different picture of movements in the money supply. The figure also
shows that the growth rate of both measures of the money supply can fluctuate significantly
during a short period of time due to financial innovation and changes in monetary policy. For
example, the growth rate of M1 fell from nearly 14.4 percent in November 1992 to negative
growth rates in June 1995 reaching a low of -5.4 percent in April 1997.
End Caption
shows that M1 and M2 have similar growth rates much of the time, but significant differences
can emerge for short periods of time. The two measures of the money supply move broadly
together over long periods of time. However, some significant differences have occurred during
certain periods. For example, while the growth rate of M1 rose during the 1970s and mid-1980s,
the growth rate of the broader measure M2 actually decreased. Therefore, different measures of
the money supply can give a different picture of movements in the money supply. The figure
also shows that the growth rate of both measures of the money supply can fluctuate significantly
during a short period of time due to financial innovation and changes in monetary policy. For
example, the growth rate of M1 fell from nearly 14.4 percent in November 1992 to negative
growth rates in June 1995 reaching a low of -5.4 percent in April 1997.
What Determines the Quantity of Money?
The quantity of money consists of assets, such as currency, determined by the central bank and
assets, such as checking or savings accounts, determined by the financial system. One of the
Fed’s most important functions is to determine the money supply, which is the stock of medium
of exchange. Inside the Federal Reserve, the Federal Open Market Committee (FOMC) is the
decision-making body that determines the money supply. The FOMC consists of members of
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the seven governors of the Federal Reserve Board in Washington D.C., the president of the New
York Federal Reserve Bank and four presidents from the remaining regional Federal Reserve
Banks. The FOMC meets about eight times a year to make decisions that influence the money
supply.
As an important tool of monetary policy, the Fed conducts open market operations to
control the money supply. Open market operations are the purchase and sale of Treasury
securities in financial markets by the Federal Reserve and are the most direct route for changing
the money supply. Most banks in the United States are members of the Federal Reserve System.
As such, banks are required to hold reserves against checkable deposits. Reserves are a bank
asset consisting of cash on hand in the bank plus deposits that banks have with the Federal
Reserve. We talk about open market operations and how the banking system creates money in
more detail in Chapter 9, but for now it is enough to know that when the Fed buys Treasury
securities it pays for them by increasing reserves and when reserves increase banks tend to
increase the amount of loans they make so the money supply increases. For example, if the
Federal Reserve purchases $1 billion worth of Treasury securities from Bank of America then
reserves at Bank of America increase by $1 billion. Bank of America may then, if it chooses,
increase the amount of loans it makes. If Bank of America makes new loans then either the
amount of currency or deposits in checking accounts increases so the money supply also
increases. When the Fed sells $1 billion of Treasury securities to Bank of America, then Bank of
America pays for the securities by decreasing its reserves so Bank of America is forced to reduce
the amount of loans it makes. As a result, either the amount of currency in circulation or
deposits in checking accounts decrease — so the money supply decreases.
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(MD: Open Market Operations The purchase and sale of Treasury securities in financial
markets by the Federal Reserve. Open market operations are the most direct route for changing
the monetary base.)
(MD: Reserves A bank asset consisting of cash on hand in the bank plus deposits banks have
with the Federal Reserve.)
Strictly speaking, the Fed controls the monetary base through the purchase and sale of
Treasury securities. The monetary base equals all reserves held by banks as well as currency in
circulation.. However, M1 and M2 include assets like checking accounts, savings accounts, and
money market mutual funds that the Fed does not control. The amount of funds deposited in
these and other accounts depend on the decisions of households and firms that want to save.
Therefore, the whole financial system plays a role in determining the money supply. As you can
see in Figure 6-1, the actual amount of currency in circulation is just a part of the broader money
supply so the financial system is important. Currency rose from 20.1 percent of M1 in 1959 to
53.3 percent of M1 in 2009. Over the same time period, currency rose from 9.9 percent to 10.3
percent of M2, so currency has been a relatively constant small fraction of the broader money
supply. Because the financial system creates liquid assets such as checking accounts, we can say
that both the financial system and the Federal Reserve create money.
(MD: Monetary Base All reserves held by banks as well as currency in circulation.)
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Banks use reserves to make loans to households and firms. The interest payments on the
loans allow banks to earn a profit. When households and firms receive these loans, they often
deposit the funds into checking accounts before using the funds. Banks can use these funds to
make loans to other individuals who may then deposit them in checking accounts, which allows
other banks to make even more loans. Reserves therefore support the creation of checking
accounts, which is one of the components of M1. Usually one dollar of reserves supports more
than one dollar of demand deposits. This amount of expansion is called the money multiplier.
The money multiplier just equals the ratio of the money supply to the monetary base:
(6.1)
𝑀𝑜𝑛𝑒𝑦 𝑆𝑢𝑝𝑝𝑙𝑦
𝑀𝑜𝑛𝑒𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = 𝑀𝑜𝑛𝑒𝑡𝑎𝑟𝑦 𝐵𝑎𝑠𝑒
For example, if there are $2 of money supply for every $1 of the monetary base then the money
multiplier equals 2. Figure 6-3 shows the money multiplier for M1 since the
Figure 6-3 The M1 Multiplier for the United States, 1959-2009
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Caption: There is a long-term downward trend in the M1 multiplier, as individuals have begun
to rely on financial assets other than cash and checking accounts to conduct market transactions.
However, there is a very steep drop in the value of the multiplier during the fall of 2008. Why
did the decrease in the money multiplier occur? During the financial crisis banks became
reluctant to lend to households and firms because banks were not sure which households and
firms would be able to repay the loans. In addition, banks were concerned about the quality of
the loans that they had made in earlier years so they wanted to keep extra reserves to help protect
them in case households and firms did not repay their current loans. As a result, the amount of
demand deposits that each dollar of reserves supported decreased so the money multiplier
decreased dramatically.
End Caption
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the late 1950s. There is a long-term downward trend in the M1 multiplier, as individuals have
begun to rely on financial assets other than cash and checking accounts to conduct market
transactions. However, there is a very steep drop in the value of the multiplier during the fall of
2008. Why did the decrease in the money multiplier occur? During the financial crisis banks
became reluctant to lend to households and firms because banks were not sure which households
and firms would be able to repay the loans. In addition, banks were concerned about the quality
of the loans that they had made in earlier years so they wanted to keep extra reserves to help
protect them in case households and firms did not repay their current loans. As a result, the
amount of demand deposits that each dollar of reserves supported decreased — and the money
multiplier decreased dramatically.
[Box Begins]
Making the Connection: Banks Reluctant to Lend in the United Kingdom and United
States
From the start of the financial crisis in August 2007 to February 2010, the Federal Reserve
increased the monetary base from $853.4 billion to $2,150.9 billion. That increase is large for a
short period of time. Other central banks also dramatically increased the monetary base. For
example, the monetary base in the United Kingdom rose from £66.2 billion in August 2007 to
£211.8 billion in February 2010. However, an increase in the monetary base does not necessarily
increase the money supply. In the United States the money supply (as measured by M1)
increased $1,368.6 billion in August 2007 to just $1,710.3 billion in February 2010 while the
money supply (as measured by a broader monetary aggregate than M1) in the United Kingdom
increased from £1,636.8 billion to £2,211.2 billion during the same period. The money supply
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increased in both countries, but not by nearly as much as the monetary base. For the increase in
the monetary base to increase the money supply, banks must make loans.
During the fall of 2009, over 40 percent of firms surveyed in the United Kingdom
indicated that banks were reluctant to make loans. The United States experienced a similar
phenomenon. William Dunkelberg, chief economist for the National Federation of Independent
Businesses, said “The basic story is that banks have plenty of money to lend, but just not many
bankable applicants.” In fact, small business loans in the United States fell nearly 2 percent from
the third quarter of 2008 to the third quarter of 2009. Looking at Equation (6.1) the failure for
loans and the money supply to increase as the monetary base increased caused the money
multiplier in the United States to plummet to less than one.
Source: Marsh, Peter. “Fears of Prolonged Weakness,” Financial Times, October 19, 2009, p.4.
Davis, Paul. “Holding Pattern for Borrowers,” USBanker, February 2010, p.12. Board of
Governors of the Federal Reserve System. Bank of England.
[End Box]
6.2 Explain the Quantity Theory of Money and Use it to Explain Inflation
This section will show that the growth rate of the money supply determines the inflation rate.
Yale economist Irving Fisher formalized the relationship between money and prices using the
quantity equation. The quantity equation is an identity linking the quantity of money to
nominal expenditures:
(6.2)
𝑀𝑥𝑉 = 𝑃𝑥𝑌.
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(MD: The Quantity Equation An identity linking the quantity of money to nominal
expenditures.)
The equation states that the money supply (M) multiplied by the velocity of money (V) equals
nominal expenditures (PxY) where P is the average price level and Y is real GDP. Fisher defined
the velocity of money as the average number of times each unit of money is used to purchase
goods and services in the economy. Rewriting equation (6.l) by dividing each side by the money
supply, we have an equation for velocity:
𝑉=
𝑃𝑥𝑌
𝑀
.
We can use M1 to measure the money supply and nominal GDP to measure nominal
expenditures. So, the value of velocity in 2009 was:
𝑉2009 ≡
𝑃2009 𝑥𝑌2009
𝑀2009
=
$14,256 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$1,628 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
= 8.8 𝑡𝑖𝑚𝑒𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟.
This result tells us that, on average during 2009, each dollar of M1 was spent about 8.8 times per
year on goods and services included in GDP.
(MD: Velocity of Money the average number of times each unit of money is used to purchase
goods and services in the economy.)
Because equation (6.2) is actually an identity, we know that the quantity equation must be
true. The left side must equal the right side, and velocity takes on a value that will maintain the
identity. Economists rely on theories, simplified versions of reality, to analyze real-world
events. A theory could prove to be false. The quantity equation is always true, so it does not
qualify as a theory. Irving Fisher turned the quantity equation into the quantity theory of
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money, a theory that changes in the money supply lead to predictable changes in nominal
expenditures.) Fisher argued that the average number of times a dollar is spent depends on
factors that do not change very often, such as how often people get paid, how often they do
grocery shopping, and how often businesses mail bills. Because this assertion may be either true
or false, the quantity theory of money is a theory. Technically, velocity does not have to be
constant for the quantity theory to hold, but velocity must be predictable for the quantity theory
to be useful in predicting the price level and inflation.
(MD: Quantity Theory of Money The theory that changes in the money supply lead to
predictable changes in nominal expenditures)
Figure 6-4 shows that the assumption of constant velocity is a better one for
Figure 6-4 The Velocity of Money for the United States, 1959-2008
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SOURCE: Bureau of Economic Analysis and Board of Governors of the Federal Reserve
System.
Caption: The assumption of a constant velocity is a better one for M2 than for M1. Over time,
financial innovation has made assets like savings accounts and small deposits better substitutes
for currency and checking accounts. The velocity of M1 increased as individuals chose to hold
their wealth as the less liquid assets that paid interest. The same amount of M1 supported a large
volume of economic activity, so the velocity of M1 increased steadily and predictably from 3.6
in 1959 to 7.4 in 1981. However, since then the velocity of M1 decreased to 6.2 in 1992, before
rising to 10.1 in 2007. In contrast, the velocity of M2 has been relatively constant ranging from
a low 1.6 to a high of 2.1, although it has been unpredictable over short periods of time.
End Caption
M2 than for M1. Over time, financial innovation has made assets like savings accounts and
small deposits better substitutes for currency and checking accounts. The velocity of M1
increased as individuals chose to hold their wealth as the less liquid assets that paid interest. The
same amount of M1 supported a large volume of economic activity, so the velocity of M1
increased steadily and predictably from 3.6 in 1959 to 7.4 in 1981. However, since then the
velocity of M1 decreased to 6.2 in 1992, before rising to 10.1 in 2007. In contrast, the velocity
of M2 has been relatively constant ranging from a low 1.6 to a high of 2.1, although it has been
unpredictable over short periods of time. For simplicity, we will assume that velocity is constant
and rewrite the quantity equation as:
𝑀𝑥𝑉̅ = 𝑃𝑥𝑌,
where 𝑉 is an assumed constant velocity. Equation (6.3), which shows us the quantity theory of
money is a theory rather than an identity because it is based on the assumption of a constant
velocity, which may or may not be true.
The Quantity Theory Explanation of Inflation
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The inflation rate is the growth rate of the price level, but equation (6.3) shows the
relationship between the levels of money, velocity, prices, and real GDP. We can use algebra
and calculus to convert the quantity equationinto a theory of inflation:
(6.3)
𝑔𝑀 + 𝑔𝑉 = 𝑔𝑃 + 𝑔𝑌 ,
where ”g” stands for compound average growth rate. The right-hand side of the equation is the
growth rate of nominal GDP. The quantity theory assumes that the growth rate of velocity is
constant so, 𝑔̅𝑉 = 0. In addition, the growth rate of the price level equals inflation, 𝜋, so 𝑔𝑃 =
𝜋. Therefore,
𝑔𝑀 = 𝜋 + 𝑔𝑌 ,
which tells us that the growth rate of the money supply equals the growth rate of nominal GDP.
To understand how the growth rate of the money supply influences the inflation rate, we need to
know the growth rate of potential real GDP. In Chapter 5, we learned that the growth rate of
potential real GDP is determined by the growth rate of the labor force and the growth rate of
TFP. These are both real variables, so changes in the money supply do not influence them and
changes in the growth rate of the money supply will not influence the growth rate of potential
real GDP. Therefore, changes in the growth rate of the money supply influence the inflation
rate.
For example, in Chapter 5, we learned that the growth rate of potential real GDP for the
United States is about 3.1 percent per year, so 𝑔𝑌 = 3.1. If the Federal Reserve allows the
money supply to grow at 5 percent per year, then 𝑔𝑀 = 5, and the long-run inflation rate is 𝜋 =
5 − 3.1 = 1.9 percent. Now suppose that the Federal Reserve doubles the growth rate of the
24
money supply from 5 percent to 10 percent. The quantity theory assumes that velocity is
constant and that changes in the money supply do not influence the growth rate of potential real
GDP. The new long-run inflation rate is 𝜋 = 10 − 3.1 = 6.9 percent, so a five-percentage-point
increase in the growth rate of the money supply leads to a five-percentage-point increase in the
inflation rate. Therefore, the quantity theory predicts that if the growth rate of the money supply
increases by one percentage point then the inflation rate also increases by one percentage point.
[Box Begins]
Making the Connection: Do the United States and Other Countries Face a Severe Inflation
Threat in the Future
Central banks increased bank reserves and the monetary base to help banks and the economy
during the financial market crisis. As of April 2010, the large increases in the monetary base had
not resulted in large increases in the money supply because most banks were uncertain whether
households and firms would be able to repay new loans. As a result, most banks held onto their
new reserves — hence, the money multiplier decreased while the monetary base increased.
However, once economies begin to recover banks will be more willing to loan out their new
reserves so countries such as the United Kingdom and the United States face the possibility of a
sudden rapid increase in the money supply. Vincent Reinhart, a former chief economist for the
Federal Reserve’s Federal Open Market Committee, said “What you worry about is we have a lot
of reserves in the banking system. Ultimately they’ll get used and create a multiplier expansion
of the money supply.” In the long run, when the money supply only influences nominal
variables such as the inflation rate, and with velocity roughly constant, equation (6.3) on page xx
25
tells us that the sudden increase in the money supply will cause a sudden increase in the inflation
rate. As of April 2010, inflation has remained relatively low around the world. However, this
could change as the economies of the world recover and banks become more willing to lend.
Central banks such as the Federal Reserve understand this threat and began to take steps to
withdraw reserves and shrink the monetary base during early 2010.
Source: Hall, Kevin. “Bernanke Unveils Plan to Unwind Fed’s Massive Asset Purchases,”
McClatchy – Tribune Business News, February 10, 2010.
[End Box]
Velocity does not have to be constant in order for an increase in the money supply growth
rate of five percentage points to cause an increase in the inflation rate by five percentage points.
As long as velocity grows at a constant rate, you will find a similar result. However, when the
growth rate of velocity changes it is difficult for the central bank to predict how changes in the
money supply growth rate will influence the inflation rate.
Solved Problem 6.1: A Decrease in the Growth Rate of the Money Supply.
26
The average annual growth rate of potential real GDP for the United States is 3.1 percent.
Suppose that the growth rate of velocity is 0 percent. What happens to the inflation rate if the
money supply growth rate decreases from 5 percent to 2 percent?
Student comment, Quinnipiac: The Solved Problem just seemed to be oversimplified. I don’t
feel that understanding a problem as simple as that prepares you for the test.
Solving the Problem:
Step 1: Review the chapter material. The problem asks you to determine the effect of a
decrease in the growth rate of the money supply, so you may want to review the section “The
Quantity Theory Explanation of Inflation,” which begins on page x.
Step 2: Determine the Initial Inflation Rate. Equation (6.3) tells us that 𝑔𝑀 + 𝑔𝑉 = 𝑔𝑃 + 𝑔𝑌 ,
so if the growth rate of velocity is 0 percent, then we have:
𝑔𝑀1 = 𝜋1 + 𝑔𝑌 .
This expression is just one equation with three unknowns. If you know two of the unknowns,
then you can solve for the third unknown. The question tells you that the growth rate of potential
real GDP is 3.1 percent, so:
𝑔𝑌 = 3.1.
We also know that the growth rate of the money supply is initially 5 percent, so:
𝑔𝑀1 = 5.
27
We can plug these two values into the above equation to get:
5 = 𝜋1 + 3.1, or
𝜋1 = 5 − 3.1 = 1.9 %.
Step 3: Calculate the New Inflation Rate. If the growth rate of the money supply decreases
from 5 percent to 2 percent, then the inflation rate will also decrease. We know that changing
the inflation rate does not change real variables, so the growth rate of potential real GDP remains
3.1 percent. Equation (6.3) tells us:
𝑔𝑀2 = 𝜋2 + 𝑔𝑌 ,
where 𝑔𝑀2 = 2.
We can solve for the inflation rate as before:
2 = 𝜋2 + 3.1
𝜋2 = 2 − 3.1 = −1.1 %.
The three-percentage-point decrease in the growth rate of the money supply led to a threepercentage-point decrease in the inflation rate. In this case, the inflation rate is negative so the
average price of goods and services decreases. In other words, deflation occurs.
See related problem XXX on page XXX.
**********************************************************************
28
Does inflation really increase as the growth rate of the money supply increases? Figure
6-5 shows the relationship between the inflation rate and the growth rate of M1 for 44 countries
Figure 6-5 Relationship between M1 Growth and the Inflation Rate
SOURCES: International Financial Statistics.
Caption: The quantity theory predicts that a one-percentage point increase in the money supply
increases the inflation rate by one percentage point. The data show that inflation increases by a
little bit less than one-percentage point. However, the quantity theory assumes constant velocity,
and we have seen that velocity does change over time.
End Caption
29
between 1995 and 2007. If velocity is constant and the growth rate of potential real GDP is
independent of the money supply, then a one-percentage-point increase in the growth rate of the
money supply should lead to a one-percentage-point increase in the inflation rate. Figure 6-5
provides fairly strong support for the quantity theory. An increase in the money supply growth
rate increases the inflation rate by a little bit less than predicted. However, the quantity theory
assumes that velocity is constant, and we saw in Figure 6-4 that velocity does change over time.
But the basic prediction of the quantity theory is one of the most reliable relationships in
macroeconomics: If the central bank increases the growth rate of the money supply, then this
will lead to a higher inflation rate.
6.3 Explain the Relationship Between Money Growth, Inflation, and Nominal Interest
Rates
We learned in Chapter 3 that interest rates are critical for allocating resources in the economy
because financial markets allocate funds to those individuals willing to pay the highest interest
rates. We learned in Chapter 2 that inflation and real and nominal interest rates are related. We
discuss this relationship further in this section.
Ex Post and Ex Ante Real Interest Rates
Recall from Chapter 2 that the real interest rate is the nominal interest rate minus the
inflation rate:
𝑟 = 𝑖 − 𝜋.
30
This equation is true, but it ignores an important subtlety. When people borrow to purchase a
house, they often obtain a 30-year fixed interest rate mortgage from a lender. A typical nominal
interest rate is 6 percent. However, the borrowers do not know what the inflation rate is going to
be over the next 30 years, so they cannot really calculate the real interest rate in equation (6.6).
For borrowers to determine the real interest rate over the life of the loan, they need to use
the expected inflation rate, 𝜋 𝑒 , to calculate the ex ante real interest rate. The ex ante real
interest rate is the real interest rate expected at the time the loan is made. It equals the nominal
interest rate minus the expected inflation rate. We call it the ex ante real interest rate because it
is the real interest rate before borrowers actually know the inflation rate:
(6.4)
𝑒𝑥 𝑎𝑛𝑡𝑒 𝑟 = 𝑖 − 𝜋 𝑒 .
The ex post real interest rate is the actual real interest rate on a loan. It equals the nominal
interest rate minus the actual inflation rate::
(6.5)
𝑒𝑥 𝑝𝑜𝑠𝑡 𝑟 = 𝑖 − 𝜋.
Economists call it the ex post real interest rate because it is the real interest rate after borrowers
know the actual interest rate. The two real interest rates are related: If the inflation and expected
inflation are equal, then the ex ante and ex post real interest rates are also the same. However, if
inflation does not equal expected inflation, then the ex ante and ex post real interest rates are not
the same.
(MD: Ex Ante Real Interest Rate The real interest rate expected at the time a loan is made. It
equals the nominal interest rate minus the expected inflation rate.)
31
(MD: Ex Post Real Interest Rate The actual real interest rate on a loan. It equals the nominal
interest rate minus the actual inflation rate.)
If the nominal interest rate on a mortgage is 6 percent and the expected inflation rate is 2
percent, then the ex ante real interest rate = (6 percent) – (2 percent) = 4 percent. If the actual
inflation rate also turns out to be 2 percent, then the ex post real interest rate also equals 4
percent. However, if the actual inflation rate is 5 percent, then ex post real interest rate = (6
percent) – (5 percent) = 1 percent. In this case, then,the ex post real interest rate is less than the
ex ante real interest rate. Similarly, if the actual inflation rate is 0 percent, then the ex post real
interest rate = (6 percent) – (0 percent) = 6 percent. Here, then, the ex post real interest rate is
greater than the ex ante real interest rate. Table 6-3 summarizes this result.
Table 6-3 The Relationship Between Ex Ante and Ex Post Real Interest Rates
If …
𝝅=𝝅
Then…
For example…
ex ante r = ex post r
If the nominal interest rate
on a mortgage is 6 percent
and the expected inflation
rate is 2 percent, then the ex
ante real interest rate is
𝒆
(6 percent) – (2 percent) = 4
percent.
If the actual inflation rate
also turns out to be 2
percent, then the ex post
real interest rate also equals
4 percent.
𝝅 > 𝝅𝒆
ex ante r > ex post r
32
If the actual inflation rate is
5 percent, then ex post real
interest rate is:
(6 percent) – (5 percent) = 1
percent, so the ex post real
interest rate is less than the
ex ante real interest rate.
𝝅 < 𝝅𝒆
ex ante r < ex post r
If the actual inflation rate is
0 percent, then the ex post
real interest rate is
(6 percent) – (0 percent) = 6
percent, so the ex post real
interest rate is greater than
the ex ante real interest rate.
The Fisher Effect
In the mortgage interest rate example, the nominal mortgage interest rate was fixed, so
we could see what happens to the real interest rate when the inflation rate rises above or falls
below the expected inflation rate. However, the nominal mortgage interest rate, as with other
interest rates, is only fixed once the borrowers sign a mortgage contract. Before the borrowers
and lenders agree on a nominal interest rate, market participants are free to adjust it based on
their own assessment of market conditions including the expected inflation rate over the duration
of the loan. To figure out what nominal interest rate lenders will set, rearrange equation (6.7) as
follows:
(6.6)
𝑖 = 𝑒𝑥 𝑎𝑛𝑡𝑒 𝑟 + 𝜋 𝑒 ,
which states that the nominal interest rate is the sum of the ex ante real interest rate and the
expected inflation rate. Equation (6.6) is called the Fisher equation, after the same Irving Fisher
associated with the quantity theory of money. The Fisher equation states that the nominal
33
interest rate is the sum of the real interest rate and the expected inflation rate. Therefore, the
nominal interest rate changes when the real interest rate changes or when the expected inflation
rate changes.
(MD: Fisher Equation An equation stating that the nominal interest rate is the sum of the real
interest rate and the expected inflation rate.)
As we learned in Chapter 3, there are many different real interest rates in the economy. If
we think of the market for government securities, then r is the real interest rate that the
government must pay to borrow funds. This real interest rate is determined by the market for
loanable funds. That is, factors such as the willingness of households to save, the government’s
spending and taxing decisions and potential real GDP influence the real interest rate. For
example, if the government raises expenditures or cuts taxes and finances this change in fiscal
policy by borrowing, the supply of loanable funds will fall, so the real interest rate will increase.
According to the Fisher equation, the nominal interest rate will also rise as long as inflationary
expectations are constant.
The Fisher equation tells us that the nominal interest rate will also change when
inflationary expectations change. If inflation does not influence the real interest rate, then
changes in expected inflation translate into changes in the nominal interest rate. For example,
assume the real interest rate in the market for loanable funds is 4 percent and the expected
inflation rate is 2 percent over the life of a loan. In that case, the nominal interest rate on a loan
is 4 percent plus 2 percent, or 6 percent. Now, if the expected inflation rate rises from 2 percent
34
to 3 percent, then the nominal interest rate equals the 4 percent real interest rate plus the 3
percent expected inflation rate — for a nominal interest rate of 7 percent. This change is called
the Fisher effect, which states that a one-percentage-point increase in the expected inflation rate
leads to a one-percentage-point increase in the nominal interest rate.
(MD: The Fisher Effect States that a one-percentage-point increase in the expected
inflation rate leads to a one-percentage-point increase in the nominal interest rate.)
Do the data support the Fisher effect? Figure 6-6 shows the relationship between the
Figure 6-6 Relationship between Inflation and the Nominal Interest Rate, 1995-2008
35
SOURCES: International Financial Statistics
Caption: The figure shows the relationship between the inflation rate and the nominal interest
rate on Treasury bills for 88 countries over the period from 1995 to 2008. There is a clear
positive relationship between inflation and the nominal interest rate, which is consistent with the
Fisher effect. In addition, the nominal interest rate tends to rise by 0.9 percent when the inflation
rate increases by 1 percent. Therefore, the Fisher effect and equation (6.9) provide a good
approximation of how inflation influences interest rates around the world.
End Caption
inflation rate and the nominal interest rate on Treasury bills for 88 countries over the period
from 1995 to 2007. There is a clear positive relationship between inflation and the nominal
interest rate, which is consistent with the Fisher effect. In addition, the nominal interest rate
tends to rise by 0.9 percent when the inflation rate increases by 1 percent. Therefore, the Fisher
effect and equation (6.9) provide a good approximation of how inflation influences interest rates
around the world.
Money Growth and the Nominal Interest Rate
If we combine the quantity theory of money with the Fisher effect, then we learn an
important relationship: An increase in the growth rate of the money supply causes the inflation
rate to increase, which then causes the nominal interest rate to increase. The inflation rate
therefore varies across time and countries because of changes in the growth rate of the money
supply, and the nominal interest rates vary across time and countries because of differences in
the growth rate of the money supply.
36
Consider the United States. The growth rate of M2 velocity is approximately 0 percent,
the growth rate of potential real GDP is 3.1 percent, and the ex ante real interest rates on Aaa
corporate bonds has averaged 2.8 percent since 1919. Suppose that the Fed sets the growth rate
of the money supply at 5 percent. According to the Fisher equation, what should the nominal
interest rate on the Aaa corporate bond be? To answer this question we must first calculate the
expected inflation rate. For simplicity, we will assume that the actual and expected inflation
rates are the same. So, we can use the equation (6.3) which is the quantity equation in growth
rates to find the inflation rate. The quantity equation in growth rates is:
𝑔𝑀 + 𝑔𝑉 = 𝑔𝑃 + 𝑔𝑌 .
The growth rate of the price level is the inflation rate and we are assuming that the growth rate of
velocity is zero, so:
𝑔𝑀 = 𝜋 + 𝑔𝑌 , or
5 = 𝜋 + 3.1, so that
𝜋 = 5 − 3.1 = 1.9 %.
If we are willing to assume that this is also the expected inflation rate, then we can use the Fisher
equation in equation (6.6) to calculate the nominal interest rate on a corporate Aaa bond as:
𝑖 = 𝑟 + 𝜋 𝑒 , or
𝑖 = 2.8 + 1.9 = 4.7%.
Solved Problem 6.2: An Increase in the Growth Rate of the Money Supply.
37
The average annual growth rate of potential real GDP for the United States is 3.1 percent, and
the ex ante real interest rate on corporate Aaa has averaged 2.8 percent. Suppose that the growth
rate of velocity is 0 percent. What happens to the nominal interest rate if the money supply
growth rate increases from 5 percent to 10 percent?
Solving the Problem:
Step 1: Review the chapter material. The problem asks you to determine the effect of a
decrease in the growth rate of the money supply, so you may want to review the material in the
section entitled “Money Growth and the Nominal Interest Rate,” which begins on page x.
Step 2: Determine the Initial Nominal Interest Rate. Recall from the Solved Problem on page
x of this chapter that the initial nominal interest rate, 𝑖1 , is 4.7 percent.
Step 3: Calculate the New Inflation Rate. If the growth rate of the money supply increases
from 5 percent to 10 percent, then the inflation rate will also change. We know that changing the
inflation rate does not change real variables, so the growth rate of potential real GDP remains 3.1
percent. Equation (6.3) on page xx for the quantity equation in growth rates tells us:
𝑔𝑀 + 𝑔𝑉 = 𝑔𝑃 + 𝑔𝑌
Because the growth rate of the price level is the inflation rate and the growth rate of velocity is
constant, we have:
38
𝑔𝑀2 = 𝜋2 + 𝑔𝑌
where 𝑔𝑀2 = 10.
So, we can solve for the inflation rate as before:
10 = 𝜋2 + 3.1
𝜋2 = 10 − 3.1 = 6.9 %.
The initial inflation rate, 𝜋1 , was 1.9 percent, so an increase of 5 percent in the growth rate of the
money supply led to an increase of 5 percent in the inflation rate.
Step 4: Calculate the New Nominal Interest Rate. If we assume that 𝜋2 is also the new
expected inflation rate, then we can use the Fisher equation to calculate the new nominal interest
rate, i2, as:
𝑖2 = 𝑟 + 𝜋2𝑒 , or
𝑖2 = 2.8 + 6.9 = 9.7 %.
The 5 percent increase in the money supply growth rate caused a 5 percent increase in the
expected inflation rate, leading to a 5 percent increase in the nominal interest rate on Aaa
corporate bonds.
See related problem XXX on page XXX.
**********************************************************************
39
6.4 Explain the Costs of Inflation
In the previous sections, you learned about the quantity theory of money, inflation, and
nominal interest rates. You also learned how to use equations to predict inflation. We now
explain the costs of inflation and the benefits of reducing inflation. As it turns out, the costs to
inflation depend on whether the inflation is expected or unexpected. The costs arise partly
because inflation interferes with the ability of money to serve the four functions that we
discussed on page x.
Figure 6-7 shows the inflation rate for the Japan, Mexico, and the United States over the
1961
Figure 6-7 Inflation Rates in Japan, Mexico and the United States, 1961-2008
40
SOURCE: International Financial Statistics. Inflation rates are the annual growth rates of the
consumer price index.
Caption: For most nations, the inflation rate rose from the late 1960s to early 1980s, before
decreasing to much lower levels in the 1990s and 2000s. In fact, Japan experienced deflation
during part of the 1990s and 2000s. In contrast, some countries like Mexico experienced
hyperinflation, rapid inflation in excess of hundreds or thousands of percentage points per year
for a significant period of time. The United States experienced an increase in the inflation rate
during the 1970s, and then a decrease during the 1980s and 1990s. However, the changes in the
United States inflation rate were small relative to countries such as Mexico. Economists
generally believe that the decrease in the inflation rate from the 1980s to the 2000s improved the
functioning of the economy and made people better off.
41
End Caption
2008 time period. For most nations, the inflation rate rose from the late 1960s to early 1980s,
before decreasing to much lower levels in the 1990s and 2000s. In fact, Japan experienced
deflation during part of the 1990s and 2000s. In contrast, some countries like Mexico
experienced hyperinflation, rapid inflation in excess of hundreds or thousands of percentage
points per year for a significant period of time. The United States experienced an increase in the
inflation rate during the 1970s, and then a decrease during the 1980s and 1990s. However, the
changes in the United States inflation rate were small relative to countries such as Mexico.
Economists generally believe that the decrease in the inflation rate from the 1980s to the 2000s
improved the functioning of the economy and made people better off. Why?
(MD: Hyperinflation Rapid inflation in excess of hundreds or thousands of percentage points
per year.
Costs of Expected Inflation
There are three costs to expected inflation: seigniorage, shoe-leather costs, and menu
costs. Seigniorage refers to the revenue raised by the government from printing more money;
also known as the inflation tax. When the government increases the money supply it gets to use
the extra money to purchase goods and services or pay for transfer programs such as Social
Security and unemployment insurance. However, we have also seen that an increase in the
money supply causes inflation. Inflation causes the purchasing power of money to decrease.
Suppose you want to purchase a plasma TV next year. The current price of the TV is $1,000,
and you decide to keep $1,000 in your checking account for one year and then purchase the TV.
If the government finances its expenditures by increasing the money supply to the extent that the
42
inflation rate is 10 percent for the year, then the price of the TV will rise to $1,100. Your $1,000
can no longer purchase the TV, so the purchasing power of your money has decreased. The
government’s actions caused the decrease in the purchasing power of your $1,000 so the
increase in inflation is essentially a tax. Therefore, inflation acts like a transfer of wealth from
the holders of money to the government. What the government gains in revenues, the holders of
money lose so seigniorage does not directly decrease aggregate well-being.
(MD: Seigniorage: The revenue raised by the government from printing more money;
also known as the inflation tax. )
Like most taxes, individuals change their behavior to avoid the tax by choosing to hold
less of their wealth as money. The nominal interest rate on money is 0 percent, so if the
expected inflation rate is 3 percent, then the ex ante real interest rate for money is 0 percent
minus 3 percent, or -3 percent. Other assets such as savings accounts, certificates of deposits,
and bonds have a nominal interest rate greater than zero. To protect themselves from
seigniorage, individuals transfer their wealth from money to interest-bearing assets.
Unfortunately, these other assets are less liquid than money. When individuals want to use their
wealth to purchase goods and services, they must first transfer their wealth from the less liquid
interest-bearing assets into money. This transfer takes time and effort, so it is costly.
Economists use the term shoe leather costs to refer to the costs of inflation to consumers and
businesses due to reducing holding less money and making more frequent trips to the bank. In
the past, individuals had to go to the bank and transfer funds from savings accounts to checking
43
accounts or cash and doing so took time and wore out the soles of their shoes — hence, the term
shoe leather costs. These costs are lower today because of online banking and automated teller
machines.
(MD: Shoe Leather Costs The costs of inflation to consumers and businesses due to
reducing holding less money and making more frequent trips to the bank.)
Expected inflation also creates inefficiencies in the tax system. Most countries have
income tax systems based on nominal income and progressive tax systems with higher marginal
tax rates at higher levels of nominal income. Inflation increases nominal income and can push
individuals into higher income tax brackets. As a result, individuals may pay higher taxes even
if the purchasing power of the income stays constant or even decreases. Economists call this
process bracket creep. To the extent that higher marginal tax rates reduce labor supply, bracket
creep can make the labor market less efficient. In addition, the tax code fails to adjust the values
of inventories and the value of depreciation allowances for inflation, which also makes the
economy less efficient by raising the corporate tax burden, and depressing business investment
during periods of high inflation.
In response to the rapid inflation of the 1970s, the United States indexed income tax
brackets to inflation in 1985, and so reduced the adverse effects of bracket creep. However, not
all taxes were indexed. Capital gains taxes are not indexed for inflation, so investors pay taxes
on the nominal capital gains rather than real capital gains. For example, suppose that the
expected inflation rate is 2 percent and that an individual earns $75,000 per year, so that she is in
44
the 25 percent marginal income tax bracket. She purchases a bond with a nominal interest rate of
5 percent. The pre-tax ex ante real interest rate is 5 percent – 2 percent = 3 percent. The aftertax ex ante real interest rate is (1 – 0.25) x (5 percent) – (2 percent) = 1.75 percent. Now
suppose the expected inflation rate rises to 4 percent and the nominal interest rate rises by the
same amount to 7 percent. Now the pre-tax ex ante real interest rate is 7 percent – 4 percent = 3
percent. This rate is exactly the same as before. However, now the post-tax ex ante real interest
rate is (1 – 0.25) x (7 percent) – (4 percent) = 1.25 percent. The investment has become less
profitable simply due to the increase in expected inflation. This example illustrates how inflation
combines with the tax code to distort the incentives for individuals to save and invest.
Expected inflation combines with the tax code to distort decisions about debt.
Corporations and homeowners can deduct interest payments on debt and mortgages from their
income before paying taxes. An increase in the expected inflation rate will increase the nominal
interest rate that individuals pay, so the value of interest payments also increases. Higher
expected inflation reduces the taxable component of income and decreases the after-tax cost of
borrowing, which means corporations and individuals are more willing to take on debt.
Menu costs are another cost to expected inflation. These are the costs to firms of
changing prices due to reprinting price lists, informing customers, and angering customers. The
higher the inflation rate, the more frequently firms change prices so the greater the menu costs.
In addition, not all firms have the same menu costs, so when expected inflation occurs some
firms will change prices and others will not. For example, restaurants often have to pay to have
new menus printed up, so the menu costs for restaurants are high and restaurants do not change
prices frequently. However, the price of a gallon of gas can change every day because it is
relatively cheap and easy for gasoline stations to change posted prices. Therefore, gasoline
45
prices often respond quickly to inflation while prices at restaurants do not respond quickly.
Relative prices in the economy will change, and the economy’s allocation of resources in the
economy will become less efficient. The phenomenon is very similar to what happens with real
interest rates. In this case, firms set nominal prices partly based on what they think the inflation
rate will be. If inflation is higher or lower than expected, then the real price of a firm’s product
is also higher or lower than expected. Firms with low menu costs are likely to adjust their prices
to the desired level quickly, but firms with high menu costs will not. As a result, the relative
price of goods and services can change and make markets less efficient.
(MD: Menu Costs The costs to firms of changing prices due to reprinting price lists, informing
customers, and angering customers.)
How Large are the Costs of Expected Inflation?
Inflation has averaged around 2 percent in the United States for the past 20 years. That is
a very low inflation rate, but the rate is still positive, so the average price of goods and services
rises over time. Harvard economist Martin Feldstein argues that there would be substantial
benefit to the economy of going from 2 percent to 0 percent inflation.1 Feldstein believes that
even at a 2 percent inflation rate the welfare costs from inflation range from 0.63 to 1.01 percent
of GDP. Given the size of U.S. economic activity in 2008, the welfare costs of 2 percent
inflation range from $73 billion to $118 billion per year.2 This cost is paid every year. The
1
“The Costs and Benefits of Going from Low Inflation to Price Stability,” in Reducing Inflation: Motivation and
Strategy eds. Christina Romer and David Romer, University of Chicago Press, 1997. See also Darrell Cohen, Kevin
Hassett, and R. Glenn Hubbard “Inflation and the User Cost of Capital: Does Inflation Still Matter?” in The Costs and
Benefits of Price Stability ed. Martin Feldstein, University of Chicago Press, 1999.
2
Data are in chained 2000 dollars.
46
associated present value of the welfare gain of going from 2 percent to 0 percent inflation is 35
percent of GDP, or $4,078 billion.
The welfare costs are large because the distortions caused by inflation persist into the
future. When inflation combines with the tax code to reduce the incentive for firms to invest, the
capital stock falls over time. In addition, if individuals save less because of inflation and the tax
code, the supply of loanable funds falls. This should raise real interest rates and reduce
investment expenditures. All else equal, this decline also reduces the capital stock. The
reduction in the capital stock depresses economic activity today and into the future. Because the
economic activity grows over time, even a one percent welfare loss is very large in an economy
the size of the United States.
Unexpected Inflation
When the inflation rate turns out to be higher or lower than expected, wealth is
redistributed in the economy. For example, suppose you borrowed $1,000 to purchase a plasma
TV instead of paying cash. The bank charges you a nominal interest rate of 10 percent, and you
repay the loan after one year. That is, you pay the bank $1,100 at the end of the year in exchange
for the bank giving you $1,000 at the beginning of the year to purchase the plasma TV. If the
expected inflation rate for the year is 4 percent, then the ex ante real interest rate is 10 percent –
4 percent = 6 percent. That means you expect to pay — and the bank expects to receive — a 6
percent real interest rate. The nominal compensation to the bank for the loan is $100, but the real
compensation is $60. What happens if the inflation rate turns out to be 8 percent? In that case,
the ex post real interest rate is 10 percent – 8 percent = 2 percent. While the nominal
compensation to the bank remains $100, the real compensation is just $20. You gain, and the
47
bank loses. When inflation is higher than expected, borrowers gain and creditors lose. Table 6-4
shows who gains and loses when inflation deviates from expectations.
Table 6-4 Winners and Losers from Unexpected Inflation
If …
𝝅 = 𝝅𝒆
Then…
so …
ex ante r = ex post r
creditors neither lose nor gain because the real
interest rate is exactly what they expected.
𝝅 > 𝝅𝒆
ex ante r > ex post r
creditors lose because the real interest rate is
lower than expected
𝝅 < 𝝅𝒆
ex ante r < ex post r
creditors gain because the real interest rate is
higher than expected
This deviation represents a redistribution of wealth from creditors to debtors, so as with
seigniorage, the total wealth in the economy does not change. In this sense, unexpected inflation
is not a true cost to the entire economy since what creditors lose debtors gain. Nevertheless,
unexpected inflation can generate true costs for the economy. First, both creditors and debtors
devote resources to forecasting inflation and avoiding the costs of unexpectedly high or low
inflation. These resources could be used elsewhere to produce goods and services for investment
or consumption. Second, one way in which creditors and debtors can avoid the costs associated
with unexpected inflation is not to borrow or lend. To the extent that unexpected inflation
reduces economic activity, and investment activity in particular, unexpected inflation creates an
important cost.
[Box Begins]
Macro Data: What is the Expected Inflation Rate?
48
The expected inflation rate is clearly important. Although we cannot directly observe a
person’s expectations, we can infer the inflation rate that the market as a whole expects. In 1997,
the United States government started issuing Treasury Inflation Protected Securities (TIPS).
Most Treasury securities have a fixed nominal face value, so when the Treasury sells these
securities in auctions we learn the nominal interest rate. In contrast, TIPS have a fixed real face
value that is indexed to the inflation rate so when they are sold we learn the ex ante real interest
rate. The Fisher equation states:
𝑖 = 𝑒𝑥 𝑎𝑛𝑡𝑒 𝑟 + 𝜋 𝑒 ,
which is just one equation with three unknowns. When the Treasury auctions off standard
nominal securities, i is set in the market; when the Treasury auctions off TIPS, ex ante r is set in
the market. The difference between these two market interest rates is an approximation to the
expected inflation rate of people in the bond market. Because of differences in liquidity and
liquidity premiums in the two markets, the difference between the two interest rates is just an
approximation to the expected inflation rate. For example, on June 9, 2009, the nominal interest
rate on a standard 10-year Treasury bond was 3.86 percent, and the ex ante real interest rate on a
10-year TIPS Treasury bond was 1.88 percent. As a result, the average annual expected inflation
rate for the next ten years in the market was 3.86 – 1.88 = 1.98 percent.
Figure 6-8 shows the expected inflation rate over five-year and ten-year horizons
calculated
Figure 6-8 Expected Inflation Rate Implied by the Treasury Market
49
SOURCE: Federal Reserve Bank of Saint Louis Fred Database.
Caption: Expected inflation is calculated as the difference between the interest rate on a
standard constant-maturity Treasury bond and a constant-maturity TIPS. Inflation expectations
were stable during the 2000s until the financial market shock of 2007. By the fall of 2008,
markets were expecting negative inflation — deflation — over a five-year horizon.
End Caption
using the interest rates on standard Treasury securities and TIPS. Inflationary expectations were
stable from 2003 through the fall of 2008. Then expected inflation plummeted and actually
became negative. In Chapter 9, we discuss why economic downturns can decrease expected
inflation.
50
See related problem XX on page XXX
[End Box]
[Box Begins]
Making the Connection: Has the Monetary Stimulus During the Financial Crisis Increased
the Expected Inflation Rate?
The large increases in the monetary base during the financial market crisis did not lead to large
increases in the money supply as of April 2010. However, as economies recover, banks will
become more willing to lend. Hence, in a recovery, the new lending may lead to large increases
in the money supply and, therefore, a large increase in the inflation rate. To combat the threat of
increased inflation, central banks such as the Federal Reserve announced that they would
withdraw the monetary stimulus as the economy recovers.
How successful were central banks in convincing households and firms that inflation
would not accelerate? Figure 6-8 helps us answer this question. Inflationary expectations did
increase during the later part of the 2007-2009 recession. For example, the five-year expected
inflation rate rose from a low of -2.2 percent on November 28, 2008 to 2.0 percent on April 6,
2010, an increase of more than 4 percent in the expected inflation rate in under 18 months.
However, the expected inflation rate only rose back to pre-crisis levels. Therefore, by 2010, one
could conclude that market participants expect that the Federal Reserve will be able to withdraw
51
the monetary stimulus quickly enough to prevent inflation from increasing above the prefinancial-crisis average inflation rate.
Source: Board of Governors of the Federal Reserve System.
[End Box]
Inflation Uncertainty
Relative prices play an important role in allocating resources. Whenever markets are not
in equilibrium, either a shortage or a surplus exists, and relative prices adjust to eliminate the
shortage or surplus. In that sense, market prices signal to households and firms how to allocate
resources. For example, suppose that the price of a new residential house is $300,000, and the
price of a new office building is also $300,000. That means the price of residential housing
relative to an office building is one. If the population increases because many young families
move into an area, then the price of residential housing is likely to rise relative to the price of
commercial buildings. Suppose the price of residential housing doubles to $600,000, while the
price of commercial buildings remains $300,000. As a result, the relative price of residential
housing is now two. Building residential housing is now more profitable relative to building
commercial buildings, so resources will flow into the construction of residential housing and
satisfy the demand for housing by the young families. The relative price of residential housing
plays a critical role in allocating resources to the construction of residential housing to satisfy the
demand for housing by the young families. In a market economy, relative prices will help guide
resources to those activities in which the resources improve welfare the most.
52
When the inflation rate fluctuates significantly from year to year, relative prices become
distorted and can send misleading signals to market participants. As we discussed with menu
costs, when inflation occurs, not all prices rise by the same amount, so relative prices can change
and markets may misallocate resources. Consider the previous example of residential housing
and commercial buildings. Suppose that there is no increase in the number of young families in
the area, but inflation does occur in the economy. Furthermore, if the menu costs are higher for
commercial buildings than residential housing then the builders of commercial buildings will
increase prices more slowly than the builders of residential housing. As a result, the price of
residential housing may rise to $600,000, while the prices of commercial buildings remain at
$300,000. The relative price of residential housing has again risen to two, so resources will flow
into the construction of residential housing. However, relative prices haven not changed due to
changes in the number of young families, so the new residential housing does not satisfy
increased demand from consumers. In this situation, the economy’s resources can be
misallocated.
Figure 6-9 shows the relationship between the average inflation rate and the volatility of
Figure 6-9 Inflation and Inflation Volatility, 1996-2008
53
SOURCES: International Financial Statistics.
Caption: There is a clear tendency for the volatility of inflation to increase as the average annual
inflation rate increases. Therefore, as the inflation rate increases, it becomes less predictable so
prices give less reliable signals on how to allocate resources. As a result, the costs of inflation
are particularly high when the inflation rate is also high and unpredictable. We measure the
volatility of inflation as the standard deviation of annual inflation rates. Note the axes are in log
base 10 scale.
End Caption
54
the inflation rate. There is a clear tendency for the volatility of inflation to increase as the
average annual inflation rate increases. Therefore, as the inflation rate increases it becomes less
predictable so prices give less reliable signals on how to allocate resources. As a result, the costs
of inflation are particularly high when the inflation rate is also high and unpredictable.
Benefits of Inflation
Thus far, we have emphasized the costs of inflation. However, some economists believe that
there are benefits to low inflation, so that the optimal inflation rate is not zero. For example,
firms are often very reluctant to cut nominal wages. In that case, the only way that the real wage
can fall for a firm or for an industry is for the inflation rate to increase. Therefore, a low
inflation rate may make labor markets more efficient. In addition, nominal interest rates cannot
fall below zero. Some people believe that this once the nominal interest rate falls to zero that
monetary policy can no longer influence the economy. We will discuss these arguments in more
detail in Chapter 10. For now, it is enough to know that the central bank determines the growth
rate of the money supply and that the growth rate of the money supply determines the inflation
rate. Therefore, even if the nominal interest rate is already zero, the central bank can cause the
real interest rate to decrease by increasing the growth rate of the money supply. This action will
increase the inflation rate and reduce the real interest rate.
6.5 Explain the Causes of Hyperinflation
Hyperinflation is rapid inflation in excess of hundreds or thousands of percentage points per year
for a significant period of time. At such high rates of inflation, the volatility of inflation is high,
55
so the misallocation of resources in the economy is severe. In fact, when the rate of inflation
rises to hyperinflationary rates, a country’s currency ceases to function as money.
A classic example of hyperinflation occurred in Germany after World War I. A burst of
money creation by the government ignited inflation, increasing the price level by a factor of
more than 10 billion between August 1922 and November 1923. For example, if a candy bar
cost the equivalent of 5 cents in August 1922, this increase in the price level would have raised
its cost to more than $500,000,000 by November 1923. In October 1923, the inflation rate in
Germany reached 41 percent per day. At that rate, prices doubled every 1.7 days in Germany.
By comparison, given the inflation rate in the United States from 1913 to 2009, prices in the
United States doubled every 21.2 years. There was more inflation during one month in Germany
during than there was over an entire 96-year period in the United States. The German experience
with hyperinflation was not unique. Between 1970 and 2003, the price level in Argentina
increased 100 trillion times, the price level in Brazil rose a quadrillion times, and the price level
in the Democratic Republic of Congo rose almost 10 quadrillion times.
During a hyperinflation, the inflation rate is so rapid that currency loses its value very
quickly. Households and businesses try to minimize currency holdings, and firms must pay
employees frequently. Employees must spend money quickly or convert it to more stable
foreign currencies before prices increase further. Merchants raise prices as quickly as possible.
Prices therefore quickly fail to indicate value or direct resource allocation. The government’s
tax-collecting ability diminishes significantly during hyperinflation. Because tax bills typically
are fixed in nominal terms, households and businesses have a major incentive to delay their
payments to reduce their real tax burden.
56
Causes of Hyperinflation
The German hyperinflation came to an end suddenly in late 1923, with a strong
government commitment to stop printing money. With a significant decline in the growth rate of
the money supply, hyperinflation ended. Hyperinflations begin when governments rapidly
increase the growth rate of the money supply, and hyperinflations end when governments reverse
course and reduce the growth rate of the money supply.
All hyperinflations begin and end with fiscal problems of the central government.
Governments purchase goods and services, G, and make transfer payments, TR, such as
unemployment benefits and welfare payments. The government must raise the funds for these
expenditures. The government can fund expenditures with taxes, T, issuing more bonds, ∆𝐵, or
by printing money, ∆𝑀. In any given time period:
𝐺 + 𝑇𝑅 = 𝑇 + ∆𝐵 + ∆𝑀.
The government’s budget deficit is just the difference between its expenditures, G + TR, and its
tax revenues, T. We can therefore rewrite equation (6.10) with the government’s budget deficit
on the left-hand side as:
(6.7) 𝐺 + 𝑇𝑅 − 𝑇 = ∆𝐵 + ∆𝑀.
A government with a large persistent budget deficit can finance it either by issuing bonds or
printing money. However, a government can issue so many bonds that investors do not want to
purchase more of its bonds. When this happens and the government is unable or unwilling to
raise taxes or cut expenditures, the government can finance the budget deficit only by printing
money. As a result, the growth rate of the money supply increases dramatically, and the inflation
57
rate can rise to hyperinflationary rates. While growth in the money supply causes inflation,
governments printing money to finance budget deficit causes hyperinflation.
The Ends of Four Big Inflations: Austria, Hungary, Poland, and Germany
At the end of World War I, many of the governments of central Europe were unable to
balance their budgets by raising taxes or cutting expenditures. Once inflation began to accelerate
the government budget deficits were made worse by the structure of the tax system. Taxes were
levied in nominal terms and there were lags between when the governments levied the tax and
when the government collected the tax revenue. In addition, the governments consistently
underestimated the inflation rate and individuals had a strong incentive to delay paying taxes so
real tax revenues lagged behind real government expenditures. As a result, several governments
resorted to printing money to finance large budget deficits. From January 1919 to December
1922, the Austrian government financed 40 percent or more of its expenditures by printing
money. From 1920 to 1924, the Hungarian government financed 21 percent or more of its
expenditures by printing money. At one point, the German government financed nearly 100
percent of its expenditures by printing money. Poland had a similar experience.3 Figure 6-10
Figure 6-10 The Ends of Four Big Inflations: Austria, Hungary, Poland, Germany
3
Thomas Sargent, “The Ends of Four Big Inflations,” in Inflation: Causes and Effects ed. Robert Hall, University of
Chicago press, 1982, pp.41-97.
58
Panel (a) Austria
59
Panel (b) Hungary
Panel (c) Poland
60
Panel (d) Germany
SOURCE: Sargent (1982).
Caption:
While the central government financed expenditures through money creation, the price level rose
rapidly in all four countries. By the end of the hyperinflations, the price level was 186 times
higher in Austria, 508 times higher in Hungary, 9,633 times higher in Poland, and over 50 billion
times higher in Germany. For example, if a candy bar cost 5 cents in August 1922, this increase
in the pirce level would have raised its cost to more than $500,000,000 by November 1923. A
similar hyperinflation today in the United States would take a pack of gum from a price of $1.50
to over $75 billion during just 15 months! Such rapid increases in the price level make currency
almost worthless.
In each of the four cases, the hyperinflations ended quickly once the countries established
strong central banks independent of the central government. The new central banks no longer
had to print whatever money the government needed to finance the budget deficit. For example,
on October 15, 1923, the German government established a new central bank called the
Retenbank to control a new currency, Rentenmark, which was worth 1 trillion of the old German
marks. The German government also severely limited the ability of the Rentenbank to issue
new currency to just 3.2 billion Rentenmarks, of which only 1.2 billion Rentenmarks could be
loaned to the government. The government also changed its fiscal policy significantly on
October 27, 1923. The government decided immediately to cut the number of its employees by
25 percent and reduce its employees by another 10 percent in January 1924. The German
government was also relieved from the reparation payments that it was forced to pay to France
61
and the United Kingdom as part of the treaty to end World War I. In just a few months after the
establishment of the Rentenbank, the German government stopped borrowing from the central
bank, the government balanced its budget, and the hyperinflation ended. Austria, Hungary, and
Poland had similar experiences — the hyperinflation ended after the government was able to
balance its budget and did not have to rely on the central bank to print money.
End Caption
shows the effect of the money creation on the price level of these four countries. While the
central government financed expenditures through money creation, the price level rose rapidly in
all four countries. By the end of the hyperinflations, the price level was 186 times higher in
Austria, 508 times higher in Hungary, 9,633 times higher in Poland, and over 50 billion times
higher in Germany. For example, if a candy bar cost 5 cents in August 1922, this increase in the
pirce level would have raised its cost to more than $500,000,000 by November 1923. A similar
hyperinflation today in the United States would take a pack of gum from a price of $1.50 to over
$75 billion during just 15 months! Such rapid increases in the price level make currency almost
worthless.
In each of the four cases, the hyperinflations ended quickly once the countries established
strong central banks independent of the central government. The new central banks no longer
had to print whatever money the government needed to finance the budget deficit. For example,
on October 15, 1923, the German government established a new central bank called the
Retenbank to control a new currency, Rentenmark, which was worth 1 trillion of the old German
marks. The German government also severely limited the ability of the Rentenbank to issue
new currency to just 3.2 billion Rentenmarks, of which only 1.2 billion Rentenmarks could be
62
loaned to the government. The government also changed its fiscal policy significantly on
October 27, 1923. The government decided immediately to cut the number of its employees by
25 percent and reduce its employees by another 10 percent in January 1924. The German
government was also relieved from the reparation payments that it was forced to pay to France
and the United Kingdom as part of the treaty to end World War I. In just a few months after the
establishment of the Rentenbank, the German government stopped borrowing from the central
bank, the government balanced its budget, and the hyperinflation ended. Austria, Hungary, and
Poland had similar experiences: the hyperinflation ended after the government was able to
balance its budget and did not have to rely on the central bank to print money.
Continued from page xx
Answering the Big Question
The quantity theory and the Fisher effect help us answer one of the Big Questions from Chapter
1:
Big question 3: Why do the nominal interest rate and the inflation rate rise with the growth rate
of the money supply in the long run?
An increase in the growth rate of the money supply increases the inflation rate, according to the
quantity equation. The increase in the inflation rate then leads to an increase in the nominal
interest rate via the Fisher effect.
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Conclusion
The average prices of goods and services rise over time in most countries because the money
supply grows over time. The quantity theory predicts that a one-percentage-point increase in the
growth rate of the money supply causes a one-percentage-point increase in the inflation rate.
The data support this view. When the inflation rate increases, this causes market participants to
expect higher inflation rates. As a result, the Fisher effect tells us that nominal interest rates rise.
The data is also consistent with the Fisher effect.
In Chapter 7, we cover…..Before moving to that chapter, read the Inside Look on the next
pages to learn about ABC.
Summary
6.1 Define money and discuss its four functions (pages x – x)
Money is the most liquid of all assets. Money acts as a store of value, unit of account, medium
of exchange, and a standard of deferred payment. Commodity money is an asset used as money
that also has value independent of its use of money. Gold is the most common form of
commodity money. Fiat money is money authorized by the central bank that is not backed by
commodities. Fiat money is valuable because the government makes it legal tender and because
individuals have confidence that the fiat currency will maintain its value. There are many
potential measures of the money supply. M1 consists of currency plus demand deposits. These
are the two most liquid assets because currency and demand deposits are widely accepted as
64
payment for goods and services. M2 consists of all the assets in M1 plus savings accounts, small
denomination time deposits, money market mutual funds, and other short-term deposits. The
additional assets in M2 are not quite as liquid as the assets in M1. However, with the advent of
automated teller machines and online banking it is easy to switch assets from the additional
assets in M2 into currency and demand deposits. The central bank helps determine the quantity
of money in circulation through open-market operations. However, because the volumes of
demand deposits and other assets are determined in financial markets, financial markets also play
a role in determining the quantity of money.
6.2 Explain the quantity theory of money and use it to explain inflation (pages x – x)
The quantity equation shows the relationship between the stock of money times velocity
and nominal GDP. The quantity theory assumes a constant or predictable velocity of money.
Based on the known velocity of money, changes in the money supply cause the price level to
change. The assumption of a constant or predictable velocity of money is a better assumption for
M2 than M1. If velocity is constant or predictable and the growth rate of real GDP is not
influenced by the money supply, then a one-percentage-point increase in the growth rate of the
money supply causes the inflation rate to increase by one percentage point.
6.3 Discuss the Relationship between Money Growth, Inflation, and Nominal Interest Rates
The ex ante real interest rate is the real interest calculated using expected inflation, and
the ex post real interest rate is the real interest rate calculated using the actual inflation rate. The
65
ex ante and ex post real interest rates are the same if the inflation rate equals the expected
inflation rate. The Fisher equation states that the nominal interest rate is the sum of the ex ante
real interest rate and the expected inflation rate. The Fisher effect states that if the expected
inflation rate increases by one-percentage point then the nominal interest rate also increases by
one-percentage point. The quantity theory and the Fisher effect together predict that a onepercentage-point increase in the growth rate of the money supply causes a one-percentage-point
increase in the expected inflation rate and the nominal interest rate.
6.4 Explain the Costs of Inflation
When inflation occurs, money becomes less valuable so individuals choose to hold less of
their wealth in the form of money. As a result, individuals incur the costs of transferring their
wealth from less liquid assets into money more frequently. These costs are called shoe leather
costs. Expected inflation also interacts with the tax system to increase the tax on capital income.
The existence of menu costs means that not all prices rise at the same rate so inflation causes
relative prices to change and this makes the economy less efficient. When inflation is greater
than or less than expected there is a transfer of wealth among borrowers and lenders. As a result,
both borrowers and lenders devote resources to predicting inflation that could be used to produce
goods and services. In the extreme case, unexpected inflation can lead to reduced borrowing and
lending and reduce investment activity. When inflation fluctuates significantly from year to
year, it is hard to predict so large changes in relative prices become possible. The large
fluctuations in relative prices means the economy does not allocate resources efficiently.
66
6.5 Explain the Causes of Hyperinflation
Hyperinflation occurs when the inflation rate reaches hundreds or thousands of
percentage points per year. The rate of inflation is so high that money loses all of its value
extremely quickly. Hyperinflation is the result of the failure of both fiscal and monetary policies
and almost always has a fiscal cause. If the central government runs large persistent budget
deficits that it is unable or unwilling to eliminate then it must rely on the central bank to finance
the budget deficits by increasing the money supply. Hyperinflation occurs when the central bank
allows the money growth rate to rise to very high rates to finance these fiscal deficits. The
experience of four European countries after World War I shows that once the budget deficits end
and the central bank becomes independent of the central government, the hyperinflation ends
very quickly.
Mathematical Appendix
Derivation of the Quantity Equation in Growth RatesThe first step is to take recognize the all
four variables - money, velocity, prices, and real GDP - can change over time so we can think of
them as a function of time:
𝑀𝑡 𝑉𝑡 = 𝑃𝑡 𝑌𝑡
where the “t” subscript indicates that the variable is a function of time. Next take the natural
logarithm to get:
𝑙𝑛 𝑀𝑡 + 𝑙𝑛𝑉𝑡 = 𝑙𝑛𝑃𝑡 + 𝑙𝑛𝑌𝑡 .
The derivative of the natural logarithm of the variable Xt with respect to time is
67
𝑑𝑙𝑛𝑋𝑡
𝑑𝑡
1 𝑑𝑋𝑡
=𝑋
𝑡
𝑑𝑡
=
𝑑𝑋𝑡⁄
𝑑𝑡
𝑋𝑡
= 𝑔𝑋 .
Taking the derivative with respect to time and applying the above rule to the equation in natural
logarithms produces
𝑔𝑀 + 𝑔𝑉 = 𝑔𝑃 + 𝑔𝑌 ,
which we can also express in terms of compound average growth rates:
𝑔𝑀̅ + 𝑔𝑉̅ = 𝑔𝑃̅ + 𝑔𝑌̅ .
68