Economists for Consideration: Introductions to Economic Thought and Ideas
12th Grade Honors/AP Macroeconomics
Lesson: Irving Fisher and the Equation of Exchange
Unit: Money & Prices
Enduring Understanding / Essential Question(s)
How do changes in the money supply impact the macro economy in the short-run and the long-run?
Monetarists show us that in the short-run, money can sway demand and output. The forces of money supply
and demand will impact interest rates, unemployment and output in the short-run. Yet in the long run,
changing the money supply only changes prices, not the growth rate of output.1 Students will come to
understand that, in the short-run, monetary policy (increasing or decreasing the money supply) is like pushing
or pulling on a rope2. Making that rope perfectly taut, i.e. price stability, is one of the main policy goals of the
Federal Reserve. As such, Fed bankers must act carefully and with caution when using their tools to
manipulate the money supply. Irving Fisher’s Equation of Exchange is a powerful tool for analyzing
macroeconomic conditions and events. His Equation of Exchange helps students understand how monetarist
thought influences central bankers’ decisions when it comes to the money supply and the overall health of our
economy.
Objective(s)
SWBAto:
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Define the terms Velocity of Money and Equation of Exchange
Define each variable of the Equation of Exchange
Use the Equation of Exchange to calculate velocity
Use the Equation of Exchange to calculate inflation
Use the Equation of Exchange to explain why money growth and inflation are linked
Explain the short-run and long-run effects of imbalances in the Equation of Exchange, both in terms of
an increase and a decrease in the money supply by the Federal Reserve
ISBE Economics Standards Addressed
15.A.4c Analyze the impact of inflation on an individual and the economy as a whole.
15.B.5b Analyze how inflation and interest rates affect consumer purchasing power.
15.E.5b Describe how fiscal, monetary and regulatory policies affect overall levels of employment, output and
consumption.
15.E.5c Describe key schools of thought (e.g., classical, Keynesian, monetarist, supply-side) and explain their
impact on government policies.
1
2
Buchholz, T. (2007) New Ideas from Dead Economists. p. 235.
Prof. Tim Schilling
Materials: whiteboard; computer with internet connection; projector; two photos – one each of Irving Fisher
and Milton Friedman; M1 velocity graph; handouts of text The Black Obelisk; four photo images of Weimar
Germany; overhead projector; lecture notes study sheet handouts; homework assessment handouts
Time Allotted: 75 min. (block schedule)
Key Vocabulary: Equation of Exchange, Federal Reserve, GDP deflator, Hyperinflation, Inflation, Monetarism,
Money Supply, Price Stability, Velocity of Money, Real GDP
Procedures
Anticipatory Set (5 min.)
1) Teacher projects two quotes and two photos (one of Fisher and one of Friedman):
a. “When we say ‘the prices of goods are determined by supply and demand’ we almost always
ignore money. We only think of the supply and demand of goods. But that is only half of the
story.” – Irving Fisher, 1913.
b. “Money does matter.” – Milton Friedman, 1956
2) Think/Pair/Share – students discuss these two quotes with a partner. Teacher asks students: “What
are Fisher and Friedman saying? Paraphrase and give examples.”
3) Teacher takes attendance and subsequently debriefs students.
Mini –lecture part one: Introduction to Velocity/Historical Background/Why is Fisher important? (10 min.)
4) Teacher asks students: “How many times per year do you think the typical dollar bill is used to pay for a
newly produced good or service?” Let them mull it over and survey for answers. Follow up with
projection of current M1 velocity figure from FRED database:
http://research.stlouisfed.org/fred2/series/M1V?rid=193 Explain to students that Velocity is the
number of times money changes hands or turns over. M1 Velocity in the 2nd Qtr. of 2010 was
approximately 8.5.
5) Teacher asks students: “Does velocity matter?” “What can this figure help show us?” Wait for
responses. “What’s happening here? (point out: peaks and troughs, recession shades – what goes up
must come down, but V growing in the long-run) Indeed, the amount of money and the speed by
which it flows through our economy does matter.”
6) Lecture and questions: “About 100 years ago, Irving Fisher, a monetarist and Yale economist, showed
us how and why money matters! During the early part of 20th Century (especially after World War I),
monetarism helped some nations understand that they needed to get off of the gold standard. Policymakers realized that a flexible monetary system (fiat) would allow us to better match money supply
growth to real growth in order to maintain relative price stability. Why was price stability of great
concern to central bankers during this time? What happens if the money supply grows too fast?”
Read-aloud & Discussion: The Black Obelisk (1956) by Erich Maria Remarque3 (25 min.)
7) Teacher surveys students for prior knowledge: “What happened to the price level in post-WWI Weimar
Germany?”
3
Reproduced from: Watts, T. (2003) The Literary Book of Economics. pp. 267-270.
8) Teacher scaffolds the text by showing photos from Weimar Germany: children playing with money; a
man pushing a wheelbarrow full of money; a man sweeping Deutschmarks off the street; chart
demonstrating hyperinflation in nominal terms
a. “Note: from 1921-1924, the German money supply rose by more than 25 million percent.
Correspondingly, the price index went from 1 to 200 million in 18 months during this period4.”
9) Teacher scaffolds the text by giving students background information and setting the scene:
a. Scene takes place in Weimar Germany during the hyperinflationary period.
b. Our narrator works in a shop of some sort, where people can bring things to be sold on
consignment (like a pawn shop) and prices are negotiable.
c. The narrator and his boss, Georg, fought together in WWI just a few years prior.
10) Teacher and students take turns reading aloud. Teacher makes sure to check for understanding of
potentially unfamiliar vocabulary during the read-aloud.
11) Teacher asks discussion questions:
a. What’s the first clue that our scene takes place during a period of hyperinflation?
b. Why does our narrator think the situation will end in a “wholesale crash”? Think about what’s
happening, physically speaking. Why is the situation unsustainable?
c. Imagine we now live in similar circumstances. What would be happening to the value of the
money in our pockets and bank accounts right now as we speak?
d. What are our characters saying about Lisa? What do they mean by the statement, “you can’t
get rich on tombstones”?
e. Why does our narrator refer to money as “wallpaper”?
f. At the end, why does our narrator ask the question “the best thing would be to sell nothing at
all, wouldn’t it?” What would be an alternative method of exchange if they stopped making
transactions with Deutschmarks?
Mini-lecture part two: Why is Fisher important? (5 min.)
12) Lecture: “Despite monetarists’ theories, fiscal policy ruled the day from the 1930s onward. It took
many years for Fisher’s ideas to take hold in the minds of policy makers and those central bankers who
controlled the money supply. Fisher’s disciple, Milton Friedman, battled Keynesians for decades
throughout the 20th century and was able to demonstrate that yes, money does indeed matter. His
monetarist theories reached the Fed by the late 1970s and early 1980s. In the early 1980s, Fed
chairman Paul Volcker drastically reduced the money supply to break the back of persistent high
inflation. A deep recession ensued and unemployment and interest rates sky-rocketed during the early
Reagan years. While many economists believe that Volcker ‘slammed the monetary brakes’ too hard,
his anti-inflationary course worked and proved the power of money5. Monetarism was finally
vindicated. As a result, Irving Fisher’s legacy continues to influence monetary policy decision-making in
central banks around the world.”
4
5
Buchholz, T. (2007) New Ideas from Dead Economists. p. 234.
Ibid. p. 247.
Understanding the Equation of Exchange: Lecture & Application Exercises (30 min.)
NOTE: Subsequent information will be delivered via lecture. Teacher has option of using whiteboard,
overhead, or projector to write down or project key points from the information set forth below and work
application exercises. Teacher will hand out the attached Lecture Notes Study Sheet (double-sided), which acts
as a note-taking aid for students. Students will be expected to take notes on the sheet during class and use it
to complete their homework assignment. The homework assignment (also attached) contains acceptable
answers to the questions posed.
13) Irving Fisher’s Equation of Exchange: MV=PQ (“things x prices”)6
a. shows us that the amount and speed of money spent equals the prices we pay for everything
we purchase.
b. No one disputes this equation. By definition, the amount of money multiplied by the number
of times it changes hands equals the nominal value of goods and services purchased.7
14) Teacher breaks down the equation. NOTE: Students must understand each variable before they can
understand the equation of exchange, so the teacher must repeatedly check for understanding.
a. M = Money
i. Any measure of a money supply
b. V = Velocity
i. Rate of spending/turnover of money
ii. Related to our desire to hold or use money
iii. The inverse of our willingness to hold balances8
c. P = Price level
i. GDP deflator or measure of inflation
d. Q = quantity of output
i. Real GDP or all transactions
e. Right-hand side: MV = nominal money or the amount of money multiplied by the number of
times per year that the money is spent9
f. Left-hand side: PQ = “stuff” or nominal GDP10
15) Equation applications:
a. Velocity
i. P x Q/M = V or Nominal GDP/Money Supply = Velocity
ii. Teacher completes this application with students: At the end of 2009, the money supply
(M1) was $1,700 billion, the GDP deflator was 109.7, and real GDP was $12,881 billion.
What was the value for Velocity in 2009?
1. P x Q / M = V
2. Remember, we need to divide the GDP deflator by 100! (because its base is
always 100)
3. 1.097 x 12,881 / 1,700 = 8.3
6
Prof. Tim Schilling
Buchholz, T. (2007) New Ideas from Dead Economists. p. 234.
8
Prof. Tim Schilling
9
Anderson, D. (2007). Economics by Example. p. 162.
10
Prof. Tim Schilling
7
4. In 2009, V = 8.3
5. What does this result tell us? In 2009, the average dollar (in M1) was spent
about 8 times on goods and services.
b. Money supply, Real GDP, Velocity & Inflation11
i. ∆M + ∆V = ∆P + ∆Q or Growth rate of the money supply + Growth rate of velocity =
Growth rate of price level (or inflation rate) + Growth rate of quantity of output
ii. to help us understand the factors that determine inflation, we can re-write the equation
as:
iii. π = ∆M + ∆V - ∆Q or inflation rate = Growth rate of the money supply + Growth rate of
velocity - Growth rate of quantity of output
iv. Fisher believed that velocity was constant, so he assumed that ∆V was 0. This
assumption leads to re-writing the equation one last time as:
v. π = ∆M - ∆Q or the inflation rate = Growth rate of the money supply - Growth rate of
quantity of output
c. If we apply π = ∆M - ∆Q we can understand three key predictions12:
i. If the money supply grows faster than real GDP, inflation will occur
ii. If the money supply grows at a slower rate than real GDP, there will be deflation
iii. If the money supply grows at the same rate as real GDP, the price level will be stable
d. Yet, V is not stable
i. Fisher was incorrect in his assertion, known as the quantity theory of money
ii. But, Fisher’s theory does help us understand the long-run relationship between the
money supply and inflation: In the long-run, inflation results from the money supply
growing faster than real GDP.13
iii. Teacher completes this application with students: If the money supply (M2) is growing at
a rate of 6% per year, real GDP is growing at a rate of 3% per year, and velocity is
constant, what will the inflation rate be? If velocity is increasing 1% per year instead of
remaining constant, what will the inflation rate be14?
1. π = ∆M - ∆Q
2. π = 6% - 3%
3. π = 3%
4. inflation will be 3%
5. π = ∆M + ∆V - ∆Q
6. π = 6% + 1% - 3%
7. π = 4%
8. inflation will be 4%
11
Hubbard & O’Brien (2009). Macroeconomics. pp. 453-454.
Hubbard & O’Brien (2009). Macroeconomics. p. 454.
13
Ibid.
14
Hubbard & O’Brien (2009). Macroeconomics. p. 464.
12
e. MV MUST ALWAYS EQUAL PQ if the price level is to remain stable!
i. With any increase in the money supply, the equation must be balanced by an increase in
the price level. Thus, in the long-run, the Fed can only affect the inflation rate and not
the growth rate of output (Q)15.
f. What happens when short-run imbalances in the equation of exchange occur?
i. Variations in the money supply do affect demand and output (Q) in the short-run.
ii. Sharp variations in MV can negatively impact the price level (P), interest rates and
unemployment.
iii. This is why Fed uses its tools to increase/decrease the money supply in order to
maintain a stable price level.
16) Historical Context:
a. “Friedman & Schwartz’s A Monetary History of the United States put U.S. economic history in
perspective using Fisher’s famous equation MV=PQ. What did they find? Monetary misuse
accompanied every severe recession and every significant inflationary period from 1867 to
1960.16 Thus, the Fed must be very careful when it manipulates the money supply, as one of its
primary goals is to maintain price stability.”
NOTE: End of lesson. Teacher hands out a copy of the homework assessment worksheet (double-sided) to each
student. Teacher informs each student that the assignment will be checked and reviewed at the beginning of
the next class session. Please see below for handouts.
15
16
Anderson, D. (2007). Economics by Example. p. 162.
Buchholz, T. (2007) New Ideas from Dead Economists. p. 242.
Understanding the Equation of Exchange: Lecture Notes Study Sheet
Define the Equation of Exchange:
Break down the Equation of Exchange and define each variable:
M=
V=
P=
Q=
Right-hand side MV =
Left-hand side PQ =
How do we measure velocity? What does V tell us?
Money supply, Real GDP, Velocity & Inflation: What are the 2 equations? What did Fisher assume?
If we apply π = ∆M - ∆Q what are the three key predictions we can make?
1)
2)
3)
Is V stable? What must happen if V is to be stable?
What is the long-run relationship between the money supply and inflation?
What happens when short-run imbalances in the equation of exchange occur and how does the Fed
respond?
Understanding the Equation of Exchange - Homework Assessment
MV = PQ
Please answer the questions below. You will receive extra credit for correct answers to bonus questions!
In 2006, real GDP was 2.9% and the money supply (M2) grew at 5.3%. If velocity was constant, what should
the inflation rate have been? Suppose we discover that the inflation rate during 2006 was 3.2%. What does
this new information tell us about velocity in 2006?
π = ∆M - ∆Q
π = 5.3% - 2.9%
π = 2.4%
--------------------π = ∆M + ∆V - ∆Q
3.2% = 5.3% + ∆V – 2.9%
3.2% - 5.3% + 2.9% = ∆V
0.8% = ∆V
Let us assume that at the end of 2010, the money supply (M1) will be $1,900 billion, the GDP deflator will be
108.3, and real GDP will be $12,005 billion. What will the value for Velocity be in 2010?
*Bonus question: If in 2009 velocity was 8.3, and the following year the Fed increased the money supply by
$200 billion, what does our Velocity measure for 2010 tell us, generally, about the macro economy in 2010?
PxQ/M=V
1.083 x 12,005 / 1900 = 6.8
V will be 6.8 in 2010.
--------------*Velocity decreased from 8.3 in 2009 to 6.8 in 2010. Despite the fact the Fed increased the money
supply in 2010, our velocity measure for 2010 tells us that fewer transactions were taking place
compared to 2009. People were holding more money. Furthermore, MV = PQ tells us that economic
conditions were worse in 2010 as compared to 2009 because there was deflation and a drop in real
GDP from 2009 to 2010.
Use the quantity equation to explain why money growth and inflation are linked. According to the quantity
theory of money, what is the effect of an increase in the quantity of money relative to real GDP? A
decrease?
If the money supply grows faster than real GDP, inflation will occur. If the money supply grows at a slower rate
than real GDP, there will be deflation.
If V falls by 2%, what would the Fed have to do to M to maintain Q x P at previous level?
*Bonus question: What might the Fed do, specifically, to accomplish this?
∆M + ∆V = ∆P + ∆Q
M would have to rise by 2%.
-------------------*The Fed could use open market operations to buy treasury securities, lower the reserve requirement, or lower
the discount rate, or a combination of these tools.
*Bonus question: What might cause V to drop?
*People holding money, i.e. money demand increases; a deflationary period
Think about the past 20 years. How might technology have affected velocity? Hint: think ATMs, credit
cards, online payment software, etc.
Velocity has increased because advances in technology make transactions quicker and easier, thus allowing us
to make more of them.