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:

• 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 Buchholz, T. (2007) New Ideas from Dead Economists, p. 235.

2 Prof. Tim Schilling

Materials: whiteboard; computer with internet connection; projector; two photos - one each of Irving Fisher

and Milton Friedman; Ml 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 Ml velocity figure from FRED database:

http://research.stlouisfed.org/fred2/series/MlV?rid=193 Explain to students that Velocity is the

number of times money changes hands or turns over. Ml 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 Vgrowing 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. Policy-

makers 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?"

1 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 Buchholz, T. (2007) New Ideas from Dead Economists, p. 234.

5 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

(Ml) 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. 1.097x12,881/1,700 = 8.3

6 Prof. Tim Schilling7 Buchholz, T. (2007) New Ideas from Dead Economists, p. 234.8 Prof. Tim Schilling9 Anderson, D. (2007). Economics by Example, p. 162.10 Prof. Tim Schilling

4. In 2009, V = 8.3

5. What does this result tell us? In 2009, the average dollar (in Ml) was spent

about 8 times on goods and services.

b. Money supply, Real GDP, Velocity & Inflation11

i. AM + AV = AP + AQ 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. 7i = AM + AV - AQ 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 AV was 0. This

assumption leads to re-writing the equation one last time as:

v. n = AM - AQ or the inflation rate = Growth rate of the money supply - Growth rate of

quantity of output

c. If we apply n = AM - AQ 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

Fisher was incorrect in his assertion, known as the quantity theory of money

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

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. Ti = A M - A Q

2. n = 6%-3%

4. inflation will be 3%

5. n= AM + AV-AQ

6. n = 6% + 1% - 3%

7 TT A O// L — *r /O

8. inflation will be 4%

11 Hubbard & O'Brien (2009). Macroeconomics, pp. 453-454.12 Hubbard & O'Brien (2009). Macroeconomics, p. 454.

13 Ibid.Hubbard & O'Brien (2009). Macroeconomics, p. 464.

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

I960.16 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 Anderson, D. (2007). Economics by Example, p. 162.16 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 n = AM - AQ 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 -/W V -*\

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?

n = AM-AQ

n = 5.3%-2.9%

n = 2.4%

n= AM + AV-AQ

3.2% = 5.3% + AV-2.9%

3.2%-5.3% +2.9% = AV

0.8% = AV

Let us assume that at the end of 2010, the money supply (Ml) 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?

// 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?

AM + AV = AP + AQ

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.

Wtocity CM1VJSource: federal Smmvei itenfe uf St. Louis

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