Grade 11

Advanced

7 min

Lesson 10 of 12

The Quantity Theory of Money and Inflation

Not Started

Exploring the mathematical relationship between money supply, velocity, and price levels.

If everyone in the world suddenly had an extra million dollars in their bank account tomorrow, would we all be millionaires, or would a loaf of bread just cost $50,000?

Learning Objectives

1.Apply the Equation of Exchange ( $MV = PQ$ ) to predict changes in the price level.
2.Explain why rapid increases in the money supply lead to hyperinflation.
3.Distinguish between nominal and real interest rates using the Fisher Equation.

The Equation of Exchange

At the heart of monetary theory lies the Equation of Exchange:

MV = PQ

. This identity states that the total amount of money spent in an economy must equal the total value of goods and services sold. Here,

M

represents the Money Supply, and

V

is the Velocity of Money (the rate at which a single dollar is spent per year). On the other side,

P

is the Price Level, and

Q

is the Real GDP (quantity of goods). Think of

V

as the 'speed' of money; if people hold onto cash,

V

drops. If they spend it rapidly,

V

rises. Because

PQ

represents the total dollar value of output, it is also known as Nominal GDP.

Let's find the price level of a small island economy. 1. Given: Money Supply ( $M$ ) = $500, Velocity ($ V $) = 4, and Real Output ($ Q $) = 1,000 units. 2. Set up the equation:$ 500 \times 4 = P \times 1,000 $. 3. Solve for$ P $:$ 2,000 = 1,000P $. 4. Result:$ P = 2 $. The average price of a unit is$ 2.

Quick Check

If the Money Supply ( $M$ ) doubles while Velocity ( $V$ ) and Real Output ( $Q$ ) remain constant, what happens to the Price Level ( $P$ )?

Look at the balance of the equation

MV = PQ

Answer

The Price Level ( $P$ ) will also double.

The Quantity Theory and Inflation

The Quantity Theory of Money assumes that in the long run, $V$ is relatively stable and $Q$ is determined by labor and technology, not money. Therefore, any change in $M$ must result in a proportional change in $P$ . This is the foundation of the famous quote by Milton Friedman: 'Inflation is always and everywhere a monetary phenomenon.' When a government prints money much faster than the economy grows ( $M$ increases faster than $Q$ ), the result is inflation. If this gap becomes extreme, it leads to hyperinflation, where prices spiral out of control because the currency loses its value almost instantly.

Economists often use percentages to predict inflation: 1. Formula: $\%\Delta M + \%\Delta V = \%\Delta P + \%\Delta Q$ . 2. Scenario: The central bank increases the money supply by 10% ( $\%\Delta M = 10$ ). Real GDP grows by 3% ( $\%\Delta Q = 3$ ). Velocity is constant ( $\%\Delta V = 0$ ). 3. Calculation: $10 + 0 = \%\Delta P + 3$ . 4. Result: $\%\Delta P = 7$ . The inflation rate is 7%.

Quick Check

Why does hyperinflation usually occur during times of government crisis?

Think about how a government pays for things when it has no revenue.

Answer

Governments often print massive amounts of money to pay off debts when they cannot raise enough through taxes, causing $M$ to skyrocket.

The Fisher Equation

Inflation doesn't just change prices; it changes the value of loans. The Fisher Equation helps us understand the relationship between interest rates and inflation:

i = r + \pi

. Here,

i

is the Nominal Interest Rate (the rate the bank tells you),

r

is the Real Interest Rate (the actual purchasing power gained), and

\pi

is the Inflation Rate. If you earn 5% interest but inflation is 5%, your real return is 0%. Lenders must predict future inflation to set nominal rates that ensure they actually make a profit in real terms.

Imagine you take a loan at a fixed interest rate, but inflation suddenly spikes. 1. Loan Agreement: Nominal rate ( $i$ ) = 8%. Expected inflation ( $\pi$ ) = 3%. 2. Expected Real Rate: $r = i - \pi = 8 - 3 = 5\%$ . 3. Scenario: Unexpected hyperinflation occurs, and $\pi$ jumps to 20%. 4. Actual Real Rate: $r = 8 - 20 = -12\%$ . 5. Outcome: The borrower wins because they are paying back the loan with 'cheaper' money, while the lender loses 12% of their purchasing power.

Key Takeaways

1The Equation of Exchange ( $MV = PQ$ ) shows that total spending equals total nominal output.
2According to the Quantity Theory, rapid growth in the money supply is the primary cause of inflation.
3The Fisher Equation ( $i = r + \pi$ ) demonstrates that nominal interest rates must account for inflation to protect real returns.
4Hyperinflation occurs when the growth of $M$ far outpaces the growth of $Q$ .

Quick Check

Multiple Choice

In the equation $MV = PQ$ , what does $PQ$ represent?

Multiple Choice

If the nominal interest rate is 4% and the inflation rate is 6%, what is the real interest rate?

True/False

The Quantity Theory of Money assumes that Velocity ( $V$ ) is highly unstable in the long run.

What's Next?

Review Tomorrow

In 24 hours, try to write down the Equation of Exchange and the Fisher Equation from memory and define each variable.

Practice Activity

Look up the current 'Federal Funds Rate' (Nominal Rate) and the current 'CPI Inflation Rate.' Use the Fisher Equation to calculate the current Real Interest Rate in the economy.

Browse

Browse

The Quantity Theory of Money and Inflation

Learning Objectives

The Equation of Exchange

The Quantity Theory and Inflation

The Fisher Equation

Key Takeaways

Quick Check

What's Next?

The Quantity Theory of Money and Inflation

Learning Objectives

The Equation of Exchange

The Quantity Theory and Inflation

The Fisher Equation

Key Takeaways

Quick Check

What's Next?