AP® Macroeconomics review sheet from Aim for Five (aimforfive.com/macro/units/5/5-3)
Unit 5 · Topic 5.3
5.3 Money Growth and Inflation
The quantity theory of money says that, over long periods, how fast the money supply grows decides how fast prices rise. It's built on the equation of exchange, M × V = P × Y. Lasting inflation happens when the money supply grows faster than real output for a long time.
Key terms
- quantity theory of money
- equation of exchange (MV = PY)
- velocity of money
- nominal GDP
- money neutrality
The equation of exchange
The equation of exchange is M × V = P × Y. P × Y is nominal GDP, so the equation says total spending (the money supply times how often each dollar is spent) equals the dollar value of everything produced. You can rearrange it: V = (P × Y) ÷ M, and P = (M × V) ÷ Y.
- M: the money supply.
- V: the velocity of money, the average number of times each dollar is spent on final goods and services in a year.
- P: the price level.
- Y: real output (real GDP).
From an identity to a theory
The equation is always true, because velocity is defined to make it true. It becomes the quantity theory of money when you add two assumptions. First, velocity is stable, because it depends on payment habits that change slowly. Second, in the long run, real output is set by the economy's resources and technology at full employment (the LRAS level), not by the money supply.
With V and Y fixed, any increase in M has to show up as an equal percentage increase in P. Double the money supply and you double the price level.
In growth rates, approximately: % change in M + % change in V = % change in P + % change in Y. With stable velocity, inflation ≈ money growth − real GDP growth.
Money is neutral in the long run
In the short run, more money can lower interest rates, raise AD and increase real GDP (4.6). But if the economy starts at full employment, the extra output doesn't last. Wages and other input prices catch up, SRAS shifts left, and real GDP returns to full employment at a higher price level.
This is money neutrality: in the long run, a change in the money supply changes prices but not real output. That's why economists call inflation a monetary phenomenon. Inflation that lasts for years traces back to the money supply growing faster than the economy's output. In the same way, a shrinking money supply can cause deflation, a falling price level.
Seeing it on other graphs
On an AD–AS graph, fast money growth keeps shifting AD right. In the long run the economy stays on the vertical LRAS, so each shift raises only the price level.
On a Phillips curve graph, the economy ends up on the vertical LRPC at a higher inflation rate. Unemployment is back at its natural rate (5.2).
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Finding velocity
Nominal GDP is $10 trillion and the money supply is $2 trillion. What's the velocity of money?
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- Step 1: Velocity = nominal GDP ÷ money supply, since P × Y is nominal GDP.
- Step 2: V = $10 trillion ÷ $2 trillion = 5.
- Step 3: On average, each dollar is spent 5 times a year on final goods and services.
Answer: Velocity is 5.
- Example 2
Solving for the price level
The money supply is $500, velocity is 4 and real output is 1,000 units. (a) What's the price level? (b) If the money supply doubles while velocity and real output don't change, what happens to the price level?
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- Step 1: (a) P = (M × V) ÷ Y = (500 × 4) ÷ 1,000 = 2,000 ÷ 1,000 = 2.
- Step 2: (b) New M = $1,000. P = (1,000 × 4) ÷ 1,000 = 4.
- Step 3: The price level doubled, just like the money supply, because V and Y stayed fixed.
Answer: (a) 2. (b) It doubles, from 2 to 4.
- Example 3
Inflation from growth rates (classic trap)
The money supply grows 7% a year, velocity is constant and real GDP grows 3% a year. According to the quantity theory, about what's the inflation rate?
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- Step 1: Use the growth-rate version: % change in M + % change in V ≈ % change in P + % change in Y.
- Step 2: 7% + 0% ≈ inflation + 3%.
- Step 3: Inflation ≈ 7% − 3% = 4%.
- Step 4: The trap is answering 7%. Part of the new money is used to buy the extra real output, so prices rise by less than the money supply.
Answer: About 4%.
Common mistakes
- Using real GDP when the equation needs nominal GDP. P × Y is nominal GDP, so velocity = nominal GDP ÷ money supply.
- Saying more money raises real output in the long run. In the long run, money growth changes the price level, not real GDP.
- Setting inflation equal to money growth when real GDP is also growing. With stable velocity, inflation ≈ money growth − real output growth.
On the exam
- Multiple-choice questions often give three of M, V, P and Y (or nominal GDP) and ask for the fourth, or ask what the quantity theory predicts when the money supply grows.
- If a free-response question asks about the long-run effect of money growth, say that real output stays at full employment and the price level (or inflation rate) rises.
Connected topics
Videos
Check yourself
4 questions on 5.3 Money Growth and Inflation. Pick an answer to see if you got it, and why.
| Variable | Value |
|---|---|
| Money supply (M) | $2 trillion |
| Velocity of money (V) | 5 |
| Real GDP (Y) | $8 trillion in base-year dollars |
Hypothetical data
What is Country V's nominal GDP?
What is Country V's price level (P)?
Suppose the central bank raises the money supply to $2.4 trillion. If velocity and real GDP stay the same, what is the new price level?
The quantity theory of money predicts that a larger money supply mainly raises the price level in the long run. Which assumptions does this prediction depend on?
0 of 4 answered