Unit 5 · Topic 5.3

Money Growth and Inflation

The quantity theory says M x V = P x Y.

Practice 1: Principles and ModelsPractice 2: Interpretation

Part 1 · Hook

Why this matters

Germany in 1923 and Zimbabwe in 2008 both printed money to pay government bills, and prices rose so fast that shops changed price tags several times a day. Few economies go that far, but the same rule works at any speed: when the money supply grows much faster than the output it buys, the price level rises.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. Real GDP measures output at which prices?

Base-year prices, so it changes only when output changes
This year's prices
Prices adjusted for the money supply
The prices of imports

Show the answer

Real GDP values output at constant (base-year) prices; nominal GDP uses current prices.

Correct: Base-year prices, so it changes only when output changes:
This year's prices:
Prices adjusted for the money supply:
The prices of imports:

2. In the limited-reserves framework, the central bank buys bonds. What happens on the money market graph?

The money supply shifts right and the nominal interest rate falls
Money demand shifts right and the nominal rate rises
The money supply shifts left and the nominal rate rises
Nothing: the graph shows only money demand

Show the answer

Buying bonds adds reserves and money, so the vertical money supply curve shifts right.

Correct: The money supply shifts right and the nominal interest rate falls:
Money demand shifts right and the nominal rate rises:
The money supply shifts left and the nominal rate rises:
Nothing: the graph shows only money demand:

Part 4 · See it

See it first

An AD-AS graph: AD shifts right after money growth, then SRAS shifts left as wages adjust, ending at full-employment output with a higher price level. — More money raises AD in the short run; once wages adjust, only the price level is higher. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

The money supply grows faster than real outputnominal spending, M x V, grows faster than output
Nominal spending grows fasterAD shifts right
Output above full employment pushes nominal wages upSRAS shifts left until output returns to full employment
Real output ends where it startedthe price level is higher: faster money growth means higher inflation

Part 6 · Key ideas

Key ideas

The equation of exchange: $M \times V = P \times Y$ . M is the money supply, V velocity, P the price level and Y real output, so $P \times Y$ is nominal GDP.
Velocity is how often the average dollar is spent on final goods and services in a year: $V = \frac{P \times Y}{M}$ .
In the long run, V is steady and Y is set by resources and technology, so P moves with M. In growth rates: inflation $\approx$ money growth + velocity growth - real output growth.
Money neutrality: in the long run money changes nominal variables (the price level, nominal GDP, nominal wages and interest rates), not real GDP or unemployment. In the short run, sticky wages let money change output.

Part 7 · Misconception

A common mistake

The wrong idea: Printing more money makes a country richer in the long run.

What actually happens: Real output depends on resources and technology. Extra money with no extra output raises the price level, so each dollar buys less; real GDP ends where it started.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data

Money, velocity and real GDP in Kelvar (invented)

Kelvar, an invented country: money supply, velocity and real GDP
Year	Money supply (billions of dollars)	Velocity	Real GDP (billions of base-year dollars)
1	500	4	2,000
2	550	4	2,000

1. Use $M \times V = P \times Y$ . What is Kelvar's nominal GDP in Year 1, in billions of dollars?

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

Nominal GDP is $P \times Y$ $= M \times V$ $= 500 \times 4$ $= 2{,}000$ billion dollars.

Answer: 2000

2. What is Kelvar's price level in Year 2? Give it as a number, where 1.0 means the base-year price level.

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

$P$ $= \frac{M \times V}{Y}$ $= \frac{550 \times 4}{2{,}000}$ $= 1.1$ .

Answer: 1.1

3. In the table, the money supply grows 10 percent while velocity and real GDP stay the same. Which statement fits the quantity theory?

Real GDP rises 10 percent, and the price level is unchanged
The price level rises by the same 10 percent, and real output is unchanged
Velocity falls 10 percent, so nothing else changes
The price level falls 10 percent, since each dollar can now buy more output

Show the answer

If $V$ and $Y$ are fixed, $M \times V = P \times Y$ means $P$ moves in proportion to $M$ .

Real GDP rises 10 percent, and the price level is unchanged: The table shows real GDP unchanged; with V fixed, the extra money shows up in P.
Correct: The price level rises by the same 10 percent, and real output is unchanged: Right: with V and Y fixed, P must rise in proportion to M so that both sides of the equation stay equal.
Velocity falls 10 percent, so nothing else changes: The table holds velocity at 4 in both years.
The price level falls 10 percent, since each dollar can now buy more output: More money chasing the same output raises prices; each dollar buys less.

4. An economy starts at full employment. The central bank increases the money supply once, and over time nominal wages adjust. Shift both curves that move and mark the new long-run equilibrium.

Work on the graph (it needs JavaScript), then check.

Show the answer

More money lowers interest rates and raises spending, so AD shifts right. Output above full employment pushes nominal wages up, so SRAS shifts left. The economy ends at full-employment output with a higher price level.

Key: aggregate demand shifts right; short-run aggregate supply shifts left

5. A central bank permanently raises the money supply. Which of these changes in the long run?

Real GDP
The natural rate of unemployment
The real interest rate
The price level

Show the answer

The long-run neutrality of money: money changes nominal variables, not real ones.

Real GDP: Real GDP returns to full-employment output, which depends on resources and technology.
The natural rate of unemployment: The natural rate depends on frictional and structural unemployment, not on the amount of money.
The real interest rate: In the long run the real interest rate is set by saving and investment, not by the money supply.
Correct: The price level: Right: in the long run the extra money raises the price level and other nominal values.

6. Velocity rises because people start paying with cards and spend money faster. If the money supply and real GDP stay the same, what happens to the price level?

It rises, because M x V is now larger while Y is unchanged
It falls, because money is spent faster and so is worth more
It stays the same, because the money supply did not change
It rises by exactly the rise in the money supply

Show the answer

Both M and V feed nominal spending: with Y fixed, a rise in either raises the price level.

Correct: It rises, because M x V is now larger while Y is unchanged: Right: P = (M x V) / Y, so a larger V raises P.
It falls, because money is spent faster and so is worth more: Faster spending of the same money raises nominal spending, which raises prices.
It stays the same, because the money supply did not change: The price level depends on M x V, not on M alone.
It rises by exactly the rise in the money supply: The money supply did not change; the rise comes from velocity.

Part 9 · Summary

Summary

The quantity theory says M x V = P x Y. With velocity steady and real output fixed by resources and technology in the long run, the price level rises in proportion to the money supply, so sustained inflation comes from money growing faster than output. Money is neutral in the long run: it changes nominal variables, not real GDP or unemployment, although it can change output in the short run while wages are sticky.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections

Question set for this topic