AP Macroeconomics · Unit 3 · Topic 3.2

The Multipliers Study Lab

One person's spending is another person's income, so a change in spending ripples through the economy and changes real GDP by more than the first dollar spent. Watch the rounds of spending shrink and add up, then use the calculator to work AP-style spending, tax, and balanced-budget multiplier problems step by step.

1. The multiplier at work

Pick an MPC and an initial change in spending. Each round, the people who receive the new income spend the MPC share of it and save the rest. Press Play to watch the chain build.

A. The spending chain

Spending in each round round 1 = initial change

Running total total change in real GDP

New spending this roundRunning totalMaximum change in real GDP

Try a scenario

Marginal propensity to consume (MPC) MPS = 1 − MPC

Initial change in spending Change in C, I, G, or net exports ($ billions)

Animation speed How fast Play runs the rounds

MPS = 1 − MPC

Spending multiplier = 1 / MPS

Running total so far

Maximum change in real GDP

B. Multiplier calculator

Choose a preset AP problem or set your own numbers. The calculator shows every line of work an FRQ grader wants to see.

AP-style presets

What does the question give you?

What does the question ask for?

MPC

Change in spending ($ billions)

2. Key ideas

MPC + MPS = 1

Spend it or save it

Each extra dollar of disposable income is either spent or saved. If the MPC is 0.8, the MPS is 0.2. When a question gives you one, subtract from 1 to get the other.

The chain

The multiplier effect

A change in autonomous spending becomes someone's income. They spend the MPC share of it, which becomes income for someone else. Each round is smaller, and the rounds add up to a total change in real GDP larger than the first change.

1 / MPS

Spending multiplier

Spending multiplier = 1 / MPS = 1 / (1 − MPC). It applies to any change in C, I, G, or net exports. A bigger MPC means less leaks into saving each round, so the multiplier is bigger.

−MPC / MPS

Tax multiplier

A tax cut raises disposable income, but households save the MPS share before spending anything. First-round spending is only MPC × ΔT, so the tax multiplier is smaller in absolute value than the spending multiplier. It is negative: higher taxes lower real GDP. A change in transfer payments works the same way with a positive sign.

Equals 1

Balanced-budget multiplier

If government spending and taxes rise by the same amount, real GDP rises by that same amount. The spending effect (1/MPS) minus the tax effect (MPC/MPS) equals MPS/MPS = 1.

Upper limit

Why it is the maximum

The simple multiplier assumes only saving leaks out and the price level stays fixed. In practice, taxes, imports, a rising price level, and higher interest rates make the actual change smaller. That is why AP asks for the maximum change in real GDP.

3. Worked examples by MPC

Each row uses a $10 billion change. Notice that the tax multiplier is always the spending multiplier minus 1 (ignoring the sign), and the balanced-budget result is always $10 billion.

MPC	MPS	Spending multiplier (1/MPS)	Tax multiplier (−MPC/MPS)	G rises $10B	Taxes cut $10B	G and taxes both rise $10B
0.5	0.5	2	−1	+$20B	+$10B	+$10B
0.6	0.4	2.5	−1.5	+$25B	+$15B	+$10B
0.75	0.25	4	−3	+$40B	+$30B	+$10B
0.8	0.2	5	−4	+$50B	+$40B	+$10B
0.9	0.1	10	−9	+$100B	+$90B	+$10B

4. Showing your work on the FRQ

Tips that earn points

Write the formula, then plug in: "Spending multiplier = 1 / (1 − 0.8) = 5." Graders look for the multiplier value and the final answer.
Finish with units and direction: "Real GDP increases by a maximum of $50 billion (5 × $10 billion)."
For "minimum change in government spending needed to close a gap," divide: ΔG = gap ÷ spending multiplier. A $100 billion gap with MPC 0.8 needs $20 billion.
For a tax question, use −MPC/MPS and say whether taxes are cut or raised. A tax change needed to close a gap is always larger than the spending change.
Treat a change in transfer payments like a tax change with the opposite sign: multiplier MPC/MPS.
If a question gives the MPS, use it directly. If it gives a change in consumption and income, compute MPC = ΔC / ΔDisposable income first.

Common mistakes

Using the spending multiplier for a tax change. A $10 billion tax cut with MPC 0.8 raises real GDP by $40 billion, not $50 billion.
Dropping the sign. A tax increase lowers real GDP; a tax cut raises it.
Multiplying when you should divide. If the question gives the gap and asks for the policy, divide the gap by the multiplier.
Saying a balanced-budget increase has no effect. Real GDP rises by the amount of the spending increase.
Mixing up the spending multiplier with the money multiplier (1 / required reserve ratio), which belongs to banking in Unit 4.
Calling the result the exact change. Say "maximum," because leakages and price level changes shrink the real effect.

5. Practice questions

AP-style multiple choice. Pick an answer to see the explanation.

0 / 0 correct

6. Key terms

The vocabulary for topic 3.2. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 3 terminology guide.