Unit 3 · Topic 3.2

3.2 Multipliers

When spending in the economy changes, the effect on real GDP is bigger than the first change, because one person's spending becomes another person's income, and part of that gets spent again. The spending multiplier and the tax multiplier measure how much bigger. Both depend on the marginal propensity to consume.

Key terms

marginal propensity to consume (MPC)
marginal propensity to save (MPS)
spending (expenditure) multiplier
tax multiplier
disposable income

MPC and MPS

Disposable income is income after taxes, the money households can spend or save. The marginal propensity to consume (MPC) is the share of each extra dollar of disposable income that people spend: MPC = change in consumption ÷ change in disposable income.

The marginal propensity to save (MPS) is the share they save: MPS = change in saving ÷ change in disposable income. Every extra dollar is either spent or saved, so MPC + MPS = 1. If MPC is 0.8, MPS is 0.2.

Why spending multiplies

Say a company spends an extra $100 million building a factory, and MPC = 0.8. The construction workers and suppliers receive $100 million in income. They spend 80% of it, $80 million, at stores and restaurants. Those businesses' owners and workers then spend 80% of that, $64 million, and so on. Each round is smaller, and the rounds add up to $100 + $80 + $64 + … = $500 million.

The shortcut is the spending (expenditure) multiplier: spending multiplier = 1 ÷ MPS = 1 ÷ (1 − MPC). With MPC = 0.8, it's 1 ÷ 0.2 = 5. Change in real GDP = initial change in spending × spending multiplier. It applies to a change in any component of AD: C, I, G or Xn.

MPC	MPS	Spending multiplier	Tax multiplier
0.5	0.5	2	−1
0.75	0.25	4	−3
0.8	0.2	5	−4
0.9	0.1	10	−9

The tax multiplier

A tax change works differently. If the government cuts taxes by $100 million, households don't spend all of it. With MPC = 0.8, they spend $80 million and save $20 million. So the first round of new spending is only $80 million, and the effect is one round smaller.

Tax multiplier = −MPC ÷ MPS. With MPC = 0.8, it's −0.8 ÷ 0.2 = −4. The negative sign means a tax increase lowers real GDP and a tax cut raises it. Change in real GDP = change in taxes × tax multiplier.

Transfer payments (like unemployment benefits) work the same way as a tax cut: an increase in transfers raises real GDP by the change × MPC ÷ MPS. And because the tax multiplier is always one smaller in size than the spending multiplier, a change in government spending moves real GDP more than an equal change in taxes.

What the number means

The multiplier tells you how far AD shifts horizontally. In the simple model, that's the maximum change in real GDP, which is how exam questions often word it. On a real AD–AS graph, part of the shift can show up as a higher price level instead of more output, and the simple multiplier also ignores leaks such as imports and taxes on each round.

If the government raises spending and taxes by the same amount, the two effects don't cancel: with MPC = 0.8, $10 billion more spending adds $50 billion and $10 billion more taxes subtracts $40 billion, for a net rise of $10 billion. This is called the balanced-budget multiplier, and in this model it equals 1.

Worked examples

Try each one yourself first, then open the solution.

Example 1Calculator allowed
From MPC to the change in real GDP
When disposable income rises from $1,000 billion to $1,500 billion, consumption rises from $900 billion to $1,300 billion. (a) Find the MPC and the MPS. (b) Businesses then increase investment spending by $20 billion. What is the maximum change in real GDP?
Show the solutionHide the solution
1. Step 1: (a) MPC = change in consumption ÷ change in disposable income = (1,300 − 900) ÷ (1,500 − 1,000) = 400 ÷ 500 = 0.8. MPS = 1 − 0.8 = 0.2.
2. Step 2: Notice that you use the changes, not the levels. 900 ÷ 1,000 = 0.9 is the share of total income spent, which isn't the MPC.
3. Step 3: (b) Spending multiplier = 1 ÷ 0.2 = 5.
4. Step 4: Change in real GDP = $20 billion × 5 = $100 billion.
Answer: (a) MPC = 0.8, MPS = 0.2. (b) Real GDP rises by up to $100 billion.
Example 2Calculator allowed
Closing a recessionary gap
An economy has a recessionary gap of $200 billion. The MPC is 0.8. (a) By how much would government spending need to rise to close the gap? (b) If the government used a tax cut instead, how big would the cut need to be?
Show the solutionHide the solution
1. Step 1: (a) Spending multiplier = 1 ÷ (1 − 0.8) = 5. Required increase in G = gap ÷ multiplier = $200 billion ÷ 5 = $40 billion.
2. Step 2: (b) Tax multiplier = −0.8 ÷ 0.2 = −4. Required change in taxes = −$200 billion ÷ 4 = −$50 billion, a tax cut of $50 billion.
3. Step 3: The tax cut must be bigger because households save part of it (here, 20%) before any spending happens.
Answer: (a) Increase G by $40 billion. (b) Cut taxes by $50 billion.
Example 3Calculator allowed
Spending vs. taxes (classic trap)
MPC = 0.75. The government increases spending by $20 billion. Separately, it cuts taxes by $20 billion. Compare the maximum effect of each on real GDP.
Show the solutionHide the solution
1. Step 1: MPS = 1 − 0.75 = 0.25. Spending multiplier = 1 ÷ 0.25 = 4. Tax multiplier = −0.75 ÷ 0.25 = −3.
2. Step 2: Spending increase: $20 billion × 4 = $80 billion increase in real GDP.
3. Step 3: Tax cut: −$20 billion × (−3) = $60 billion increase in real GDP.
4. Step 4: The trap is using 4 for both. The first $20 billion of government spending is all new spending; only $15 billion of the $20 billion tax cut gets spent in the first round.
Answer: The spending increase raises real GDP by up to $80 billion; the tax cut by up to $60 billion.

Common mistakes

Using 1 ÷ MPC as the multiplier. The spending multiplier is 1 ÷ MPS.
Using the spending multiplier for a tax change. Taxes and transfers use MPC ÷ MPS (with a minus sign for taxes).
Finding MPC from levels (consumption ÷ income) instead of changes (change in consumption ÷ change in disposable income).
Multiplying the gap by the multiplier when asked what policy closes it. Divide the gap by the multiplier.

On the exam

Free-response questions regularly give an MPC and ask for the multiplier, the maximum change in real GDP, or the change in spending or taxes needed to close a gap. Show the formula and the numbers; a four-function calculator is allowed.
When you explain the multiplier in words, say that the initial spending becomes income for others, who spend part of it (based on the MPC), creating further rounds of spending.

Connected topics

Videos

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Check yourself

4 questions on 3.2 Multipliers. Pick an answer to see if you got it, and why.

Question 1 of 4Calculator allowed

In an economy with a marginal propensity to consume (MPC) of 0.75, business investment spending increases by $50 billion. Assuming the price level is constant, what is the maximum possible increase in real GDP?

Disposable income (billions of dollars)	Consumption (billions of dollars)
1,000	850
1,200	1,030
1,400	1,210

Hypothetical consumption data

Question 2 of 4Calculator allowed

Based on the table, what is the marginal propensity to consume?

Question 3 of 4Calculator allowed

If taxes increase by $10 billion, what is the maximum change in real GDP, assuming the price level is constant?

Question 4 of 4

Which of the following would increase the size of the spending multiplier?

0 of 4 answered