Spending Multipliers
Imagine a new sneaker factory opens in a small Ohio town and pays workers $\$1$ million in wages. The workers don't bury that money. They eat at restaurants, buy cars, and pay for haircuts, and those businesses pay their own workers, who spend again. So does the town's income grow by $\$1$ million, or by more? This page shows how to calculate the answer.
MPC and MPS
When your income goes up, you split the extra dollars between spending and saving. Economists measure that split with two numbers.
Every extra dollar is either spent or saved, so the two fractions add up to 1:
$$MPC + MPS = 1 \qquad MPS = 1 - MPC$$When a household's disposable income rises by $\$500$ per month, its consumption rises by $\$400$ per month. Compute the household's MPC and MPS.
When a household's disposable income rises by $\$500$ per month, its consumption rises by $\$400$ per month. Compute the household's MPC and MPS.
The spending multiplier
Back to the sneaker factory. Suppose the MPC is 0.8 and the first round of spending is $\$100$ million. The people who receive it spend $0.8 \times 100 = 80$ million, and the next group spends $0.8 \times 80 = 64$ million. Each round is 0.8 times the one before.
The rounds keep shrinking but never quite stop. Adding all of them gives:
$$100 + 80 + 64 + 51.2 + \dots = \frac{100}{1 - 0.8} = 500$$Why does the formula work? Each round is $MPC$ times the previous one, so the total is $1 + MPC + MPC^2 + \dots$, which equals $\frac{1}{1 - MPC}$. A smaller MPS means less leaks out in each round, so the multiplier is bigger.
The marginal propensity to consume (MPC) in an economy is 0.8. Compute the marginal propensity to save (MPS) and the simple spending multiplier. Write the formula you…
The marginal propensity to consume (MPC) in an economy is 0.8. Compute the marginal propensity to save (MPS) and the simple spending multiplier. Write the formula you use for each.
The spending multiplier in an economy is 4. Autonomous spending increases by $\$50$ billion. Compute the change in real GDP, ignoring price-level effects.
The spending multiplier in an economy is 4. Autonomous spending increases by $\$50$ billion. Compute the change in real GDP, ignoring price-level effects.
Business investment in an economy falls by $\$30$ billion because firms are pessimistic about future sales. When disposable income rises by $\$1{,}000$ in this economy,…
Business investment in an economy falls by $\$30$ billion because firms are pessimistic about future sales. When disposable income rises by $\$1{,}000$ in this economy, saving rises by $\$200$. Compute the MPS, the MPC, the spending multiplier, and the resulting change in real GDP. Explain in one or two sentences why the final change is larger than the initial $\$30$ billion drop.
The tax multiplier
Taxes work in the other direction and are a little weaker. A tax cut gives households more disposable income, but they don't spend all of it. Part goes to saving, so the first round of new spending is only $MPC$ times the tax cut.
The balanced-budget change
What happens if the government raises spending and taxes by the same amount? The spending effect is $\frac{1}{1 - MPC} \times \Delta G$ and the tax effect is $-\frac{MPC}{1 - MPC} \times \Delta T$. Adding them with $\Delta G = \Delta T$ gives a multiplier of $\frac{1 - MPC}{1 - MPC} = 1$. So real GDP rises by the amount of the change, which is not zero.
The MPC in an economy is 0.75. (a) Compute the spending multiplier and the tax multiplier. (b) By how much does real GDP change if the government increases spending by…
The MPC in an economy is 0.75. (a) Compute the spending multiplier and the tax multiplier. (b) By how much does real GDP change if the government increases spending by $\$40$ billion? (c) By how much does real GDP change if the government cuts taxes by $\$40$ billion? Explain why the answers to (b) and (c) differ.
The MPC is 0.9. The government raises both its spending and taxes by $\$100…
The MPC is 0.9. The government raises both its spending and taxes by $\$100$ billion. (a) Compute the change in real GDP caused by the increase in spending alone. (b) Compute the change caused by the increase in taxes alone. (c) Compute the net change, and explain why a balanced-budget change is not neutral.
Closing a gap, and real-world limits
Policymakers use multipliers backward. If they know how large the output gap is, they can find how big a policy change must be.
Why the real multiplier is smaller
The simple formula assumes that every dollar of new income that isn't saved is spent on goods made here. In the real world, more dollars leak out of the spending stream:
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Taxes. Households pay part of each extra dollar of income to the IRS and state governments, so they have less to spend.
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Imports. Money spent on goods made in Mexico or China becomes income abroad, not for U.S. workers.
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Saving. This is already counted in the MPS.
Also, the government may have to borrow to pay for the spending, which can push up interest rates and reduce private investment, and rising prices can eat into the real effect.
An economy has real GDP of $\$4{,}800$ billion while full-employment output is $\$5{,}000$ billion. The MPC is 0.8, and you may ignore price-level changes. (a) Compute…
An economy has real GDP of $\$4{,}800$ billion while full-employment output is $\$5{,}000$ billion. The MPC is 0.8, and you may ignore price-level changes. (a) Compute the size of the output gap. (b) Compute the increase in government spending needed to close the gap. (c) Compute the tax cut needed to close the gap. (d) Explain why the required tax cut is larger than the required spending increase. (e) Explain two reasons why the actual effect of the policy might be smaller than your calculation.
The government spends an extra $\$100…
The government spends an extra $\$100$ million on a highway project, and the MPC is 0.6. (a) Compute the additional spending generated in each of the first four rounds, counting the initial $\$100$ million as round 1. (b) Compute the total change in real GDP after all rounds using the multiplier. (c) In the real world, the measured multiplier is often smaller than the simple formula. Explain how taxes and imports act as leakages that reduce it.
Back to the sneaker factory: with an MPC of 0.8 the town's income grows by 5 times the first $\$1$ million of wages, in the simple model. Real towns see less, because of taxes and imports.