Multipliers
Introduced| English | Meaning |
|---|---|
| multiplier/ˌmʌltɪˈplaɪə/ | A number by which another quantity is multiplied. |
| marginal propensity to consume/ˈmɑːdʒɪnl prəˈpensɪti tə kənˈsjuːm/ | The proportion of an additional unit of disposable income that is spent on consumption. |
| marginal propensity to save/ˈmɑːdʒɪnl prəˈpensɪti tə seɪv/ | The proportion of an additional unit of disposable income that is saved rather than consumed. |
| spending multiplier/ˈspendɪŋ ˌmʌltɪˈplaɪə/ | The change in equilibrium aggregate output per unit change in autonomous spending; in the simplest closed-economy model it is one divided by one minus the marginal propensity to consume. |
| tax multiplier/tæks ˌmʌltɪˈplaɪə/ | The change in equilibrium aggregate output per unit change in lump-sum taxes; in the simplest model it is minus the marginal propensity to consume divided by one minus that propensity. |
One dollar, spent many times
- When the government spends an extra dollar, output rises by more than a dollar.
- How? Your spending is someone else's income, which they partly spend again.
- That spending is another person's income... and around it goes.
- This ripple is the multiplier 乘数 effect.
MPC and MPS
- The marginal propensity to consume 边际消费倾向 (MPC) is the share of each extra dollar of income a household spends.
- The marginal propensity to save 边际储蓄倾向 (MPS) is the share it saves.
- Every extra dollar is spent or saved, so $MPC + MPS = 1$.
The marginal propensity to consume plus the marginal propensity to save equals ______.
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Every extra dollar is either spent or saved, so MPC + MPS = 1.
The spending multiplier
- Trace it: the government spends 100, people spend 80 of it, the next earner spends 64... a shrinking chain.
- Its sum gives the spending multiplier 支出乘数: $\dfrac{1}{1 - MPC} = \dfrac{1}{MPS}$.
- A higher MPC means more is re-spent, so the multiplier is larger.
- Worked idea. With $MPC = 0.75$, the multiplier is $\dfrac{1}{0.25} = 4$, so 50 of extra spending raises GDP by 200.
Income rounds and the multiplier’s assumptions
$\Delta Y=k\Delta J$
Compare the first few income rounds with the infinite model total. Domestic re-spending and total consumption must be distinguished when tax and imports are present.
If MPC = 0.75, what is the spending multiplier?
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Spending multiplier = 1 ÷ (1 − 0.75) = 1 ÷ 0.25 = 4.
With a spending multiplier of 4, a 50 billion rise in government spending raises GDP by how much (in billions)?
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ΔGDP = multiplier × initial change = 4 × 50 = 200.
A higher MPC makes the spending multiplier:
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A higher MPC means a longer re-spending chain, so a bigger multiplier.
The tax multiplier
- A tax cut is weaker: people save part of it, so only $MPC$ of it is spent in the first round.
- The tax multiplier 税收乘数 is $-\dfrac{MPC}{1 - MPC}$ — smaller in size and negative (a tax cut raises output).
- Total effect: $\Delta \text{GDP} = \text{multiplier} \times \text{initial change}$.
- With $MPC = 0.75$ the tax multiplier is $-3$, so a 50 tax cut raises GDP by only 150 — less than spending.
The tax multiplier is larger in size than the spending multiplier.
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False. Only the MPC fraction of a tax change is spent in the first round (part is saved), so the tax multiplier is smaller in size.
The tax multiplier is negative because:
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Taxes and output move in opposite directions, so the tax multiplier carries a minus sign.
The multiplier turns one dollar of new spending into a larger change in GDP. $MPC + MPS = 1$. The spending multiplier is $\dfrac{1}{1 - MPC}$; the tax multiplier is $-\dfrac{MPC}{1 - MPC}$ — smaller, because part of a tax change is saved first.
Write from a multiplier of 5 and a GDP rise of 150
- The marginal propensity to consume is 0.80.
- Government spending rises by 30 billion. Find the multiplier and the rise in GDP.
The marginal propensity to consume is 0.80. What is the spending multiplier? If government spending then rises by 30 billion, by how much does GDP rise?
1 divided by 0.20 is 5, and 5 times 30 is 150.
By how much does GDP rise?
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A multiplier of 5 turns a spending rise of 30 into a GDP rise of 150. Other options — 200 billion (the lesson change); 30 billion (the first round only).