Multipliers
Introduced| English |
|---|
| multiplier/ˌmʌltɪˈplaɪə/ |
| marginal propensity to consume/ˈmɑːdʒɪnl prəˈpensɪti tə kənˈsjuːm/ |
| marginal propensity to save/ˈmɑːdʒɪnl prəˈpensɪti tə seɪv/ |
| spending multiplier/ˈspendɪŋ ˌmʌltɪˈplaɪə/ |
| tax multiplier/tæks ˌmʌltɪˈplaɪə/ |
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 ______.
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.
The multiplier, round by round
Set the MPC and watch each spending round shrink by that fraction — the total settles at the multiplier times the initial injection.
If MPC = 0.75, what is the spending multiplier?
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)?
ΔGDP = multiplier × initial change = 4 × 50 = 200.
A higher MPC makes the spending multiplier:
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 smaller in size than the spending multiplier, because part of a tax change is saved first.
Only the MPC fraction of a tax change is spent in the first round, so it does less.
The tax multiplier is negative because:
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.