Multipliers · 乘数
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| multiplier/ˌmʌltɪˈplaɪə/ | 乘数 | chéng shù |
| marginal propensity to consume/ˈmɑːdʒɪnl prəˈpensɪti tə kənˈsjuːm/ | 边际消费倾向 | biān jì xiāo fèi qīng xiàng |
| marginal propensity to save/ˈmɑːdʒɪnl prəˈpensɪti tə seɪv/ | 边际储蓄倾向 | biān jì chǔ xù qīng xiàng |
| spending multiplier/ˈspendɪŋ ˌmʌltɪˈplaɪə/ | 支出乘数 | zhī chū chéng shù |
| tax multiplier/tæks ˌmʌltɪˈplaɪə/ | 税收乘数 | shuì shōu chéng shù |
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.
一块钱,被花很多次
- 当政府多花一块钱,产出上升的却多于一块钱。
- 怎么会?你的支出是别人的收入,他们又把它花掉一部分。
- 那笔支出又是另一个人的收入……如此循环下去。
- 这种涟漪就是乘数(multiplier)效应。
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 $MPC + MPS = 1$.
MPC 与 MPS
- 边际消费倾向(marginal propensity to consume,MPC)是家庭把每多一块钱收入花掉的比例。
- 边际储蓄倾向(marginal propensity to save,MPS)是它存起来的比例。
- 每多一块钱要么花要么存,所以 $MPC + MPS = 1$。
The marginal propensity to consume plus the marginal propensity to save equals . · 边际消费倾向加边际储蓄倾向等于。
Every extra dollar is either spent or saved, so MPC + MPS = 1. · 每多一块钱要么花要么存,所以 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.
支出乘数
- 追踪一下:政府花 100,人们花掉其中的 80,下一个赚到的人花 64……一条递减的链条。
- 它的和给出支出乘数(spending multiplier):$\dfrac{1}{1 - MPC} = \dfrac{1}{MPS}$。
- 更高的 MPC 意味着更多被再花掉,所以乘数更大。
- 例题。 当 $MPC = 0.75$,乘数是 $\dfrac{1}{0.25} = 4$,所以 50 的额外支出使 GDP 上升 200。
The multiplier, round by round · 一轮一轮看乘数
Set the MPC and watch each spending round shrink by that fraction — the total settles at the multiplier times the initial injection. · 设定 MPC,看每一轮支出都按这个比例递减——总量收敛于乘数乘以初始注入。
If MPC = 0.75, what is the spending multiplier? · 如果 MPC = 0.75,支出乘数是多少?
Spending multiplier = 1 ÷ (1 − 0.75) = 1 ÷ 0.25 = 4. · 支出乘数 = 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)? · 当支出乘数为 4 时,政府支出增加 50 十亿使 GDP 上升多少(十亿)?
ΔGDP = multiplier × initial change = 4 × 50 = 200. · ΔGDP = 乘数 × 初始变化 = 4 × 50 = 200。
A higher MPC makes the spending multiplier: · 更高的 MPC 使支出乘数:
A higher MPC means a longer re-spending chain, so a bigger multiplier. · 更高的 MPC 意味着更长的再支出链条,所以乘数更大。
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.
税收乘数
- 减税更弱:人们会存起其中一部分,所以第一轮只有 $MPC$ 那部分被花掉。
- 税收乘数(tax multiplier)是 $-\dfrac{MPC}{1 - MPC}$——大小更小,且为负(减税抬升产出)。
- 总效果:$\Delta \text{GDP} = \text{multiplier} \times \text{initial change}$。
- 当 $MPC = 0.75$,税收乘数是 $-3$,所以 50 的减税只使 GDP 上升 150——比支出少。
The tax multiplier is smaller in size than the spending multiplier, because part of a tax change is saved first. · 税收乘数在大小上小于支出乘数,因为减税的一部分会先被存起来。
Only the MPC fraction of a tax change is spent in the first round, so it does less. · 减税只有 MPC 那部分在第一轮被花掉,所以作用更小。
The tax multiplier is negative because: · 税收乘数为负,是因为:
Taxes and output move in opposite directions, so the tax multiplier carries a minus sign. · 税收与产出方向相反,所以税收乘数带负号。
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.
乘数把一块钱的新支出变成 GDP 的更大变化。$MPC + MPS = 1$。支出乘数是 $\dfrac{1}{1 - MPC}$;税收乘数是 $-\dfrac{MPC}{1 - MPC}$——更小,因为减税的一部分会先被存起来。