📚 The Multiplier | 乘数效应
The multiplier is one of the most important concepts in A-Level Economics because it links an initial change in spending to a much larger final change in national income. Cambridge International A-Level frequently tests the multiplier through definitions, numerical calculations, aggregate demand diagrams and evaluation of its size.
乘数是A-Level经济学中最重要的概念之一，因为它将最初的支出变化与最终更大的国民收入变化联系起来。剑桥国际A-Level经常通过定义、数值计算、总需求图表以及对乘数大小的评估来考查这一概念。
1. Definition of the multiplier | 乘数的定义
The multiplier (k) is the ratio of the change in real national income (ΔY) to the initial change in aggregate demand or injection (ΔJ) that caused it.
乘数（k）是实际国民收入变化量（ΔY）与引起该变化的初始总需求或注入变化量（ΔJ）之比。
Multiplier (k) = ΔY ÷ ΔJ
For example, if a $50 billion rise in investment raises real GDP by $200 billion, the multiplier is 4.
例如，如果500亿美元的投资增加使实际GDP增加2000亿美元，则乘数为4。
The initial change can come from any injection: investment (I), government spending (G) or exports (X).
初始变化可以来自任何注入：投资（I）、政府支出（G）或出口（X）。
2. The circular flow and injections/withdrawals | 循环流动与注入/漏出
In the circular flow of income, households spend on domestic goods and services, creating income for firms and households. An injection adds new spending into this flow.
在收入循环流动中，家庭购买国内商品和服务，为企业与家庭创造收入。注入为这一流动增加新的支出。
However, not all income is passed on in each round because of withdrawals: saving (S), taxation (T) and imports (M). These leakages reduce the amount of extra income that is re-spent on domestic output.
然而，并非所有收入都会在每一轮中传递，因为存在漏出：储蓄（S）、税收（T）和进口（M）。这些漏出减少了用于国内产出的额外收入再支出。
- Injections: I + G + X | 注入：I + G + X
- Withdrawals: S + T + M | 漏出：S + T + M
The multiplier is therefore stronger when withdrawals are small and weaker when withdrawals are large.
因此，漏出较小时乘数较强，漏出较大时乘数较弱。
3. Marginal propensities | 边际倾向
Marginal propensity to consume (MPC) is the proportion of extra income spent on domestic goods and services.
边际消费倾向（MPC）是额外收入中用于国内商品和服务的比例。
MPC = ΔC ÷ ΔY
The marginal propensity to save (MPS) is the proportion of extra income saved; the marginal propensity to tax (MPT) is the proportion taken in tax; the marginal propensity to import (MPM) is the proportion spent on imports.
边际储蓄倾向（MPS）是额外收入中储蓄的比例；边际税收倾向（MPT）是征税的比例；边际进口倾向（MPM）是用于进口的比例。
In a simplified two-sector economy without government or trade, MPC + MPS = 1. In an open economy with government, MPC + MPS + MPT + MPM = 1.
在无政府和贸易的两部门简化经济中，MPC+MPS=1。在有政府的开放经济中，MPC+MPS+MPT+MPM=1。
The sum of the marginal withdrawals is called the marginal propensity to withdraw (MPW): MPW = MPS + MPT + MPM.
边际漏出之和称为边际漏出倾向（MPW）：MPW=MPS+MPT+MPM。
4. The multiplier formula | 乘数公式
Because each round of spending is reduced by the fraction that leaks out, the multiplier can be calculated as the reciprocal of the marginal propensity to withdraw.
由于每一轮支出都会因漏出的比例而减少，乘数可以计算为边际漏出倾向的倒数。
Multiplier (k) = 1 ÷ MPW = 1 ÷ (MPS + MPT + MPM)
In a closed economy without government, this simplifies to k = 1 ÷ MPS or k = 1 ÷ (1 − MPC).
在无政府的封闭经济中，这一公式简化为k=1÷MPS或k=1÷(1−MPC)。
The relationship between the total change in income and the initial injection is therefore:
因此，收入总变化与初始注入之间的关系为：
ΔY = k × ΔJ
If MPC = 0.8 and MPS = 0.2, the multiplier is 1 ÷ 0.2 = 5.
如果MPC=0.8且MPS=0.2，则乘数为1÷0.2=5。
5. Worked example of the multiplier process | 乘数过程的计算示例
Suppose the government increases spending on infrastructure by $100 million and the marginal propensity to withdraw is 0.2. The multiplier is 5, so the final rise in real income is $500 million.
假设政府增加基础设施支出1亿美元，边际漏出倾向为0.2。乘数为5，因此实际收入最终增加5亿美元。
The process can be shown round by round. In round one, income rises by $100m. With MPW = 0.2, $80m is re-spent domestically in round two. In round three, 0.8 × $80m = $64m is re-spent, and so on.
这一过程可以逐轮展示。第一轮收入增加1亿美元。由于MPW=0.2，第二轮在国内再支出8000万美元。第三轮再支出0.8×8000万=6400万美元，依此类推。
| Round | 轮次 | Additional income ($m) | 额外收入（百万美元） | Additional domestic spending ($m) | 额外国内支出（百万美元） |
|---|---|---|
| 1 | 100 | 80 |
| 2 | 80 | 64 |
| 3 | 64 | 51.2 |
| … | … | … |
| Total | 总计 | 500 | 400 |
The total additional income is the sum of the geometric series 100 + 80 + 64 + … = 100 ÷ (1 − 0.8) = 500.
额外收入总额是几何级数100+80+64+…之和=100÷(1−0.8)=500。
Cambridge questions often ask you to calculate the missing values in such a table, so practise using MPW to move from one round to the next.
剑桥考试常要求计算此类表格中的缺失值，因此要练习使用MPW计算每一轮到下一轮的变化。
6. The multiplier and aggregate demand | 乘数与总需求
An initial rise in investment, government spending or exports shifts the aggregate demand curve to the right. The multiplier process causes a second, larger shift.
投资、政府支出或出口的初始增加使总需求曲线向右移动。乘数过程导致第二次更大的移动。
This is why the multiplier is central to fiscal policy: a relatively small increase in government spending can raise AD by a much larger amount.
这就是乘数对财政政策至关重要的原因：政府支出的较小增加可以使总需求大幅上升。
However, the final impact on real output and the price level depends on the slope of the aggregate supply curve and the amount of spare capacity in the economy.
然而，对实际产出和价格水平的最终影响取决于总供给曲线的斜率以及经济中的闲置产能数量。
For Cambridge essays, always state that the multiplier is a demand-side concept, so its real effects depend on supply-side conditions.
对于剑桥论文题，务必说明乘数是一个需求侧概念，因此其实际效果取决于供给侧条件。
7. Determinants of the multiplier size | 决定乘数大小的因素
A higher marginal propensity to consume increases the multiplier because more of each income round is re-spent domestically.
边际消费倾向越高，乘数越大，因为每一轮收入中有更多部分在国内再支出。
A lower marginal propensity to save, a lower tax rate and a lower marginal propensity to import all reduce leakages and raise the multiplier.
边际储蓄倾向越低、税率越低、边际进口倾向越低，都会减少漏出并提高乘数。
Open economies with high import penetration tend to have smaller multipliers because a large share of extra income leaks abroad.
进口渗透率高的开放经济体往往乘数较小，因为额外收入的很大一部分漏出到国外。
The availability of spare capacity also matters: if firms can expand output easily, the multiplier raises real income; if not, it mainly raises prices.
闲置产能的可得性也很重要：如果企业能轻松扩大产出，乘数会提高实际收入；如果不能，则主要推高价格。
| Factor | 因素 | Effect on multiplier | 对乘数的影响 |
|---|---|
| Higher MPC | 更高的MPC | Increase | 增大 |
| Higher MPS | 更高的MPS | Decrease | 减小 |
| Higher tax rate | 更高的税率 | Decrease | 减小 |
| Higher MPM | 更高的MPM | Decrease | 减小 |
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