The Multiplier Effect and Its Calculation | 乘数效应及其计算

📚 The Multiplier Effect and Its Calculation | 乘数效应及其计算

The multiplier effect is a central concept in macroeconomics. It explains how an initial change in autonomous expenditure, such as investment, government spending, or exports, leads to a larger final change in national income. This amplification happens through repeated rounds of spending and income generation.

乘数效应是宏观经济学中的核心概念。它解释了自主性支出的初始变动，例如投资、政府支出或出口，如何最终导致国民收入更大的变动。这种放大作用通过支出与收入生成的反复循环得以实现。

1. What Is the Multiplier Effect? | 什么是乘数效应？

The multiplier is the ratio of the change in national income to the initial change in autonomous expenditure. For example, if an economy receives an extra £100 million of investment and total national income rises by £300 million, the multiplier is 3.

乘数是国民收入变动量与自主性支出初始变动量之间的比率。例如，如果一个经济体额外获得1亿英镑投资，而国民总收入增加了3亿英镑，那么乘数就是3。

Autonomous expenditure includes spending that is not directly dependent on current income, such as investment, government purchases, and exports. When these components change, they set off a chain reaction across the economy.

自主性支出包括不直接取决于当前收入水平的支出，例如投资、政府购买和出口。当这些组成部分发生变化时，会引发整个经济中的连锁反应。

2. Marginal Propensity to Consume (MPC) | 边际消费倾向（MPC）

The marginal propensity to consume is the fraction of an extra unit of income that households spend on consumption. If a household receives an additional £1,000 and spends £800, the MPC is 0.8.

边际消费倾向是家庭将额外增加的每一单位收入用于消费的比例。如果一个家庭额外获得1000英镑并消费了800英镑，那么MPC就是0.8。

The marginal propensity to save (MPS) is the fraction saved. Since income is either spent or saved, MPC + MPS = 1. If MPC = 0.8, then MPS = 0.2.

边际储蓄倾向是储蓄的比例。由于收入要么被消费，要么被储蓄，所以MPC + MPS = 1。如果MPC = 0.8，那么MPS = 0.2。

MPC + MPS = 1

Other withdrawals from the circular flow, such as taxes and imports, also affect the multiplier. The marginal propensity to tax (MPT) and the marginal propensity to import (MPM) reduce the size of the multiplier.

循环流动中的其他漏出，例如税收和进口，也会影响乘数。边际税率（MPT）和边际进口倾向（MPM）都会使乘数变小。

3. The Multiplier Formula | 乘数公式

In a simple closed economy with no government, the multiplier is calculated as 1 divided by the marginal propensity to save.

在没有政府和对外贸易的简单封闭经济中，乘数等于1除以边际储蓄倾向。

k = 1 / MPS = 1 / (1 – MPC)

In an open economy with government, the multiplier becomes smaller because some income leaks into taxes and imports. The denominator then includes all withdrawal rates.

在存在政府和开放经济中，由于部分收入漏出为税收和进口，乘数会变小。此时分母包含所有漏出率。

k = 1 / (1 – MPC + MPT + MPM)

Here, MPT is the marginal tax rate and MPM is the marginal propensity to import. The more leakages, the lower the value of the multiplier.

其中，MPT是边际税率，MPM是边际进口倾向。漏出越多，乘数的值就越低。

4. Why Is the Multiplier Greater Than One? | 为什么乘数大于1？

When an injection increases national income, it becomes factor income for workers and resource owners. They spend a proportion of this income, which becomes someone else’s income, and so on.

当一笔注入使国民收入增加时，这笔收入会成为工人和资源所有者的要素收入。他们会将其中一部分用于消费，这又成为其他人的收入，如此循环往复。

If MPC = 0.8, the initial injection of £100 million creates £80 million of second-round spending, then £64 million, then £51.2 million, and so on. The total increase is the sum of an infinite geometric series.

如果MPC = 0.8，初始注入1亿英镑会产生8000万英镑的第二轮支出，然后是6400万英镑、5120万英镑，以此类推。总增加量是一个无限几何级数的总和。

Round	Additional spending	Cumulative total
1	£100m	£100m
2	£80m	£180m
3	£64m	£244m
4	£51.2m	£295.2m

As the number of rounds approaches infinity, the total increase approaches 1 / (1 – 0.8) × £100m = £500m. Hence the multiplier is 5.

当轮次趋近于无穷时，总增加量趋近于1 / (1 – 0.8) × 1亿英镑 = 5亿英镑。因此乘数为5。

5. Calculating the Multiplier: A Worked Example | 计算乘数：一个实例

Suppose an economy has MPC = 0.7, MPT = 0.2, and MPM = 0.1. First, place these values into the multiplier formula.

假设一个经济的MPC = 0.7，MPT = 0.2，MPM = 0.1。首先，将这些值代入乘数公式。

k = 1 / (1 – 0.7 + 0.2 + 0.1) = 1 / 0.6 = 1.67

The multiplier is 1.67. If government spending rises by £200 million, the total increase in national income will be:

乘数为1.67。如果政府支出增加2亿英镑，国民收入的总增加量将是：

ΔY = k × ΔJ = 1.67 × £200m = £334m

This shows that the final change in national income is larger than the initial injection, but smaller than it would be in a simpler economy.

这表明国民收入的最终变动大于初始注入，但会比在更简单经济中的变动小。

6. The National Income Change Formula | 国民收入变动公式

The general relationship between an injection and national income is written as:

注入与国民收入之间的一般关系可写成：

ΔY = k × ΔJ

Here, ΔY is the change in national income, k is the multiplier, and ΔJ is the change in injections. Injections include investment, government spending, and exports.

其中，ΔY是国民收入变动量，k是乘数，ΔJ是注入变动量。注入包括投资、政府支出和出口。

The same formula applies when injections fall. A decrease in investment of £50 million with a multiplier of 4 would reduce national income by £200 million.

该公式同样适用于注入减少的情形。投资减少5000万英镑，若乘数为4，将使国民收入减少2亿英镑。

7. Factors That Affect the Size of the Multiplier | 影响乘数大小的因素

The multiplier is large when the marginal propensity to consume is high, because every round of income leads to substantial spending. In contrast, a high marginal propensity to save reduces the multiplier.

当边际消费倾向较高时，乘数较大，因为每一轮收入都会带来大量支出。相反，较高的边际储蓄倾向会减小乘数。

A high MPC leads to a large multiplier.

高MPC导致较大的乘数。
A high MPS, MPT, or MPM leads to a small multiplier.

高MPS、MPT或MPM导致较小的乘数。
If firms and households are confident, they are more willing to spend, increasing the multiplier.

如果企业和家庭信心充足，他们更愿意支出，从而提高乘数。
If the economy is near full capacity, the multiplier effect may be weakened by supply constraints.

如果经济接近充分产能，乘数效应可能因供给约束而被削弱。

Open economies with high import levels tend to have smaller multipliers because spending leaks abroad.

进口水平较高的开放经济体往往乘数较小，因为支出会漏出到国外。

8. The Multiplier in Fiscal Policy | 乘数在财政政策中的应用

Governments use the multiplier to estimate the effect of changes in tax or spending. For example, an increase in government expenditure can stimulate aggregate demand and boost national income.

政府利用乘数来估计税收或支出变动的效果。例如，增加政府支出可以刺激总需求并推动国民收入增长。

However, the multiplier also works in reverse. During a recession, a fall in investment or exports can cause a disproportionately large drop in national income. This is known as the negative multiplier.

然而，乘数也会反向起作用。在经济衰退期间，投资或出口的下降可能导致国民收入出现不成比例的大幅下滑。这被称为负乘数效应。

Fiscal policy aims to smooth these fluctuations, but its success depends on the size of the multiplier. If the multiplier is small, government stimulus may not be very effective.

财政政策旨在平抑这些波动，但其成功取决于乘数的大小。如果乘数很小，政府刺激措施可能效果有限。

9. Limitations and Criticisms | 局限性与批评

The multiplier model assumes that spending continues to circulate indefinitely, but in reality leakages such as saving, taxation, and imports stop this process. Also, a rise in income may not be spent if households are pessimistic.

乘数模型假设支出会无限循环下去，但实际上储蓄、税收和进口等漏出会终止这一过程。此外，如果家庭对未来感到悲观，收入增加也未必会被用于支出。

Leakages reduce the actual multiplier.

漏出会降低实际乘数。
Time lags mean that the full effect may take months or years.

时滞意味着乘数的完全效应可能需要数月或数年才能显现。
If the economy is at full employment, extra spending may cause inflation rather than higher output.

如果经济处于充分就业状态，额外支出可能引发通胀而非提高产出。
The multiplier is not a constant; it changes with economic conditions.

乘数并非恒定不变，它会随经济状况而变化。

Despite these criticisms, the multiplier remains a useful tool for understanding how injections and leakages affect national income.

尽管存在这些批评，乘数仍然是理解注入与漏出如何影响国民收入的有用工具。

10. Conclusion | 总结

The multiplier effect shows that an initial change in autonomous expenditure can generate a multiple change in national income. Its value depends on the marginal propensities to consume, save, tax, and import.

乘数效应表明，自主性支出的初始变动可以引致国民收入的多倍变动。其数值取决于边际消费倾向、边际储蓄倾向、边际税率和边际进口倾向。

To calculate it, use the formula k = 1 / (1 – MPC) when only consumption and saving exist, or the extended version that includes withdrawals. Understanding the multiplier helps economists and policymakers evaluate the impact of fiscal and monetary decisions.

在只有消费和储蓄时，可使用公式k = 1 / (1 – MPC)计算；在包含漏出时，则使用扩展公式。理解乘数有助于经济学家和政策制定者评估财政与货币政策决策的影响。

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The Multiplier Effect and Its Calculation | 乘数效应及其计算