关于marginal propensity to consumption (MPC)的计算

问题如下：

Question

In a hypothetical economy, consumption is 70% of pre-tax income, and the average tax rate is 25% of total income. If planned government expenditures are expected to increase by $1.25 billion, the increase in total income and spending, in billions, is closest to:

选项：

A.$2.6. B.$4.2. C.$1.3.

解释：

Solution

B is correct.The fiscal multiplier is $\frac{1}{1-c\left(1-T\right)}$ where

c = marginal propensity to consume = consumption/disposable income

T = the tax rate

Assuming pre-tax income of $100

Disposable income: $100 × (1 – 0.25) = $75

Marginal propensity to consume: $70/$75 = 0.933

The fiscal multiplier: 1/[1 – 0.933(1 – 0.25)] = 3.33

With government expenditure of $1.25 billion, total incomes and spending will rise by $1.25 billion × 3.33 = $4.2 billion

A is incorrect. It calculates the MPC from pre-tax income (MPC = 0.70) but applies the formula correctly: 1/[1 – c(1 – T)]: 1/[1 – 0.70(1 – 0.25)] = 2.10; resulting in an overall stimulus effect of 2.10 × 1.25 = 2.60.

C is incorrect. It uses G/MPC: 1.25/0.933 = 1.34

中文解析

依据公式： $\frac{1}{1-c1-T}$

假设税前收入是100美元

可支配收入:100美元×(1 - 0.25) = 75美元

边际消费倾向:$70/$75 = 0.933

财政乘数:1/[1 - 0.933(1 - 0.25)]= 3.33

在政府支出12.5亿美元的情况下，总收入和支出总额将增加12.5亿美元× 3.33 = 42亿美元

A不正确。它从税前收入计算MPC (MPC = 0.70)，但正确地应用了公式:1/[1 - c(1 - T)]: 1/[1 - 0.70(1 - 0.25)] = 2.10;总体刺激效应为2.10 × 1.25 = 2.60。

C选项不正确。它使用G/MPC: 1.25/0.933 = 1.34