How to Calculate Multipliers With MPC

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In economics, the concepts of ​marginal propensity to consume​ (MPC) and ​marginal propensity to save​ (MPS) describe consumer behavior with respect to their income. MPC is the ratio of the change in the amount a person spends to the change in that person's overall income, whereas MPS is the same ratio with savings as the metric of interest. Because people either spend or do not spend (that is, save) whatever income they earn, the sum of MPC and MPS is always equal to 1.

TL;DR (Too Long; Didn't Read)

A higher MPC results in a higher multiplier and thus a greater increase in GDP. In short, more spending results in more national income.

The Investment Multiplier

This relationship gives rise to something called the ​investment multiplier​. This is predicated on the idea of a positive-feedback loop, wherein an increase in average consumer spending ultimately leads to an increase in national income greater than the initial amount spent at a given MPC. The relationship is:

\text{ multiplier}=\frac{1}{1-MPC}

This relationship can be used to calculate how much a nation's gross domestic product (GDP) will increase over time at a given MPC, assuming all other GDP factors remain constant.

For example, assume a nation's GDP is $250 million and its MPC is 0.80. What will the new GDP be if total spending rises by $10 million?

Step 1: Calculate the Multiplier

In this case,

\frac{1}{1-MPC}=\frac{1}{1-0.80}=\frac{1}{0.2}=5

Step 2: Calculate the Increase in Spending

Since the initial increase in spending is $10 million and the multiplier is 5, this is simply:

(5)(\$10\text{ million})=\$50\text{ million}

Step 3: Add the Increase to the Initial GDP

Since the initial GDP of this nation is given as $250 million, the answer is:

\$250\text{ million} + \$50\text{ million} = \$300\text{ million}

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