# Tax Multiplier Effect: Definition & Formula

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• 0:03 The Taxes, They Multiply!
• 1:01 Marginal Propensity
• 1:39 The Simple Formula
• 2:26 Examples
• 3:49 The Complex Formula
• 5:12 Lesson Summary

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Lesson Transcript
Instructor: Martin Gibbs

Martin has 16 years experience in Human Resources Information Systems and has a PhD in Information Technology Management. He is an adjunct professor of computer science and computer programming.

Taxes and multiplication: not words you always want to hear together. However, in this lesson, we'll cover the tax multiplier effect on a macro scale to learn how taxes impact gross domestic product.

## The Taxes, They Multiply!

Taxes are a hot-button issue at both micro and macro levels. But, how do government changes to taxes impact the gross domestic product (GDP)? GDP is the value of goods and services produced by a nation within a given time frame. The tax multiplier is the measure of this effect. Basically, taxes will change available disposable income, which impacts changes in consumption and saving.

There are two methods for calculating the tax multiplier, one simple and one complex. The first method is easier to calculate and provides us with valuable information; the second includes more variables but better reflects the complex nature of economics. Each method evaluates the propensity to save and spend (the simple model looks only at these two). These variables are labeled MPC (marginal propensity to consume) and MPS (marginal propensity to save).

## Marginal Propensity

The marginal propensity to consume is the percentage of an increase in income that's spent. In other words, if you receive a bonus check of \$250 and you spend all \$250, the MPC is 1 (\$250 spent / \$250 increase in income); however, if you save \$150, the MPC is 0.4 (\$100 spent / \$250 increase in income = 0.4).

Now that we understand MPC and MPS, we can use these values to calculate the tax multiplier. In each of the following formulas, M stands for the multiplier.

## The Simple Formula

The simple tax multiplier formula is a negative marginal propensity to consume divided by the marginal propensity to save:

Why is the MPC negative in the formula? The tax multiplier is always negative! As taxes go down, demand for goods and services increases; there is an inverse relationship between taxes and GDP. When taxes go up, disposable income decreases, meaning a negative impact on GDP.

We can refine the formula even more. Because the marginal propensity to save is an INVERSE relationship to the marginal propensity to consume, we can simplify a little more by stating 1 - MPC.

The graphic below shows the formula: M (the tax multiplier) equals negative MPC divided by 1 minus MPC:

## Examples

We used a micro example (\$250 bonus) above, but we can easily increase that to a macro level. Let's say the government increases spending by \$250 million. Further, let's say taxpayers elect to spend \$225 million of that \$250 million. To figure the MPC, we divide the income elected to spend (\$225 million) by the total (\$250 million). 225 divided by 250 is 0.9. The MPC is 0.9.

Let's plug that value into our tax multiplier formula:

M = -MPC / (1 - MPC)

M = -0.9 / (1 - 0.9) = -9

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