**Marginal Propensities, Average Propensities, and Multipliers**

The propensity to save is the percentage (expressed as a decimal) of disposable income consumers save. If a consumer earns $100 (after taxes) and spends $75 while saving $25, the propensity to save will be .25 (25% of the income is saved) and the propensity to consume will be .75 (75% of the income is spent).

The average propensity to save (APS) or consume (APC) is the percentage of all income a consumer or group of consumers saves or spends. If a consumer’s total income is $50,000 per year and that consumer spends $48,000, their APC is .96 and their APS is .04. The APC plus the APS will always equal 1. While knowing and understanding APC and APS is necessary, the more important concept in macroeconomics is marginal propensity to save or consume.

The marginal propensity to save (MPS) or consume (MPC), on the other hand, is the percentage of new income a consumer or group of consumers saves or spends. Here the focus is on the change in income versus the change in spending and saving. If a consumer’s income increase from $892 per week to $1042 per week, the change in income is $150. If that consumer spends $135, their MPC will be .9 ($135 is 90% of $150). That would mean this consumer’s MPS would be .1; they have saved $15 or 10% of their marginal income. The MPS plus the MPC will always equal 1.

**What is the difference between average and marginal propensity to save (or consume)?**

The average propensity to save (APS) or consume (APC) is the percentage of all income a consumer or group of consumers saves or spends. If a consumer’s total income is $50,000 per year and that consumer spends $48,000, their APC is .96 and their APS is .04. The APC plus the APS will always equal 1. While knowing and understanding APC and APS is necessary, the more important concept in macroeconomics is marginal propensity to save or consume.

The marginal propensity to save (MPS) or consume (MPC), on the other hand, is the percentage of new income a consumer or group of consumers saves or spends. Here the focus is on the change in income versus the change in spending and saving. If a consumer’s income increase from $892 per week to $1042 per week, the change in income is $150. If that consumer spends $135, their MPC will be .9 ($135 is 90% of $150). That would mean this consumer’s MPS would be .1; they have saved $15 or 10% of their marginal income. The MPS plus the MPC will always equal 1.

**What is the spending multiplier?**

An economy’s MPC and MPS have implications for the overall economy. New spending multiplies through the economy and has a larger impact on Gross Domestic Product (GDP). This spending could take the form of a new investment from businesses, new spending from consumers or the government, or new sales of exports. Any of this new spending would multiply through the economy.

As an example, let’s assume every citizen in the fictitious nation Tanterra has an MPC of .8 and an MPS of .2. If the government purchases the services of a police officer for $1000, GDP has just increased by $1000. The police officer will now spend 80% and save 20% of the $1000 of new income. The officer purchases a plane ticket to Hawaii for $800 (while saving $200). The owner of the airline now has $800 of new income. They spend $640 on a new computer for the office and save $160. The owner of the computer store now spends $512 on an advertisement on a local billboard while saving $128. So far, the original increase in government spending has increased GDP by more than just $1000. There has been an additional increase in GDP of $1952 ($800+$640+$512). The $512 received by the billboard owner will continue to be spent and saved at a ratio of 80/20.

To calculate the maximum change in GDP, use the spending multiplier. The formula for the spending multiplier is 1/MPS or 1/(1-MPC). In the example above, the multiplier would be 5 (1/.2). The initial change in spending times the spending multiplier gives you the maximum change in GDP (5 x $1000 = $5000). The original $1000 increase in government spending can increase GDP by a maximum of $5000 with an MPC of .8.

Note: The multiplier works the same in reverse. A $1000 decrease in government spending would decrease Tanterra’s GDP by a maximum of $5000.

To calculate the maximum change in GDP, use the spending multiplier. The formula for the spending multiplier is 1/MPS or 1/(1-MPC). In the example above, the multiplier would be 5 (1/.2). The initial change in spending times the spending multiplier gives you the maximum change in GDP (5 x $1000 = $5000). The original $1000 increase in government spending can increase GDP by a maximum of $5000 with an MPC of .8.

Note: The multiplier works the same in reverse. A $1000 decrease in government spending would decrease Tanterra’s GDP by a maximum of $5000.

**What is the tax multiplier?**

Just as changes in spending multiply through the economy to have a larger impact on GDP, the impacts of changes in taxes on GDP are also magnified. The formula for the tax multiplier is MPC/MPS. For the example above the tax multiplier in Tanterra would be 4 (.8/.2). If the police officer was given a tax rebate of $1000 instead of being hired by the government, that tax rebate would have multiplied through the economy just as the spending increase did. The difference is, the reduction in taxes would only increase GDP by a maximum of $4000 (4 x $1000).

Note: Changes in taxes have an inverse relationship to their impact on GDP. Increases in taxes decrease GDP and decreases in taxes increase GDP. You could see the tax multiplier expressed as a negative number as a result.

**Why is the tax multiplier lower than the spending multiplier?**

Spending changes have a bigger impact on GDP than tax changes do. That is because when there is a change in spending, that initial change impacts GDP directly. Changes in taxes, on the other hand, do not initially change GDP. In the first example above, the government increases spending by purchasing the services of a police officer. That initial $1000 purchase increases GDP by $1000 immediately (plus $4000 of spending as it multiplies through the economy). In the tax decrease example, the actions of the government do not immediately change GDP; it is only the subsequent spending that boosts GDP. As a result, the tax multiplier is always 1 less than the spending multiplier.

**What is the balanced budget multiplier?**

Due to the difference between the spending and tax multipliers, it is possible for the government to change GDP without increasing or decreasing the deficit. The balanced budget multiplier is always 1. Increasing taxes to pay for a spending increase of an equal amount will increase GDP by a factor of 1. Decreasing spending to pay for a tax decrease of an equal amount will decrease GDP by a factor of 1.

If the government of Tanterra increased taxes by $1000 and increased spending by $1000, the budget would be balanced (it wouldn’t change the deficit), and it would increase GDP by a maximum of $1000. Decreasing taxes and spending both by $1000 would decrease GDP by a maximum of $1000.

**Why will the actual change in GDP be less than the maximum indicated by the spending and tax multipliers?**

In reality, the actual change in GDP will be less than the multipliers imply. That is because it doesn’t include taxes on new incomes, possible spending on imports, etc. Taking those things into consideration is a bit more than is generally expected for an introductory Macroeconomics course. Just be aware that the actual change in GDP will be less than the multipliers indicate.

**How do the multipliers impact AS/AD?**

All of the changes indicated above can be illustrated as shifts of the AD curve in the AS/AD model. Increases in taxes and/or decreases in spending shift the AD curve to the left, reducing equilibrium output. Decreases in taxes and/or increases in spending shift the AD curve to the right, increasing equilibrium output.

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