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# Multipliers

The money that is spent in the economy is not just spent once. It flows through the government, through businesses, our pockets, and back to businesses in various orders. Every dollar we earn has most likely been spent multiple times already, whether it bought someone a new Rolls Royce, paid someone to mow a lawn, bought heavy machinery, or paid our taxes. Somehow it found its way into our pocket and will probably also find its way back out. Every time this cycles through the economy it affects GDP. Let's find out how!

## Multiplier Effect in Economics

In economics, the multiplier effect refers to the result a change in spending has on real GDP. The change in spending may be a result of an increase in government expenditure or a change in the tax rate.

To understand how the multiplier effect works, we first have to understand what the marginal propensity to consume (MPC) and the marginal propensity to save (MPS) are. These terms might seem daunting but in this case, "marginal" refers to each additional dollar of disposable income and "propensity" refers to the likeliness that we will do something with that additional dollar.

How likely are we to consume, or in this case, spend each additional dollar of disposable income, or how likely are we to save each additional dollar? Our likeliness to spend and save is required to determine the multiplier effect.

Marginal propensity to consume (MPC) is the rise in consumer spending when disposable income increases by a dollar.

Marginal propensity to save (MPS) is the rise in a household's savings when disposable income increases by a dollar.

A multiplier effect in broad terms refers to a formula in economics that is used to calculate the effect of a change in an economic factor on any related variables in the economy. However, this is very very broad, so the multiplier effect is usually explained in terms of the expenditure multiplier and the tax multiplier.

The expenditure multiplier tells us how much an autonomous change in aggregate spending has affected GDP. An autonomous change in aggregate spending is when aggregate spending initially rises or falls causing changes in income and spending. The tax multiplier describes how much a change in the tax level changes GDP. We can then combine the two multipliers into the balanced budget multiplier which is a combination of both.

The expenditure multiplier (also known as the spending multiplier) tells us the total rise in GDP that results from each additional dollar initially spent. It is a ratio of the total change in GDP due to autonomous change in aggregate spending to the size of that autonomous change.

The tax multiplier is the amount by which a change in the level of taxes affects GDP. It calculates the effect that tax policies have on output and consumption.

The balanced budget multiplier combines the expenditure multiplier and the tax multiplier to calculate the total change in GDP caused by both a change in spending and a change in taxes.

## Multiplier Formula

To use the multiplier formulas, we have to calculate the marginal propensity to consume (MPC) and the marginal propensity to save (MPS) first, since they feature heavily in the multiplier equations.

### MPC and MPS formula

If consumer spending increases because the consumer has more disposable income, we calculate the MPC by dividing the change in consumer spending by the change in disposable income. It will look something like this:

Here we will use the formula to calculate the MPC when disposable income increases by $100 million and consumer spending increases by$80 million.

Using the formula:

The MPC = 0.8

Consumers typically do not spend all of their disposable income. They usually set some of it aside as savings. Therefore the MPC will always be a number between 0 and 1 because the change in disposable income will exceed the change in consumer spending.

If we assume that people do not spend all of their disposable income, then where does the rest of the income go? It goes into savings. This is where the MPS comes in since it accounts for the amount of disposable income that the MPC does not. The formula for the MPS looks like this:

If consumer spending increases by $17 million and disposable income increases by$20 million, what is the marginal propensity to save? What is the MPC?

The MPS = 0.15

The MPC = 0.85

### Expenditure Multiplier Formula

Now we are ready to calculate the expenditure multiplier. Instead of calculating each round of spending individually and adding them together until we arrive at the total increase of real GDP that the initial change in aggregate spending caused, we use this formula:

Since the expenditure multiplier is a ratio of the change in GDP caused by an autonomous change in aggregate spending, and the amount of this autonomous change, we can say that the total change in GDP (Y) divided by the autonomous change in aggregate spending (AAS) is equal to the expenditure multiplier.

To see the expenditure multiplier in action let's say that if disposable income increases by $20, consumer spending increases by$16. The MPC equals 0.8. Now we must plug the 0.8 into our formula:

Expenditure multiplier = 5

### Tax Multiplier Formula

Taxes have an inverse relationship with consumer spending. The MPC is in the place of the 1 in the numerator because people do not spend the entire equivalent of their tax cut, just like they do not spend all their disposable income. They only spend in proportion to their MPC and save the rest, unlike in the expenditure formula where $1 in spending increases real GDP and disposable income by$1. The tax multiplier is negative because of the inverse relationship where an increase in taxes causes a decrease in spending. The tax multiplier formula helps us calculate the effect of a tax policy on GDP.

The government increases taxes by $40 million. This causes consumer spending to fall by$7 million and disposable income decreases by $10 million. What is the tax multiplier? MPC = 0.7 Tax multiplier= -2.33 ## Multiplier Theory in Economics The multiplier theory refers to when an economic factor increases, it generates a higher total of other economic variables than the increase of the initial factor. When there is an autonomous change in aggregate spending more money is spent in the economy. People will earn this money in the form of wages and profits. They will then save a portion of this money and put the rest back into the economy by doing things like paying rent, buying groceries, or paying someone to babysit. Now the money increases someone else's disposable income, a portion of which they will save and a portion of which they will spend. Each round of spending increases the real GDP. As the money cycles through the economy, a portion of it is saved and a portion is spent, which means the amount that is reinvested each round is shrinking. Eventually, the amount of money reinvested in the economy will equal 0. The expenditure multiplier operates under the assumption that the amount of consumer spending will translate into the same amount of output without driving up prices, that the interest rate is a given, there are no taxes or government spending, and that there are no imports and exports. Here is a visual representation of the rounds of spending: The initial increase in investment spending on new solar farms is$500 million. The increase in disposable income is $32 million and consumer spending increased by$24 million.

$24 million divided by$32 million gives us a MPC = 0.75.

 Effect on real GDP $500 million increase in spending on solar farms, MPC = 0.75 First round of spending Initial increase in investment spending =$500 million Second round of spending MPC x $500 million Third round of spending MPC2 x$500 million Fourth round of spending MPC3 x $500 million " " " " Total increase in real GDP = Table 1. The multiplier effect - StudySmarter If we were to plug in all of the values manually we would eventually discover that the total increase in real GDP is$2,000 million, which is $2 billion. Using the formula it would look like this: Even though the initial increase in investment was only$500 million, the total increase in real GDP was $2 billion. The increase in one economic factor generated a higher total of other economic variables. The more likely people are to spend or the higher the MPC, the higher the multiplier is. When the multiplier is high, there is a larger increase in the effect of the initial autonomous change in aggregate spending. If the multiplier is low, and peoples’ MPS is high, then there will be a smaller effect. So far we have been under the assumption that there are no government taxes or spending. The tax multiplier is similar to the expenditure multiplier in that the effects are multiplied through the rounds of spending. It differs in that the relationship between taxes and consumer spending is inverse. As governments increase taxes and disposable income decreases, consumer spending falls. As each$1 is taxed, disposable income decreases by less than $1. Consumer spending increases in proportion to the MPC in the case of a tax cut or the MPS in the case of a tax increase. This is why the government spending and expenditure multiplier have a greater effect than the tax multiplier. This leads to less output in each round of spending, resulting in less total real GDP. ## Economic impact of the multiplier The economic impact of the multiplier is economic growth due to injections into the economy in the form of spending and investments. As these injections flow through the economy, they contribute to a nation's GDP by stimulating production, consumption, investment, and expenditure at various stages. The multiplier effect benefits the economy because a small increase in expenditure, investment, or tax cut, has a magnified effect on the economy. Of course, the size of the effect depends on society’s marginal propensity to consume (MPC) and marginal propensity to save (MPS). If the MPC is high and people spend more of their income, injecting it back into the economy, the multiplier effect will be stronger and therefore the effect on the total real GDP will be greater. When society’s MPS is high, they save more, the multiplier effect is weaker, and the total real GDP effect will be smaller. ## Multiplier in Four Sector Economy The four sector economy is made up of households, firms, the government, and the foreign sector. As seen in Figure 1, money flows through these four sectors through government spending and investing, taxes, private income, and spending, as well as imports and exports in a circular flow. Leakages consist of taxes, savings, and imports because the money spent on those does not continue to cycle in the economy. Injections are exports, investments, and government spending because they increase the supply of money flowing through the economy. Figure 1. Four sector economy circular flow diagram The multiplier effect can be applied to several components. Firms and households account for the autonomous change in aggregate supply. For whatever reason firms and households decide they want to invest in improving their landscaping, so there is an injection of funds into the economy to pay for landscape design, purchasing soil and gravel, installing sprinklers, and gardener wages. The impact on the real GDP of these rounds of spending is explained by the expenditure multiplier. The government can also provide the initial increase in funds in the form of government spending and tax policy which both have their own multiplier effects. ## Multipliers - Key takeaways • The multiplier effect refers to the result a change in spending has on real GDP. The change in spending may be a result of an increase in government expenditure or a change in the tax rate. It is a formula in economics that is used to calculate the effect of a change in an economic factor on any related variables in the economy. • The multiplier effect relies heavily on society's MPC and MPS to calculate the effect that a change in investment, spending or tax policy will have. • Taxes have an inverse relationship with consumer spending. They only spend in proportion to their MPC and save the rest, unlike in the expenditure formula where$1 in spending increases real GDP and disposable income by $1. • The government spending and expenditure multiplier have a greater effect than the tax multiplier. • The multiplier effect benefits the economy because a small increase in expenditure, investment, or tax cut, has a magnified effect on the economy. ## Frequently Asked Questions about Multipliers To calculate the multiplier effect you need to find out the marginal propensity to consume which is the change in consumer spending divided by the change in disposable income. then you need to plug this value into the expenditure equation: 1/(1-MPC) = multiplier effect The multiplier equation is 1/(1-MPC). Examples of the multiplier effect in economics are the expenditure multiplier and the tax multiplier. The concept of a multiplier in economics is that when an economic factor increases, it generates a higher total of other economic variables than the increase of the initial factor. There is the expenditure multiplier which is a ratio of the total change in GDP due to autonomous change in aggregate spending to the size of that autonomous change. Then there is the tax multiplier which is the amount by which a change in the level of taxes affects GDP. It calculates the effect that tax policies have on output and consumption. ## Final Multipliers Quiz Question What does the multiplier effect refer to? Show answer Answer The multiplier effect refers to the result an autonomous change in aggregate spending has on real GDP. Show question Question Why do we need to know the MPC or the MPS to calculate the multiplier effect? Show answer Answer We need the MPC or the MPS to calculate the multiplier effect because we need to know what portion of the increase in disposable income people will spend to be able to figure out how much money continues to circulate in the economy. Show question Question What is the Marginal Propensity to Consume (MPC)? Show answer Answer The MPC is the rise in consumer spending when disposable income increases by a dollar. Show question Question What is the Marginal Propensity to Save (MPS)? Show answer Answer The MPS is the rise in a household's savings when disposable income increases by a dollar. Show question Question What is an autonomous change in aggregate spending? Show answer Answer It is when aggregate spending initially rises or falls causing changes in income and spending. Show question Question What is the multiplier theory? Show answer Answer The multiplier theory is that when an economic factor increases, it generates a higher total of other economic variables than the increase of the initial factor. Show question Question Who had the idea of the multiplier effect? Show answer Answer John Maynard Keynes Show question Question Who makes up the four sector economy? Show answer Answer Households, firms, the government sector, and the foreign sector. Show question Question Leakages consist of _____, _______, and ________ because the money spent on those does not continue to cycle in the economy. Show answer Answer taxes, savings, imports Show question Question If the Marginal Propensity to Save (MPS) is low, the multiplier effect will be _______. Show answer Answer stronger Show question Question If the Marginal Propensity to Consume (MPC) is high, the multiplier effect will be _______. Show answer Answer stronger Show question Question Why is the multiplier effect beneficial to the economy? Show answer Answer The multiplier effect benefits the economy because a small increase in expenditure, investment, or tax cut, has a magnified effect on the economy Show question Question Injections into the economy are ______, __________, and _________ because they increase the supply of money flowing through the economy. Show answer Answer exports, investments, government spending Show question Question The _______ tells us how much an autonomous change in aggregate spending has affected GDP. Show answer Answer Expenditure multiplier Show question Question The ________ describes how much a change in the tax level changes GDP. Show answer Answer Tax multiplier Show question Question The _________ combines the expenditure multiplier and the tax multiplier to calculate the total change in GDP. Show answer Answer Balanced budget multiplier Show question Question The _______ is the rise in consumer spending when disposable income increases by a dollar. Show answer Answer Marginal Propensity to Consume Show question Question The _______ is the rise in household savings when disposable income increases by a dollar. Show answer Answer Marginal Propensity to Save Show question Question Find the expenditure multiplier if consumer spending increases by$50, and disposable income increases by  $100. Show answer Answer 2 Show question Question The government decreases taxes. This causes consumer spending to rise by$10 million and disposable income increases by $30 million. What is the tax multiplier? Show answer Answer .5 Show question Question The government increases taxes. This causes consumer spending to rise by$20 million and disposable income increases by $80 million. What is the tax multiplier? Show answer Answer -.33 Show question Question The government spends$700 million on infrastructure. Disposable income is $50 million and consumer spending increased to$20 million. What is the change in GDP?

$1.166 billion Show question Question The change in consumer spending is$40 and the change in disposable income is \$100. What is the MPS?

.6

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Question

True or False: The expenditure multiplier is stronger than the tax multiplier.

True

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Question

True or False: the multiplier effect refers to the result a change in spending has on nominal GDP.

False

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Question

True or False: You can find the MPS or MPC by subtracting it by 1.

True

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Question

True or False: Taxes have an inverse relationship to consumer spending.

True

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Question

True or False: You do not need the MPC or MPS to accurately calculate multipliers.

False

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Question

Explain why the tax multiplier formula is negative.

Taxes have an inverse relationship to consumer spending.

Show question

Question

Explain how you can find MPS with MPC.

Subtract the MPC by 1.

Show question

Question

Explain how you can find MPC with MPS

Subtract MPS by 1

Show question

Question

Explain how the multiplier effect benefits the economy.

A small increase in expenditure, investment, or tax cut, has a magnified effect on the economy.

Show question

Question

True or False: The spending multiplier is stronger than the tax multiplier.

True

Show question

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