Expenditure Multiplier

Aggregate Expenditure

Aggregate expenditure or aggregate spending, also known as GDP, is the total spending of household consumption, government spending, investment spending, and net exports added together. It is how we calculate a nation's total spending on domestically produced final goods and services.

$AE=C+I+G+(X-M)$,

AE is aggregate expenditure;

C is household consumption;

I is investment spending;

G is government spending;

X is exports;

M is imports.

The expenditure multiplier measures the change in total real GDP that results from an initial change in one of the values above, except for imports and exports. Then, throughout the rounds of spending, there are additional changes in aggregate expenditure that occur as a chain reaction to the first round.

Expenditure Multiplier Equation

The expenditure multiplier equation requires us to take a few other steps before we calculate the expenditure multiplier. First, we will make four assumptions to help us understand the expenditure multiplier. Then we will calculate the MPC and MPS because either one is a required part of the expenditure multiplier formula.

Assumptions of the Expenditure Multiplier

The four assumptions that we make when calculating the expenditure multiplier are:

• The price of goods is fixed. Producers are willing to supply additional goods if consumer spending increases without increasing the price of those goods.
• The interest rate is fixed.
• Government spending and taxes are zero.
• Imports and exports are zero.

These assumptions are made to simplify the expenditure multiplier that we have to make an exception when considering the government expenditure multiplier.

MPC and MPS formula

If a consumer's disposable income increases, it can be expected that they will spend a portion of this additional income and save a portion. Since consumers typically do not spend or save all of their disposable income, the MPC and MPS will always be a value between 0 and 1 if we assume that consumer spending does not exceed disposable income.

To determine the marginal propensity to consume, we use this formula:

$MPC=\frac{∆consumerspending}{∆disposableincome}$

So what happens to the portion of disposable income that is not spent? It goes into savings. Whatever additional income is not spent will be saved, therefore the MPS is:

$MPS=1-MPC$

Alternatively,

$MPS=\frac{∆consumersaving}{∆disposableincome}$

Calculating Expenditure Multiplier

Now we are finally ready to calculate the expenditure multiplier. Our money goes through several rounds of spending, where each round sees some of it going to savings. With each round of spending, the amount injected back into the economy diminishes and eventually becomes zero. To avoid adding up each and every round of spending to figure out the total increase of real GDP caused by an autonomous change in aggregate spending, we use the expenditure multiplier formula:

$expendituremultiplier=\frac{1}{1-MPC}$

The expenditure multiplier compares a nation's total change in real GDP after an autonomous change in aggregate spending to the size of that autonomous change in spending. This indicates that if we divide the total change in real GDP (ΔY) by the autonomous change in aggregate spending (ΔAAS), it is equal to the expenditure multiplier.

$\frac{\Delta Y}{\Delta AAS}=\frac{1}{1-MPC}$

Expenditure Multiplier Example

If we take a look at an example of the expenditure multiplier, it will make more sense. The expenditure multiplier calculates how much real GDP increases after the economy experiences an autonomous change in aggregate spending. An autonomous change is a change that is the cause of the initial increase or decrease in spending. It is not the result. It could be something like a change in the tastes and preferences of society or a natural disaster that requires changes in spending.

Now that we have the expenditure multiplier, we can finally calculate the impact on total real GDP. If the initial increase in spending is $320 million, and the MPC is 0.75, we know that with every round of spending, 75 cents of every dollar spent will go back into the economy, and 25 cents will be saved. To find the total increase in real GDP, we add up the increases in GDP after every round. Here is a visual representation:

Table 1. Expenditure multiplier, Vaia Originals

Adding all of those values together would take a long time. Fortunately, since it is an arithmetic series and we know how to calculate the expenditure multiplier using the MPC, we do not have to add everything up individually. Instead, we can use this formula:

$totalincreaseinrealGDP=\frac{1}{1-MPC}\times \Delta Autonomouschangeinaggregatespending$

Now we insert our values:

$totalincreaseinrealGDP=\frac{1}{1-0.75}\times \$320million=4\times \$320million$

The total increase in real GDP is $1,280 million or $1.28 billion.

Expenditure Multiplier Effects

The effect of the expenditure multiplier is an increase in a nation's real GDP. This happens because the nation experiences a rise in consumer spending. The expenditure multiplier has a positive effect on the economy because it means that a small increase in spending causes a larger increase in total real GDP. The expenditure multiplier also means that a small increase in spending can make a big difference in terms of people's disposable income.

How the expenditure multiplier works

The expenditure multiplier works by increasing the effect of each additional dollar spent in the economy every time it is spent. If there is an autonomous change in aggregate spending, people will earn more money in the form of increased wages and profits. They then go out and spend a portion of this new income on things like rent, groceries, or a trip to the mall. This translates as an increase in wages and profits for other people and businesses, who then spend another portion of this income and save the rest. The money will go through multiple rounds of spending until there is eventually nothing left of the original dollar that was spent. When all those rounds of spending are added together, we get the total increase in real GDP.

Types of Expenditure Multipliers

There are several types of expenditure multipliers, just like there are several types of spending. Different types of expenditure multipliers are government expenditure multiplier, consumer expenditure multiplier, and investment expenditure multiplier. Although they are all different types of expenditures, they are calculated mostly the same. The government expenditure multiplier makes an exception to the assumption that government spending and taxes are zero.

• The government expenditure multiplier refers to the impact that government spending has on total real GDP.
• The consumer expenditure multiplier refers to the impact that a change in consumer spending has on total real GDP.
• The investment expenditure multiplier refers to the impact that a change in investment expenditure has on total real GDP.

Table 2. Types of expenditure multipliers, Vaia Originals