Aggregate Expenditure Multiplier

What is Aggregate Expenditure Multiplier?

Aggregate expenditure (AE) is the sum of consumption, investment, government purchases, and net export. Of these four sectors, the consumption represents the largest share.

The consumption function:  C = Co + MPC (Yd)

C = total consumption

Co = autonomous consumption whose amount is independent of disposable income

MPC = marginal propensity to consume. This is a fraction between 0 and 1; and MPC is equal to change in consumption brought about by a change in disposable income.

(MPC = change in C / change in Yd )

Yd = disposable income.

A similar concept as MPC is MPS: marginal propensity to save. It is equal to change in savings (S) brought about by a change in disposable income.

(MPS = change in S / change in Yd)

Since all income must be either consumed or saved, then any change in income must also be consumed or saved. Therefore: MPC + MPS = 1

The average propensity to consume (APC) is the portion of income spent on consumption.

(APC = C / Yd)

The average propensity to save (APS) is the portion of income saved.

(APS = S / Yd)

Again, APC + APS = 1

The slope is referred to as MPC (marginal propensity to consume). It's a number between 0 and 1 that refers to how much of each dollar you spend. Say the number is 0.90... then if you get an additional dollar, then you spend 90 cents of it and save 10 cents.

How is it related to the multiplier? If the government gives me $100 for some service, then GDP increases by $100... but what do I do with the $100? I spend 90% of it and save 10%. So I spend 90 dollars .... but that means GDP has now increased by $190 in total! I spend it on something (let's say a hooker!) ... she gets the $90 and spends 90% of it and saves 10%. So, GDP increases by another $81. And the process goes on and on until we are left spending pennies. When you look up the multiplier equation, it's just the short cut to get the overall net increase that GDP goes through from that initial $100 spent by the government.

Multiplier = 1/(1-MPC)

Or in my example it would equal 10 ... since 1/(1-0.90) = 10

So, that $100 actually causes GDP to increase by $1000 once it goes through every single one of those spending 'rounds' I mentioned above (the equation for the multiplier actually assumes an infinite number of rounds).

Source;

with help of illustrations from ect5150

Kaps.