The Multiplier Formula

Consider if you will the simple formula for the multiplier m stated in terms of the marginal propensity to consume and the marginal propensity to save.

m

=

1 marginal propensity to save

=

1 (1 - marginal propensity to consume)

If consumption is the only induced expenditure, then the marginal propensity to consume is the slope of the aggregate expenditures line. However, in more complex models, the slope of the aggregate expenditures line depends on other induced factors, which also affects the value of the multiplier.

As such, a more general formula for the multiplier m is stated as the slope of the aggregate expenditures line.

m

=

1 (1 - slope of aggregate expenditures line)

Changing Slopes

Changing Slopes

• This diagram displays an initial equilibrium of $12 trillion found at the intersection of the aggregate expenditures line and the 45-degree line. The slope of the aggregate expenditures line is equal to 0.75, which is the marginal propensity to consume in this simple example but it could be based on any number of induced activities.


• An investment injection of $1 trillion shifts the aggregate expenditures line higher, triggering the multiplier process and a generating a new equilibrium at $16 trillion. Click the [Inject Investment] button to illustrate this.


• The $4 trillion change in aggregate production is four times the initial change in investment. The multiplier has a value of 4 because the slope of the aggregate expenditures line is 0.75.

• Click the [Flatter Line] to display this new aggregate expenditures line. Note that this new line intersects the 45-degree line at the initial $12 trillion equilibrium level of production. This makes it possible to compare the two aggregate expenditures lines.


• Now consider the multiplier process triggered by a $1 trillion injection with this steeper aggregate expenditures line. Click the [Inject Again] button. You should now see that the new flatter aggregate expenditures line shifts vertically by the same amount as the original, flatter line.


• However, the resulting equilibrium level is different. The intersection between the new aggregate expenditures line and the 45-degree line results in an equilibrium level of aggregate production of $14 trillion rather than $16 trillion.


• The change in aggregate production is now $2 trillion, half as much as the original multiplier change of $4 trillion. This change in production is two times the initial change in investment, giving a multiplier of 2. This multiplier value can also be found by plugging 0.5 into the formula presented above.