Because saving is the complement of consumption, the marginal propensity to save reflects key aspects about household consumption and saving activity. This activity is critical to the macroeconomy and the study of Keynesian economics. First, the MPS captures induced saving, which is one aspect of the fundamental psychological law of consumer spending proposed by John Maynard Keynes as a key difference between his Keynesian theory and classical economics. Second, the MPS is the slope of the saving line, which makes it the foundation for Keynesian injections-leakages model. Third, the MPS affects the multiplier process and affects the magnitude of the expenditures and tax multipliers.

The MPS Formula

MPS

=

change in saving change in income

• First, it quantifies induced saving, that is, how much of each extra dollar of income is used for saving. If income changes by $1, then saving changes by the value of the MPS. Income induces the change in saving at a rate measured by the MPS.


• Second, the MPS is actually a measure of the slope of the saving line. The measurement of slope is generally given as the "rise" over the "run." For the saving line, the rise is the change in saving and the run is the change in income.

A Schedule Of Numbers

Saving Schedule

The marginal propensity to save is calculated by dividing the change in saving in the second column by the change in income in the first column. Beginning at the top of the schedule, household income increases from $0 to $1 trillion. This $1 trillion change in income induces a change in saving from -$1 trillion to -$0.75 trillion, a change of $0.25 trillion.

Running the numbers through the MPS formula gives:

MPS

=

change in saving change in income

=

$0.25 $1

=

0.25

In fact, a quick run through the numbers for each change in saving shows that the MPS is constant and equal to 0.25. To display all marginal propensity to save values, click the [MPS] button.

While the MPS is not necessarily constant at for all changes in income (in fact, the MPS tends to increase at higher income levels), most analysis of saving generally works with a constant MPS. It tends to make subsequent calculations for things like the multiplier a lot easier.

The Slope Of The Line

Saving Line

This saving line reflects a plot of the numbers in the saving schedule as well as the following saving function:

S

= -

1

+

0.25Y

The change in saving divided by the change in income is the specification of the marginal propensity to save. That is, the slope of the saving line is the marginal propensity to save. To highlight this point, click the [Slope] button in this exhibit.

Moreover, because the saving line is a straight line, the slope is constant over the entire range of income. This means that the marginal propensity to save is also constant, a conclusion reached when working through the saving schedule.

Multiplier

The magnified change occurs because a change in production (such as what occurs when investment expenditures purchase capital goods) generates income, which then induces consumption. However, the resulting consumption is also an expenditure on production, which generates more income, which induces more consumption. This next round of consumption also triggers a change in production, which generates even more income, and which induces even more consumption.

And on it goes, round after round. The end result is a magnified, multiplied change in aggregate production initially triggered by the change investment, but amplified by the change in consumption.

The MPS enters into the process because it indicates the division of extra income between consumption and saving. It determines how much saving is induced with each change in production and income, and thus how much consumption is induced. If the MPS is smaller, then the multiplier process is also greater as less saving is induced, but more consumption is induced, with each round of activity.

This connection between the multiplier process and the marginal propensity to save is illustrated in the standard formula for a basic expenditures multiplier:

expenditures multiplier

=

1 marginal propensity to save

For example, a marginal propensity to save of 0.25 results in a multiplier of 4. In contrast, a smaller marginal propensity to save of 0.2 results in a larger multiplier of 5.

Other Marginals

Here a few of the more important marginals:

• Marginal Propensity to Consume: The flip side of saving is consumption. The fundamental psychological law indicates that an increase in income induces changes in both consumption and saving. The marginal propensity to consume (MPC) quantifies the consumption part of this relation. It indicates the change in consumption resulting from a change in income. In fact, if the MPC and MPS are calculated based on after-tax disposable income, then the two marginals sum to one: MPC + MPS = 1.


• Marginal Propensity to Invest: Consumption is not the only one of the aggregate expenditures induced by income and with a corresponding marginal. The marginal propensity to invest (MPI) is the change in investment induced by a change in income. The induced change in investment is not nearly as big as saving, but it does affect the slope of the aggregate expenditures line and the size of the multiplier.


• Marginal Propensity for Government Purchases: Government purchases, like investment, is also induced by income and has a corresponding marginal. The marginal propensity for government purchases (MPG) is the change in government purchases induced by a change in income. The induced change in government purchases is related to the induced change in tax collections, and while it also small compared to saving, but it too affects the slope of the aggregate expenditures line and the size of the multiplier.


• Marginal Propensity to Import: The last of the four aggregate expenditures, net exports (exports minus imports), also has a corresponding marginal. However, the marginal is not for net exports proper, but for the imports part. The marginal propensity to import (MPM) is the change in imports induced by a change in income. The induced change in imports is closely connected to the marginal propensity to save. That is, a portion of saving is actually used to purchase imports, which is reflected the marginal propensity to import.

Average Propensity to Save

The formula for calculating average propensity to save (APS) looks a lot like that for the MPS, but with important differences:

APS

=

saving income