This function is presented either as a mathematical equation, most often as a simple linear equation, or as the graphical saving line. In either form, income is measured as disposable income, national income, or occasionally gross domestic product.

The saving function makes it easy to divide saving into two basic types. Autonomous saving is the intercept term. Induced saving is the slope. Of no small importance, the slope of the saving function is also the marginal propensity to save (MPS).

First, The Equation

S

=

f(Y)

Depending on the analysis, the actual functional form of the equation can be linear, with a constant slope, or curvilinear, with a changing slope. The most common form is linear, such as the one presented here:

S

=

c

+

dY

The two key parameters that characterize the saving function are slope and intercept.

• Slope: The slope of the saving function (d) measures the change in saving resulting from a change in income. If income changes by $1, then saving changes by $d. This slope is generally assumed and empirically documented to be greater than zero, but less than one (0 < d < 1). It is conceptually identified as induced saving and the marginal propensity to save (MPC).


• Intercept: The intercept of the saving function (c) measures the amount of saving undertaken if income is zero. If income is zero, then saving is $c. The intercept is generally assumed and empirically documented to be negative (c < 0). It is conceptually identified as autonomous saving.

It is often useful to state the saving function using parameters for the consumption function.

C

=

a

+

bY

In this case, the saving function can be specified as:

S

= -

a

+

(1-b)Y

Then, The Graph

Saving Line

C

= -

1

+

0.25Y

The two primary characteristics of the saving function--slope and intercept--also can be identified with the saving line.

• Slope: The slope of the saving line presented here is positive, but less than one. In this case the slope is equal to 0.25. Click the [Slope] button to highlight.


• Intercept: The saving line intersects the vertical axis at a positive value of -$1 trillion. Click the [Intercept] button to highlight.

And Other Factors

S

=

f(Y, OF)

Consumer confidence is the general optimism or pessimism the household sector has about the state of the economy. More optimism means more consumption, and thus less saving. Interest rates affect the cost of borrowing the funds used to purchase durable goods. Higher interest rates mean less consumption and thus more saving. Wealth is the financial and physical assets owned by the household sector. More financial wealth means more consumption and less saving, while more physical assets mean less consumption and more saving.