From Consumption To Saving

The exhibit to the right can be used to derived the saving line from the consumption line. The top panel presents a standard consumption line. This line is a plot of a consumption function specified as:

C

=

1

+

0.75Y

The key to deriving the saving line is the addition of a 45-degree line. This line indicates every point in the upper panel in which consumption measured on the vertical axis is exactly equal to income measured on the horizontal axis. Such a line has a slope of one and thus exactly bisects the 90-degree angle formed by the vertical and horizontal axes. Click the [45-degree Line] button to make this addition.

Because the 45-degree line indicates equality between consumption and income, when compared to the consumption line it can also be used to indicate saving. In particular, the vertical difference between the 45-degree line and the consumption line is saving. If the 45-degree line lies below the consumption line, as is the case for relatively low levels of income, then saving is negative. If the 45-degree line lies above the consumption line, as is the case for relatively high levels of income, then saving is positive.

The saving line can be derived by transferring the vertical distance between the 45-degree line and the consumption line from the top panel to the bottom panel of the exhibit. The bottom panel measures saving on the vertical axis and income on the horizontal axis. A click of the [Saving Line] works through the derivation. Note how the vertical distance in the top panel is first identified, then this value is plotted in the bottom panel.

Once all points are plotted, the result is the red saving line labeled S. The two features of the saving line are slope and intercept.

• Slope: The slope is positive, but less than one. In fact, the slope of the saving line is numerically equal to the marginal propensity to save (MPS). In this case the slope is equal to 0.25. The positive slope reflects induced saving--more income means more saving. Click the [Slope] button to illustrate.


• Intercept: The saving line intersects the vertical axis at a value of -$1 trillion. This intersection point is autonomous saving--saving unrelated to income. Click the [Intercept] button to illustrate.

Saving Schedule

• One: Supply Schedule: One alternative is simply to plot the saving-income values that make up a saving schedule, such as the one presented to the right. Once the points are plotted, they can be connected to form the saving line. A quick comparison of the numbers in the schedule and the saving line derived above should indicate the consistency of either approach.


• Two: Supply Function: Another alternative is to plot the saving line using the saving function. The two key bits of information needed for this task are the intercept and the slope. The following linear saving function can be used to illustrate.

  S

  = -

  1

  +

  0.25Y

  where: S is saving and Y is income (national or disposable). The intercept (or autonomous saving) is $1 trillion and the slope (or induced saving, which is also the marginal propensity to save) is 0.25.
  
  The saving line can be constructed by simply drawing a line with slope 0.25 that emerges for the vertical axis at intercept $1. A quick calculation of the slope and intercept of the saving line derived above should indicate the consistency of this approach, too.