  Tuesday  January 31, 2023
 AmosWEB means Economics with a Touch of Whimsy! A POSTERIORI: A conclusion reached through logical reasoning based on facts and observations about the real world. This notion is closely related to the scientific verification of hypotheses and the identification of principles. A similar sounding, but opposite term is a prior, which is a unverified presumption made before an analysis is undertaken. For example, in the study of economics of crime you might assume, a priori, that people are basically "good", and conclude, a posteriori, that people are more likely to commit crimes when the threat of capture and conviction is lower.                              SAVING FUNCTION:

A mathematical relation between saving and income by the household sector. The saving function can be stated as an equation, usually a simple linear equation, or as a diagram designated as the saving line. This function captures the saving-income relation, the flip side of the consumption-income relation that forms one of the key building blocks for Keynesian economics. The two key parameters of the saving function are the intercept term, which indicates autonomous saving, and the slope, which is the marginal propensity to save and indicates induced saving. The injections-leakages model used in Keynesian economics is based on the saving function.
The saving function is the starting point of the Keynesian economics analysis of equilibrium output determination using the injections-leakages model. It captures the relation between saving by the household sector and income. Because income is used for either consumption or saving, the saving function is a complement of the consumption function. Both reflect the fundamental psychological law put forth by John Maynard Keynes that consumption expenditures (and saving ) by the household sector depend on income and than only a portion of additional income is used for consumption, with the rest used for saving.

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

The saving function can represented in a general form as:
 S = f(Y)
where: S is saving, Y is income (national or disposable), and f is the notation for a generic, unspecified functional form.

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
where: S is saving, Y is income (national or disposable), c is the intercept, and d is the slope.

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
where: C is consumption expenditures, Y again is income, a is the intercept, and b is the slope.

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

 S = - a + (1-b)Y
where: S is saving and Y is income. However, now the intercept is -a rather than c and the slope is (1-b) rather than d. This alternative specification shows the connection between the saving function and the consumption function. The intercept of the saving function (-a) is the negative of the intercept of the consumption function (a). The slope of the saving function (1-b) is one minus the slope of the consumption function (b), meaning that the sum of the marginal propensity to consume (b) and the marginal propensity to save (1-b) is equal to one, which is just another way of saying that a portion of additional income is consumed and the rest is saved.

### Then, The Graph

Saving Line The saving function is also commonly presented as a diagram or saving line, such as the one presented in the exhibit to the right. This red line, labeled S in the exhibit is positively sloped, indicating that greater levels of income generate greater saving by the household sector. The specific saving function illustrated in this exhibit is:
 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

The saving function captures the relation between saving and income. However, income is not the only factor influencing saving.
 S = f(Y, OF)
where: S is saving, Y is income (national or disposable), and now OF is specified as other factors affecting saving. These other factors are more commonly referred to as consumption expenditures determinants because the primarily influence consumption, but also subsequent affect saving. Some of the more notable consumption/saving determinants are consumer confidence, interest rates, and wealth.

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.

These determinants cause saving to change even though income does not change. Or another way of stating this, determinants cause saving to change at every level of income. For a linear saving function, this change is reflected by a change in the intercept term (-a). For a saving line, the change is seen as an upward or downward shift.

 <= SAVING SAVING-INVESTMENT MODEL => Recommended Citation:

SAVING FUNCTION, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2023. [Accessed: January 31, 2023].

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