Marginal propensity to save - AbsoluteAstronomy.com

The marginal propensity to save (MPS) refers to the increase in saving (non-purchase of current goods and services) that results from an increase in income i.e. The marginal propensity to save might be defined as the proportion of each additional dollar of household income that is used for saving. It is also used as an alternative term for the slope of the saving line. For example, if a household earns one extra dollar, and the marginal propensity to save is 0.35, then of that dollar, the household will spend 65 cents and save 35 cents. It can also go the other way, referring to the decrease in saving that results from a decrease in income.

The MPS plays a central role in Keynesian economics

Keynesian economics

Keynesian economics is a school of macroeconomic thought based on the ideas of 20th-century English economist John Maynard Keynes.Keynesian economics argues that private sector decisions sometimes lead to inefficient macroeconomic outcomes and, therefore, advocates active policy responses by the...

as it quantifies the saving-income relation, which is the flip side of the consumption-income relation, and thus it reflects the fundamental psychological law

Fundamental psychological law

John Maynard Keynes, in 1936, proposed the psychological law in his work - The General Theory of Employment, Interest and Money. The law basically captures and understands the essential spending behavior of the household sector. Keynes uses the term 'psychology' in his law but the law is just a...

. Marginal Propensity to Save is also a key variable in determining the value of the multiplier

Multiplier (economics)

In economics, the fiscal multiplier is the ratio of a change in national income to the change in government spending that causes it. More generally, the exogenous spending multiplier is the ratio of a change in national income to any autonomous change in spending In economics, the fiscal...

Calculation of MPS

MPS can be calculated as the change in savings divided by the change in income.

Or mathematically, the marginal propensity to save (MPS) function is expressed as the derivative of the savings (S) function with respect to disposable income

Disposable income

Disposable income is total personal income minus personal current taxes. In national accounts definitions, personal income, minus personal current taxes equals disposable personal income...

(Y).

where, dS=Change in Savings and dY=Change in income.

An example

{| class="wikitable"

|-
! width=20%|
!! width=40%| Savings
!! width=40%| Income
|-
| align="center" | A
| align="center" | 200
| align="center" | 1000
|-
| align="center" | B
| align="center" | 400
| align="center" | 1500
|}

Now, MPS can be calculated as follows:

Change in savings = (400-200) = 200

Change in income = (1500-1000) = 500

MPS = (Change in savings) / (Change in income)

so, MPS = 200/500 = 0.4

This implies that for each additional one unit of income, the savings increase by 0.4.

There are different implications of this above-mentioned formula.

First it quantifies induced savings.Induced saving is the portion of saving that responds to changes in income.In other words, induced saving can be defined as the household saving that depends on income or production (especially disposable income, national income, or even gross domestic product).

Second, it is a measure of slope of the savings function.

Value of MPS

Since MPS is measured as ratio of change in savings to change in income, its value lies between 0 and 1.
Also, marginal propensity to save is opposite of marginal propensity to consume.

Mathematically,
In a closed economy, MPS + MPC = 1since an increase in one unit of income will be either consumed or saved.

In the above example, If MPS = 0.4, then MPC = 1 - 0.4 = 0.6.

Generally, it is assumed that value of marginal propensity to save for the richer is more than the marginal propensity to save for the poorer. If income increases for both parties by $1, then the propensity to save for a richer person would be more than that for the poorer person.

Slope of Saving line

Marginal propensity to save is also used as an alternative term for slope of saving line.
The slope of a saving line is given by the equation S = -a + (1-b)Y, where -a refers to autonomous savings and (1-b) refers to marginal propensity to save (here b refers to marginal propensity to consume but as MPC + MPS = 1, so (1-b) refers to MPS).

In this diagram, the savings function is an increasing function of disposable income i.e. savings increase as income increases.

Multiplier effect

An important implication of Marginal Propensity to Save is measurement of the multiplier. A multiplier measures the magnified change in aggregate product i.e. the gross domestic product, resulting from a change in an autonomous variable (for example, government expenditure,investment expenditures,etc.).

The effect of a change in production creates a multiplied impact because it creates income which further creates consumption. However, the resulting consumption is also an expenditure which thus, generates more income, which creates more consumption. This next round of consumption leads to a further change in production, which generates even more income, and which induces even more consumption.

And thus,as it goes on and on, it results in a magnified, multiplied change in aggregate production initially triggered by a change in autonomous variable, but amplified by the creation of more income and increase in consumption.

Mathematical implication

Mathematically, the above effect can be stated as:

In round 1, there is a change in an autonomous variable (say the government invests in a bridge making project for which it approaches a construction company) by an amount $1 (just an assumption for simplification). Now let the marginal propensity to consume for the construction company be 'c'. Thus, the construction company would spend an amount c×$1 i.e. $c.
In round 2, the construction company incurs expenditure ($c) by procuring raw materials, say cement,steel,gravel,mortar,etc. from respective companies and thus, this amount $c becomes income for these companies. Now again the marginal propensity to consume for these companies is same as the construction company at 'c' and thus, their consumption becomes c×$c i.e. $c².

And it goes on and on.
We can express this as:

{| class="wikitable"

|-
!width=20% |Round
!!width=40% |Change in income
!!width=40% |Amount consumed
|-
| align="center"|Round 1
| align="center"|$1
| align="center"|$c
|-
| align="center"|Round 2
| align="center"|$c
| align="center"|$c²
|-
| align="center"|Round 3
| align="center"|$c²
| align="center"|$c³
|-
|}

And so on...

Thus, total magnified change in production due to change in an autonomous variable by $1

= 1 + c + c² + .................(infinite series)
=

Measuring the multiplier

The effect of a multiplier effect

Multiplier (economics)

can be measured as:

If the MPS is smaller, then the multiplier process is also greater as less saving is induced, and more consumption is induced with each round of activity.

For example, if MPS = 0.2, then multiplier effect is 5, and if MPS = 0.4, then the multiplier effect is 2.5. Thus, we can see that a higher propensity to save implies a lower multiplier effect and vice-versa.

External links

"Marginal propensity to save" Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc., 2011. Web.
"Marginal Propensity to save", AmosWEB LLC,Economic WEB*pedia,2010-2011.[Accessed: November 8,2011] Web.