# Marginal propensity to save

The marginal propensity to save (MPS) is the fraction of an increase in income that is not spent and instead used for saving. It is the slope of the line plotting saving against income.[1] 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. Likewise, it is the fractional decrease in saving that results from a decrease in income.

The MPS plays a central role in Keynesian economics as it quantifies the saving-income relation, which is the flip side of the consumption-income relation, and according to Keynes it reflects the fundamental psychological law. The marginal propensity to save is also a key variable in determining the value of the multiplier.

## Calculation

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

${\displaystyle MPS={\frac {\text{Change in Savings}}{\text{Change in Income}}}}$

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

${\displaystyle MPS={\frac {dS}{dY}}}$  where, dS=Change in Savings and dY=Change in income.

### An example

Saving Income
A 200 1000
B 400 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[check spelling] saving is the portion of saving that responds to changes in income.[2] 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).[3]
• Second, it is a measure of slope of the savings function.

#### Value

Since MPS is measured as ratio of change in savings to change in income, its value lies between 0 and 1.[4] Also, marginal propensity to save is opposite of marginal propensity to consume.

Mathematically, in a closed economy, MPS + MPC = 1,[5][6] since 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.[7] ## 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,[8][9] 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.[10] The savings function ## 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:

Round Change in income Amount consumed
Round 1 $1$c
Round 2 $c$c2
Round 3 $c2$c3
And so on.

The end result is a magnified, multiplied change in aggregate production initially triggered by the change in investment, but amplified by the change in consumption i.e. the initial investment multiplied by the consumption coefficient (Marginal Propensity to consume).

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.[11]

Thus, in this highly simplified model, total magnified change in production due to change in an autonomous variable by \$1

                 = ${\displaystyle 1+c+c^{2}+\cdots ={\frac {1}{1-c}}={\frac {1}{1-MPC}}={\frac {1}{MPS}}}$


### Measuring the multiplier

The effect of a multiplier effect can be measured as:

${\displaystyle {\text{Spending Multiplier}}={\frac {1}{MPS}}}$

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.[12]

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 lower propensity to save implies a higher multiplier effect.

## Notes

1. ^ Blanchard, O. (2006). Macroeconomics. (Fourth ed., p. 59). Pearson Education Inc.
2. ^ Robert Marks, "Macroeconomics for manager", Lecture Series, March 1997, Australian Graduate School of Management, University of New South Wales
3. ^ "Induced Savings", AmosWEB LLC, Economic WEB*pedia,2010-2011.[Accessed: November 8, 2011] Web.
4. ^ Blanchard, O. (2006). Macroeconomics. (Fourth ed., p. 59). Pearson Education Inc.
5. ^ Chamberlin, G., & Yeuh, L. (2006). Macroeconomics. (p. 23). Italy: Thomson Learning Inc.
6. ^ Ahuja, H. L. (2008). Macroeconomics : Theories and policies. (14th ed., pp. 125-126). Delhi: S.Chand and Co. Ltd.
7. ^ Carroll, C. (2000) Why do the rich save so much, in Does Atlas Shrug? Economic Consequences of Taxing the Rich, Slemrod, J. (Ed.), Cambridge University Press, London.
8. ^ Froyan, R. T. (2005). Macroeconomics : Theories and policies. (Eighth ed., p. 123,130). Pearson Education Inc. Pvt. Ltd. and Dorling Kindersley Publishing Inc.
9. ^ Dwivedi, D. N. (2005). Macroeconomics: Theory and policy. (2nd ed., p. 73). New York: Tata McGraw-Hill Publishing Co. Ltd.
10. ^ Dornbusch, R., Fischer, S., & Startz, R. (2004). Macroeconomics. (Ninth ed., pp. 217,221-23). New York: Tata McGraw-Hill Publishing Co. Ltd.
11. ^ http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=marginal%20propensity%20to%20save
12. ^ Chamberlin, G., & Yeuh, L. (2006). Macroeconomics. (p. 23). Italy: Thomson Learning Inc.