The marginal propensity to save (MPS) is the fraction of an increase in

income Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms. Income is difficult to define conceptually and the definition may be different across fields. For ...

that is not spent and instead used for

saving Saving is income not spent, or deferred consumption. Methods of saving include putting money aside in, for example, a deposit account, a pension account, an investment fund, or as cash. Saving also involves reducing expenditures, such as recur ...

. It is the slope of the line plotting saving against income. 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 Keynesian economics ( ; sometimes Keynesianism, named after British economist John Maynard Keynes) are the various macroeconomic theories and models of how aggregate demand (total spending in the economy) strongly influences economic output an ...

as it quantifies the saving-income relation, which is the flip side of the consumption-income relation, and according to

Keynes John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in m ...

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. :

MPS=\frac

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 is total personal income minus current income taxes. In national accounts definitions, personal income minus personal current taxes equals disposable personal income. Subtracting personal outlays (which includes the major c ...

(Y). :

MPS=\frac

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

Value

Also, marginal propensity to save is opposite of marginal propensity to consume.

Slope of saving line

Multiplier effect

Mathematical implication

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

1 + c + c^2 + \cdots
                  =\frac
                  =\frac = \frac

Measuring the multiplier

Notes

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. ccessed: November 8, 2011Web. {{DEFAULTSORT:Marginal Propensity To Save Macroeconomics Economics curves Marginal concepts