Marginal propensity to save

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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. For example, if a family earns one extra dollar, and the marginal propensity to save is 0.35, then of that dollar, the family 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. It is crucial to Keynesian economics and is the key variable in determining the value of the multiplier.

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

$MPS=\frac{dS}{dY}$

In other words, the marginal propensity to save is measured as the ratio of the change in saving to the change in income, thus giving us a figure between 0 and 1. It is the opposite of the marginal propensity to consume (MPC). In the example above, the marginal propensity to consume would be 0.65. In general MPS = 1 - MPC.