Tariq Trier-Mørch

A person or household's additional income can be either spent or saved. The marginal propensities to consume and to save are respectively calculated by dividing the change in spending and in saving by the total change in income. The MPC formula can be expressed symbolically as:

$$MPC = \dfrac{ \Delta C}{\Delta I} $$

and the MPS formula is expressed similarly:

$$MPS = \dfrac{ \Delta S}{\Delta I} $$

The Greek letter {eq}\Delta {/eq} ("delta") is often used to signify a change in a certain quantity. The variables used in the formulas are:

The calculated decimal values of the MPS and MPC can be interpreted as the portion of each new dollar of income that will be saved or consumed, or converted to a percentage by multiplying by 100%. For example, an MPS value of 0.20 would represent 20 cents (0.20/$1.00) is saved out of every dollar, which is a savings rate of 20%.

Here are some example scenarios showing how to calculate MPS and how to calculate MPC.

Last year, Shireen earned $40,000 and was able to save $5,000. This year, she received a raise, increasing her salary to $45,000, which allowed her to save $6,000. What is her marginal propensity to save?

The MPS formula provided above can be applied, after identifying the year-over-year change in Shireen's income and savings. Her change in income was:

$$\Delta I = \$45,\!000 - \$40,\!000 = \$5,\!000 $$

The corresponding change in her savings was:

$$\Delta S = \$6,\!000 - \$5,\!000 = \$1,\!000 $$

Shireen's MPS was

$$MPS = \dfrac{ \Delta S}{\Delta I} = \dfrac{ \$1,\!000 } {\$5,\!000 } = 0.20 = 20\% $$

Shireen was able to save 20% of the additional income she earned, or 20 cents out of every additional dollar. The MPS can be interpreted visually as the slope between initial and final points on a graph of savings versus income.

Steve earns a regular bi-weekly pay check of $2,586.50. At the end of his most recent pay period, he received a $400 performance bonus, of which he spent $249.53 in a shopping spree. What is his marginal propensity to consume?

The change in Steve's income is only the amount of the bonus, since the regular, total amount represents his current level of income and not a change in circumstance. Stated symbolically:

$$\Delta I = \$400 $$

The corresponding change in consumption was

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