# Marginal propensity to save

The marginal propensity to save measures the part of income earmarked for saving or investing when income increases by one unit.

In other words, the marginal propensity to save measures the part that consumers, be they organizations, individuals or territories, dedicate to saving when their income grows. It is an indicator, among others, of the level of development of a society, since as a society enjoys a higher level of economic development, it will allocate a greater part of the income to savings or investment, for having covered all the possible consumption, which is the other part to which the income is dedicated.

This ratio is an indicator of the distribution of disposable income, so if the marginal propensity to save is around 0.25, it means that for each increase in income, the individual spends 25% on saving. Meanwhile, the remaining 75% would go to consumption.

The marginal term refers to movements (increases or decreases) of economic variables, in this case income. Thus, it clarifies to what extent an individual, organization or country uses the growth in income.

## Formulation

The function of aggregate consumption is:

where:

C: Consumption expenditure

Y: Disposable income

a: Autonomous consumption

c = 1 – s: Marginal propensity to consume or, in other words, the part of income increases destined for consumption.

In this case, since they are marginal values, that is, increments per unit, we solve for c.

c: C / Y = a / Y + c

and in turn, we have that C / Y = a / Y + (1-s), since c = 1-s

We substitute c for 1-s, where s is the marginal propensity to save, that is, that part of the increases in income that we do not dedicate to consumption, such that Y = C + S (where S is the income earmarked for savings), and to calculate the increases in rent per unit, we use the following expression:

where Δ is the increments of the variables in one unit.

Finally, we substitute again so that savings and consumption add up to the total income (1 = ΔC / ΔY + ΔS / ΔY), reaching the initial conclusion of 1 = c + s, where s is the marginal propensity to consume .