Marginal savings rate

The marginal savings rate (also: marginal tendency to save , Grenzrate zum Sparen ) describes the proportion of income that private households in an economy save on the next additional (marginal) income unit , i.e. H. do not consume (spend). It is fundamental to the development of the Keynesian total model and the multiplier .

The marginal propensity to save can be derived from the consumption function. In a simple (model) economy without the state and foreign trade, the national income can be represented as follows:

(a) , d. That is, the entire national income ( ) goes to the private sector, which consumes ( ) and saves ( ) it. ${\displaystyle {\mathit {Y}}=C+S\!}$ ${\displaystyle Y}$ ${\displaystyle C}$ ${\displaystyle S}$

Both consumption and saving can thus be assumed to be dependent on national income, i.e. This means that consumption increases as income increases:

(b) ${\displaystyle C=\mathbb {C} _{a}+cY,{\mbox{ wobei }}\mathbb {C} _{a}>0{\mbox{ und }}0<c<1}$

${\displaystyle \mathbb {C} _{a}}$describes the so-called autonomous consumption , which is carried out with an income of zero ( ) (saving, e.g. by selling assets such as securities or residential property). For every increase in income by one currency unit, consumption increases by currency units. If the propensity to consume is marginal , then consumption increases by € 0.85 with every increase in income of € 1.00: ${\displaystyle Y=0}$ ${\displaystyle c}$ ${\displaystyle c=0{,}85}$

${\displaystyle C=\mathbb {C} _{a}+0{,}85\cdot 1=\mathbb {C} _{a}+0{,}85}$

The marginal propensity to consume is less than one, i.e. This means that if the income is increased by one euro, a share is spent on consumption. The rest is saved because of the saving function ${\displaystyle c}$

(c) applies. ${\displaystyle {\mathit {S}}=Y-C\!}$

By substituting (b) in (c) you get the marginal savings rate

(d) ${\displaystyle S=Y-(\mathbb {C} _{a}+cY)=-\mathbb {C} _{a}+(1-c)Y}$

or in other words: ${\displaystyle {\mathit {s}}=1-c\!}$

In the example, the marginal propensity to save is . ${\displaystyle {\mathit {s}}=1-0{,}85=0{,}15\!}$