# 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 {where}} \ mathbb {C} _ {a}> 0 {\ mbox {and}} 0

${\ displaystyle \ mathbb {C} _ {a}}$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. ${\ displaystyle {\ mathit {S}} = YC \!}$

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 . ${\ displaystyle {\ mathit {s}} = 1-0 {,} 85 = 0 {,} 15 \!}$