Multiplier effect

In economics, the multiplier effect refers to the fact that an increase of an economic aggregate may lead to an increase of this aggregate or another greater than the initial raise.

The multiplier effect is also known by bankers. An initial mortgage creates a deposit on a client account. This deposit can be partially lent to another client and so on.

Spending multiplier

This multiplier effect is an important idea according to Keynesian economists. It explains how a budget deficit can have a strong influence on the national output, depending on the propensity to consume. The governmental spending creates a new income for private agents who will spend a part of it and so on.

Imagine an closed economy in which private agents consume in average 80% of their income. If the government increases its purchases by 100, then the national output will increase by 500.

Agent	Consumption	Saving
Government	100	0
Client of the previous agent	80	20
Client of the previous agent	64	16
Client of the previous agent	51	13
Client of the previous agent	41	10
Client of the previous agent	33	8
Client of the previous agent	26	6
and so on ...	...	...
Total	500	125

In mathematics, this result is known as the sum of a convergent geometric serie.

An other demonstration relies on the following accountant relation in a closed economy :

Income = Consumption + Investment
Income = Private Consumption + Governmental Consumption + Saving - Taxes
Y = C + G + I - T
Since C = cY with c the propensity to consume, then
Y = cY + G + I - T
(1-c)Y = G + I - T
Y = (G + S - T)/(1-c)
Thus, an increase of G by 1 implies an increase of Y by 1/(1-c).