Spending Multiplier#Tutorials

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	Tutorials relating to the topic of Spending multiplier.

The algebra of the spending multiplier identity[edit]

An injection of 100 currency units is assumed to be made into a circular flow of income model of the economy and that the marginal propensity to consume of its recipients is c (round 1).

Of the 100 units injected, an amount equal to 100 times c is spent (round 2)

The recipients of that amount spend the same proportion of it (round 3)

- and so on as below

	expenditure	saving
round 1	100
round 2	100c	100(1 - c)
round 3	100c2	100(1 - c)2
...
round n	100cn	100(1 - c)n

The total spending in the economy after n rounds is

100 + 100c + 100c² + 100c³ ....+ 100cⁿ

- which is a geometric progression.

It can be proved that such a geometric progression converges to the value  100/(1 - c) as n approaches infinity.

The final outcome is therefore a total expenditure in the economy that is a multiple 1/(1 - c) of the initial injection, where 1 - c is definitionally equal to the marginal propensity to save.