Spending multiplier#Tutorials

| Main Article
| Discussion
| Related Articles  [?]
| Bibliography  [?]
| External Links  [?]
| Citable Version  [?]
| Tutorials [?]

|
|
|
|
|
|
|
|
|

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.