Spending multiplier/Tutorials: Difference between revisions
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==The algebra of the spending multiplier identity== | |||
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 | |||
::::{|class="wikitable" | |||
| | |||
|expenditure | |||
| saving | |||
|- | |||
|round 1 | |||
|align="center"| 100 | |||
| | |||
|- | |||
|round 2 | |||
|align="center"| 100c | |||
|align="center"| 100(1 - c) | |||
|- | |||
|round 3 | |||
|align="center"|100c<sup>2</sup> | |||
|align="center"|100(1 - c)<sup>2</sup> | |||
|- | |||
|... | |||
| | |||
| | |||
|- | |||
|round n | |||
|align="center"|100c<sup>n</sup> | |||
|align="center"|100(1 - c)<sup>n</sup> | |||
|} | |||
The total spending in the economy after n rounds is | |||
::100 + 100c + 100c<sup>2</sup> + 100c<sup>3</sup> ....+ 100c<sup>n</sup> | |||
- 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]]. | |||
Latest revision as of 06:29, 16 November 2012
The algebra of the spending multiplier identity
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.