Spending multiplier: Difference between revisions

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In [[economics]], the spending [[multiplier effect]] describes a process by which an initial increase of one economic aggregate is amplified and provokes an increase in the same or/and other aggregate(s) larger than the initial raise. The idea is that the raise of a first agent income improves the situation of a second agent by the way of consumption, and so on.  
{{subpages}}
The '''spending multiplier''' occurs when an increase in one agent's spending provokes a succession of increases in spending by other agents with a  cumulative effect that exceeds the initial stimulus. It is a definitionally inherent property of the [[circular flow of income]] model of an economy. An injection of income into such an economy results in  expenditure by its recipients which forms the income of a second round of recipients. The expenditure of  the  second round of recipients becomes the income of a third round - and so forth . The cumulative sum of the changes in income of the successive rounds of recipients is necessarily greater than the initial injection.  


The spending multiplier is a key concept in [[Keynesian economics]] for it explains how the government purchases can have a strong stimulating effect on the national output, depending on the marginal propensity to consume.
How large that cumulative sum becomes depends upon the proportion of the income that is returned to the circular flow of income in each round - the proportion that does not "leak" from the income-spending flow. The greater such leakage, the smaller is the multiple by which the cumulative sum exceeds the initial injection. If the fraction that leaks is taken to be constant, it can be shown  that the final spending multiplier is the reciprocal of that fraction. In the particular case when all of the leakage is into savings the spending multiplier is the reciprocal of the [[marginal propensity to save]] (''as demonstrated on the [[/Tutorials|tutorials subpage]]'').
 
== Example in an closed economy ==
 
Consider a 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.
<center>
{| class="wikitable"
|-
! Agent
! Consumption
! Saving
|-
| Government
| 100
| 0
|-
| colspan="3" | ''Through consumption, the government increases by 100 the income of one of its suppliers (agent #2).''
|-
| #2
| 80
| 20
|-
| colspan="3" | ''Agent #2 saves 20% of its new wealth and spends the remaining money, increasing by 80 the income of agent #3.''
|-
| #3
| 64
| 16
|-
| #4
| 51
| 13
|-
| #5
| 41
| 10
|-
| #6
| 33
| 8
|-
| #7
| 26
| 6
|-
| ...
| ...
| ...
|-
! Total
! 500
! 100
|}
</center>
 
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 :
<center>
Income = Consumption + Investment<br>
Income = Private Consumption + Governmental Consumption + Saving - Taxes<br>
Y = C + G + I - T<br>
Since C = cY with c the propensity to consume, then<br>
Y = cY + G + I - T<br>
(1-c)Y = G + I - T<br>
Y = (G + S - T)/(1-c)<br>
Thus, an increase of G by 1 implies an increase of Y by 1/(1-c).
</center>
 
== Influence of imports in an open economy ==
 
<center>
{| class="wikitable"
|-
! Agent
! Consumption of domestic products
! Imports
! Saving
|-
| Government
| 100
| 0
| 0
|-
| colspan="4" | ''Through consumption, the government increases by 100 the income of one of its suppliers (agent #2).''
|-
| #2
| 60
| 20
| 20
|-
| colspan="4" | ''Agent #2 saves 20% of its new wealth and spends the remaining money. Because of imports, only three quarter of his purchases increase the income of another domestic agent. Thus agent #3 receives 60 instead of 80.''
|-
| #3
| 36
| 12
| 12
|-
| #4
| 21,6
| 7,2
| 7,2
|-
| #5
| 7,8
| 2,6
| 2,6
|-
| ...
| ...
| ...
| ...
|-
! Total
! 250
! 50
! 50
|}
</center>

Revision as of 05:25, 16 November 2012

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The spending multiplier occurs when an increase in one agent's spending provokes a succession of increases in spending by other agents with a cumulative effect that exceeds the initial stimulus. It is a definitionally inherent property of the circular flow of income model of an economy. An injection of income into such an economy results in expenditure by its recipients which forms the income of a second round of recipients. The expenditure of the second round of recipients becomes the income of a third round - and so forth . The cumulative sum of the changes in income of the successive rounds of recipients is necessarily greater than the initial injection.

How large that cumulative sum becomes depends upon the proportion of the income that is returned to the circular flow of income in each round - the proportion that does not "leak" from the income-spending flow. The greater such leakage, the smaller is the multiple by which the cumulative sum exceeds the initial injection. If the fraction that leaks is taken to be constant, it can be shown that the final spending multiplier is the reciprocal of that fraction. In the particular case when all of the leakage is into savings the spending multiplier is the reciprocal of the marginal propensity to save (as demonstrated on the tutorials subpage).