Difference between revisions of "Output Multiplier"
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== Definition == | == Definition == | ||
| − | An '''Output-to-Output Multiplier''' indicates how total production will change as | + | An '''Output-to-Output Multiplier''' indicates how total production will change as [[Final Demand]] is changed in any one sector of the economy. |
| + | |||
| + | The output multiplier for sector j is the sum of column j of the [[Leontief Inverse Matrix]]. This output multiplier measures the amount of output generated by a $1 change in final demand for the output of the jth sector.<ref>R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009</ref> | ||
| + | |||
== Formula == | == Formula == | ||
| − | If we represent the elements of the Leontief Inverse Matrix (<math>(I-A)^{-1}</math>) as <math>l_{ij}</math>, then the output multiplier is defined as the column sum: | + | If we represent the elements of the [[Leontief Inverse Matrix]] (<math>(I-A)^{-1}</math>) as <math>l_{ij}</math>, then the output multiplier is defined as the column sum: |
:<math> | :<math> | ||
O_{j} = \sum_{i} l_{ij} | O_{j} = \sum_{i} l_{ij} | ||
</math> | </math> | ||
| + | |||
| + | == Further Resources == | ||
| + | * [https://www.openriskacademy.com/mod/page/view.php?id=800 Crash Course on Input-Output Model Mathematics] | ||
== References == | == References == | ||
Revision as of 13:48, 18 September 2023
Definition
An Output-to-Output Multiplier indicates how total production will change as Final Demand is changed in any one sector of the economy.
The output multiplier for sector j is the sum of column j of the Leontief Inverse Matrix. This output multiplier measures the amount of output generated by a $1 change in final demand for the output of the jth sector.[1]
Formula
If we represent the elements of the Leontief Inverse Matrix (
) as 
, then the output multiplier is defined as the column sum:
Further Resources
References
- ↑ R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009
