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''', or simply output multiplier, indicates how total production will change as [[Final Demand]] is changed in any one sector of the economy. The 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> |
| + | |||
| + | Output multipliers are an example of the questions tackled by [[Input-Output Analysis]]. | ||
== Formula == | == Formula == | ||
| − | If we represent the elements of the | + | The output multiplier for sector j is the sum of column j of the [[Leontief Inverse Matrix]]. If we represent the elements of the Leontief Inverse Matrix <math>L=(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=1}^{n} l_{ij} |
</math> | </math> | ||
| − | + | == Further Resources == | |
| + | * [https://www.openriskacademy.com/course/view.php?id=70 Crash Course on Input-Output Model Mathematics] | ||
| + | * [https://www.openriskacademy.com/course/view.php?id=64 Introduction to Input-Output Models using Python] | ||
== References == | == References == | ||
Latest revision as of 18:30, 16 November 2023
Definition
An Output-to-Output Multiplier, or simply output multiplier, indicates how total production will change as Final Demand is changed in any one sector of the economy. The output multiplier measures the amount of output generated by a $1 change in final demand for the output of the jth sector.[1]
Output multipliers are an example of the questions tackled by Input-Output Analysis.
Formula
The output multiplier for sector j is the sum of column j of the Leontief Inverse Matrix. 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
