Difference between revisions of "Output Multiplier"
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== Definition == | == 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 [[ | + | 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. |
== Formula == | == Formula == | ||
| − | If we represent the elements of the | + | 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> | ||
| − | |||
| − | |||
== References == | == References == | ||
Revision as of 20:03, 7 March 2022
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.
Formula
If we represent the elements of the Leontief Inverse Matrix (
) as 
, then the output multiplier is defined as the column sum:
