Difference between revisions of "Output Multiplier"

Revision as of 18:16, 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. This 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 $L=(I-A)^{-1}$ as $l_{ij}$ , then the output multiplier is defined as the column sum:

O_{j} = \sum_{i=1}^{n} l_{ij}

Further Resources

Crash Course on Input-Output Model Mathematics

References

↑ R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009

[1] R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009

[1]

@@ Line 1: / Line 1: @@
 == Definition ==
-An '''Output-to-Output Multiplier''' indicates how total production will change as [[Final Demand]] is changed in any one sector of the economy.
+An '''Output-to-Output Multiplier''' indicates how total production will change as [[Final Demand]] is changed in any one sector of the economy. 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>
-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>
+Output multipliers are an example of the questions tackled by [[Input-Output Analysis]].
 == Formula  ==
-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:
+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>