Output Multiplier

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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

References

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