Difference between revisions of "Environmental Impact Coefficient"
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Assume a matrix of pollution output or direct impact coefficients, Dp = [dkj p, | Assume a matrix of pollution output or direct impact coefficients, Dp = [dkj p, | ||
| − | Each element of which is the amount of pollutant type k, e.g., sulfur dioxide, generated per dollar’s worth of industry j’s output. Hence, the level of pollution associated with a given vector of [[Total Output]] can be expressed as | + | Each element of which is the amount of pollutant type k, e.g., sulfur dioxide, generated per dollar’s worth of industry j’s output. Hence, the level of pollution associated with a given vector of [[Total Output]] can be expressed as xp = Dp x |
where x p∗ is the vector of pollution levels. | where x p∗ is the vector of pollution levels. | ||
| − | By adding the traditional Leontief | + | By adding the traditional [[Leontief Model]], <math>x = L f</math> where <math>L = (I - A)^{-1}</math> , we can compute xp∗ as a function of final demand, that is, the total pollution of each type generated by the economy directly and indirectly in supporting that final demand: |
x p∗ = [Dp L]f | x p∗ = [Dp L]f | ||
We can view the bracketed quantity as a matrix of total environmental impact coefficients; that is, an element of this matrix is the total pollution impact generated per dollar’s worth of final demand presented to the economy. | We can view the bracketed quantity as a matrix of total environmental impact coefficients; that is, an element of this matrix is the total pollution impact generated per dollar’s worth of final demand presented to the economy. | ||
| + | |||
| + | == Further Resources == | ||
| + | * [https://www.openriskacademy.com/mod/page/view.php?id=800 Crash Course on Input-Output Model Mathematics] | ||
== References == | == References == | ||
Revision as of 13:21, 18 September 2023
Definition
Environmental Impact Coefficient is a straightforward approach to account for pollution generation associated with interindustry activity.
Formula
Assume a matrix of pollution output or direct impact coefficients, Dp = [dkj p,
Each element of which is the amount of pollutant type k, e.g., sulfur dioxide, generated per dollar’s worth of industry j’s output. Hence, the level of pollution associated with a given vector of Total Output can be expressed as xp = Dp x
where x p∗ is the vector of pollution levels.
By adding the traditional Leontief Model, 
where 
, we can compute xp∗ as a function of final demand, that is, the total pollution of each type generated by the economy directly and indirectly in supporting that final demand:
x p∗ = [Dp L]f
We can view the bracketed quantity as a matrix of total environmental impact coefficients; that is, an element of this matrix is the total pollution impact generated per dollar’s worth of final demand presented to the economy.
