Total Output

From Open Risk Manual

Definition

Total Output in the context of an Input-Output Matrix denotes the total production of a particular sector. An Input-Output Model is fundamentally a system of linear equations where the Total Output of an industry is distributed through sales to other sectors and to Final Demand

Usage

Total Output is an additional column in the IO matrix that contains the sum of Intermediate Output and final demand.

Formula

Assume that the economy can be categorized into n sectors. Total Output is a vector, usually denoted as x_i, with i ranging between 1 and n which satisfies the system of linear equations:


\begin{align}
x_{i} & = \sum x_{j} \times  a_{ij} + y_i \\
\end{align}

See Also

References