Total Output

Definition

Total Output in the context of an Input-Output Matrix denotes the total production of a particular sector (or product). 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. It can be interpreted as market balance equation in a standard Leontief Model.

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:

$\begin{align} x_{i} & = \sum_{j=1}^{n} a_{ij} x_{j} + y_i \\ \end{align}$

See Also

• Intermediate Input

Further Resources

• Crash Course on Input-Output Model Mathematics
• Introduction to Input-Output Models using Python