# Total Output

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## 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 ${\displaystyle x_{i}}$, with i ranging between 1 and n which satisfies the system of linear equations:

{\displaystyle {\begin{aligned}x_{i}&=\sum _{j=1}^{n}a_{ij}x_{j}+y_{i}\\\end{aligned}}}