Editing Input–output model (section)

=== Example ===

Consider an economy with two goods, A and B. The matrix of coefficients and the final demand is given by

:<math>
A = \begin{bmatrix} 0.5 & 0.2 \\ 0.4 & 0.1 \end{bmatrix} \text{ and } \mathbf{y} = \begin{bmatrix} 7 \\ 4 \end{bmatrix}.
</math>

Intuitively, this corresponds to finding the amount of output each sector should produce given that we want 7 units of good A and 4 units of good B. Then solving the system of linear equations derived above gives us

:<math>
\mathbf{x} = \left(I - A\right)^{-1} \mathbf{y} = \begin{bmatrix} 19.19 \\ 12.97 \end{bmatrix}.
</math>