Chapter 4.7, Problem 31E

The technology matrix for an economy based on energy $\left(E\right)$ and mining $\left(M\right)$ is

$\begin{array}{l}\begin{array}{ccc}& E& M\end{array}\\ M=\begin{array}{c}E\\ M\end{array}\left[\begin{array}{cc}0.2& 0.3\\ 0.4& 0.3\end{array}\right]\end{array}$

The management of these two sectors would like to set the total output level so that the final demand is always $40\%$ of the total output. Discuss methods that could be used to accomplish this objective.