Chapter 4.7, Problem 16E

Problems 15-20 pertain to the following input–output model: Assume that an economy is based on three industrial sectors: agriculture (A), building (B), and energy (E). The technology matrix M and final demand matrices (in billions of dollars) are

$\begin{array}{l}ABE\\ \begin{array}{c}A\\ B\\ E\end{array}\left[\begin{array}{l}0.30.20.2\\ 0.10.10.1\\ 0.20.10.1\end{array}\right]=M\\ D_1=\left[\begin{array}{l}5\\ 10\\ 15\end{array}\right]D_2=\left[\begin{array}{l}20\\ 15\\ 10\end{array}\right]\end{array}$

How much of each of B’s output dollars is required as input for each of the three sectors?