Chapter 3.5, Problem 2E

For the economy in Problem 1, what industry is most dependent on utilities?

Problem 1.

The following technology matrix for a simple economy describes the relationship of certain industries to each other in the production of $1$ unit of product.

$\begin{array}{l}\begin{array}{lllll}\hfill & \text{A}\hfill & \text{M}\hfill & \text{F}\hfill & \text{U}\hfill \end{array}\\ \left[\begin{array}{cccc}\text{0}\text{.36}& \text{0}\text{.03}& \text{0}\text{.10}& \text{0}\text{.04}\\ \text{0}\text{.06}& \text{0}\text{.42}& \text{0}\text{.25}& \text{0}\text{.33}\\ \text{0}\text{.18}& \text{0}\text{.15}& \text{0}\text{.10}& \text{0}\text{.41}\\ \text{0}\text{.10}& \text{0}\text{.20}& \text{0}\text{.31}& \text{0}\text{.15}\end{array}\right]\begin{array}{l}\text{Agriculture}\hfill \\ \text{Manufacturing}\hfill \\ \text{Fuels}\hfill \\ \text{Utilities}\hfill \end{array}\end{array}$

For each $100$ units of manufactured products produced, how many units of fuels are required?

How many units of utilities are required to produce $40$ units of agricultural products?