Chapter 4.7, Problem 1MP

An economy is based on three sectors, coal, oil and transportation. Production of a dollar's worth of coal requires an input of $\$0.20$ from the coal sector and $\$0.40$ from the transportation sector. Production of a dollar’s worth of oil requires an input of $\$0.10$ from the oil sector and $\$0.20$ from the transportation sector. Production of a dollar’s worth of transportation requires an input of $\$0.40$ from the coal sector, $\$0.20$ from the oil sector, and $\$0.20$ from the transportation sector.

(A) Find the technology matrix $M$.

(B) Find ${\left(1-M\right)}^{-1}$

(C) Find the output from each sector that is needed to satisfy a final demand of $\$30$ billion for coal, $\$10$ billion for oil and $\$20$ billion for transportation.