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 (I – M)^–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.