Chapter 2.6, Problem 26E

Three-Sector Economy An economy consists of the three sectors agriculture, energy, and manufacturing. For each $1 worth of output, the agriculture sector requires $.08 worth of input from the agriculture sector, $.10 worth of input from the energy sector, and $.20 worth of input from the manufacturing sector. For each $1 worth of output, the energy sector requires $.15 worth of input from the agriculture sector, $.14 worth of input from the energy sector, and $.10 worth of input from the manufacturing sector. For each $1 worth of output, the manufacturing sector requires $.25 worth of input from the agriculture sector, $.12 worth of input from the energy sector, and $.05 worth of input from the manufacturing sector.

(a) Give the input–output matrix A for this economy.

(b) Determine the matrix ${\left(I-A\right)}^{-1}$. (Round entries to two decimal places.)

(c) At what level of output should each sector produce to meet a demand for $4 billion worth of agriculture, $3 billion worth of energy, and $2 billion worth of manufacturing?

(d) How much of the output of each sector is used to meet internal consumption?