An economy is based on three sectors: Agriculture, Manufacturing, and Energy. Production of a dolar worth of agriculture requires inputs of $0.2 from agriculture, $0.15 from manufacturing, and $0.2 from energy. Production of a dolar worth of manufacturing requires inputs of $0.40 from agriculture, $0.10 from manufacturing, and $0.10 from energy. Production of a dolar worth of energy requires inputs of $0.3 from agriculture, $0.10 from manufacturing, and $0.10 from energy.
An economy is based on three sectors: Agriculture,
Manufacturing, and Energy. Production of a dolar worth
of agriculture requires inputs of $0.2 from agriculture,
$0.15 from manufacturing, and $0.2 from energy.
Production of a dolar worth of manufacturing
requires inputs of $0.40 from agriculture, $0.10
from manufacturing, and $0.10 from energy.
Production of a dolar worth of energy requires
inputs of $0.3 from agriculture, $0.10 from
manufacturing, and $0.10 from energy.
There is a final demand of $10 billion for agriculture,
$15 billion for manufacturing, and $20 billion for
energy.
(a) Formulate the system of linear equations which
must be solved to give the combination of output
for the three sectors that will satisfy the final demand.
(b) Write the equations in matrix form
(c) Determine the output for each sector using the
inverse matrix method.
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