An economy is based on three sectors: Agriculture, Manufacturing, and Energy. Production of a cedi’s worth of agriculture requires inputs of GH¢0.2 from agriculture, GH¢0.15 from manufacturing, and GH¢0.2 from energy. Production of a Ghana cedi’s worth of manufacturing 3 requires inputs of GH¢0.40 from agriculture, GH¢0.10 from manufacturing, and GH¢0.10 from energy. Production of a Ghana cedi’s worth of energy requires inputs of GH¢0.3 from agriculture, GH¢0.10 from manufacturing, and GH¢0.10 from energy. There is a final demand of GH¢10 billion for agriculture, GH¢15 billion for manufacturing, and GH¢20 billion for energy. (i) 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. (ii) Write the equations in matrix form (iii) Determine the output for each sector using the inverse matrix method.
An economy is based on three sectors: Agriculture,
Manufacturing, and Energy. Production of a cedi’s worth
of agriculture requires inputs of GH¢0.2 from agriculture,
GH¢0.15 from manufacturing, and GH¢0.2 from energy.
Production of a Ghana cedi’s worth of manufacturing 3
requires inputs of GH¢0.40 from agriculture, GH¢0.10
from manufacturing, and GH¢0.10 from energy.
Production of a Ghana cedi’s worth of energy requires
inputs of GH¢0.3 from agriculture, GH¢0.10 from
manufacturing, and GH¢0.10 from energy.
There is a final demand of GH¢10 billion for agriculture,
GH¢15 billion for manufacturing, and GH¢20 billion for
energy.
(i) 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.
(ii) Write the equations in matrix form
(iii) Determine the output for each sector using the
inverse matrix method.
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