Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 20% of its output to Fuels and 50% to Machinery and retains the rest. Fuels sells 80% of its output to Chemicals and 10% to Machinery and retains the rest. Machinery sells 20% of its output to Chemicals and 30% to Fuels and retains the rest. Complete parts (a) through (c) below. a Construct the exchange table for this economy. Distribution of Output from: Chemicals Fuels 0.3 0.8 0.2 0.5 Machinery 0.2 Purchased by: Chemicals Fuels Machinery 0.1 0.1 (Type integers or decimals.) b. Develop a system of equations that leads to prices at which each sector's income matches its expenses. Then write the augmented matrix that can be row reduced to find these prices. The first, second, and third columns of the matrix should correspond to Chemicals, Fuels, and Machinery, respectively. 0.3 0.5 The augmented matrix is (Type an integer or decimal for each matrix element.)

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Chapter2: Systems Of Linear Equations
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Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 20% of its output to Fuels and 50% to Machinery and
retains the rest. Fuels sells 80% of its output to Chemicals and 10% to Machinery and retains the rest. Machinery sells 20% of its output to Chemicals and 30% to Fuels
and retains the rest. Complete parts (a) through (c) below.
a. Construct the exchange table for this economy.
Distribution of Output from:
Chemicals Fuels
0.3
0.8
0.2
0.1
0.5
0.1
(Type integers or decimals.)
b. Develop a system of equations that leads to prices at which each sector's income matches its expenses. Then write the augmented matrix that can be row reduced
to find these prices. The first, second, and third columns of the matrix should correspond to Chemicals, Fuels, and Machinery, respectively.
Machinery
0.2
0.3
0.5
Purchased by:
Chemicals
Fuels
Machinery
The augmented matrix is
(Type an integer or decimal for each matrix element.)
Transcribed Image Text:Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 20% of its output to Fuels and 50% to Machinery and retains the rest. Fuels sells 80% of its output to Chemicals and 10% to Machinery and retains the rest. Machinery sells 20% of its output to Chemicals and 30% to Fuels and retains the rest. Complete parts (a) through (c) below. a. Construct the exchange table for this economy. Distribution of Output from: Chemicals Fuels 0.3 0.8 0.2 0.1 0.5 0.1 (Type integers or decimals.) b. Develop a system of equations that leads to prices at which each sector's income matches its expenses. Then write the augmented matrix that can be row reduced to find these prices. The first, second, and third columns of the matrix should correspond to Chemicals, Fuels, and Machinery, respectively. Machinery 0.2 0.3 0.5 Purchased by: Chemicals Fuels Machinery The augmented matrix is (Type an integer or decimal for each matrix element.)
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