Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 60% to Machinery and retains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery and retains the rest. Machinery sells 40% 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. TITE Distribution of Output from: Chemicals Machinery Fuels Purchased by: 0.1 0.7 0.4 Chemicals 0.3 0.1 0.3 Fuels 0.6 0.2 0.3 Machinery (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. The augmented matrix is (Type an integer or decimal for each matrix element.)
Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 60% to Machinery and retains the rest. Fuels sells 70% of its output to Chemicals and 20% to Machinery and retains the rest. Machinery sells 40% 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. TITE Distribution of Output from: Chemicals Machinery Fuels Purchased by: 0.1 0.7 0.4 Chemicals 0.3 0.1 0.3 Fuels 0.6 0.2 0.3 Machinery (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. The augmented matrix is (Type an integer or decimal for each matrix element.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ:
23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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Transcribed Image Text:Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 30% of its output to Fuels and 60% to Machinery and retains the rest. Fuels sells 70% of its output to Chemicals and
20% to Machinery and retains the rest. Machinery sells 40% 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
Machinery
Purchased by:
0.1
0.7
0.4
Chemicals
0.3
0.1
0.3
Fuels
0.6
0.2
0.3
Machinery
(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.
The augmented matrix is.
(Type an integer or decimal for each matrix element.)
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