Consider an economic model with three industries: agriculture, man- ufacturing and energy. The model has Leontief input-output matrix [0.6 0.1 0.1] 0.2 0.4 0.2 |0.1 0.4 0.2 A = (With the columns corresponding to the industries in the order listed). (a) If there is external demand for 800 units from agriculture, 1600 units from manufacturing and 400 from energy then calculate the total production required from each sector to meet this demand. (Note that you must show the matrix equation that you are solv- ing, but calculations can be done using technology.)
Consider an economic model with three industries: agriculture, man- ufacturing and energy. The model has Leontief input-output matrix [0.6 0.1 0.1] 0.2 0.4 0.2 |0.1 0.4 0.2 A = (With the columns corresponding to the industries in the order listed). (a) If there is external demand for 800 units from agriculture, 1600 units from manufacturing and 400 from energy then calculate the total production required from each sector to meet this demand. (Note that you must show the matrix equation that you are solv- ing, but calculations can be done using technology.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 41EQ
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![Consider an economic model with three industries: agriculture, man-
ufacturing and energy. The model has Leontief input-output matrix
[0.6 0.1 0.1]
A
0.2 0.4 0.2
0.1 0.4 0.2
(With the columns corresponding to the industries in the order listed).
(a) If there is external demand for 800 units from agriculture, 1600
units from manufacturing and 400 from energy then calculate the
total production required from each sector to meet this demand.
(Note that you must show the matrix equation that you are solv-
ing, but calculations can be done using technology.)
(b) How many units of production are used by each of the three
industries to meet this demand?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56264cc1-e81f-4002-bfc8-3eb70e858fc4%2F5589ac26-9119-452a-aa15-f85271b01b8d%2Fa0ra515_processed.png&w=3840&q=75)
Transcribed Image Text:Consider an economic model with three industries: agriculture, man-
ufacturing and energy. The model has Leontief input-output matrix
[0.6 0.1 0.1]
A
0.2 0.4 0.2
0.1 0.4 0.2
(With the columns corresponding to the industries in the order listed).
(a) If there is external demand for 800 units from agriculture, 1600
units from manufacturing and 400 from energy then calculate the
total production required from each sector to meet this demand.
(Note that you must show the matrix equation that you are solv-
ing, but calculations can be done using technology.)
(b) How many units of production are used by each of the three
industries to meet this demand?
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