3. 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?

3. 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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Algebra
3. 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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