1. Given interaction between 2 sectors in economy Industry Final Demands Gross Output II Industry 20 56 24 100 II 50 8 22 80 Primary Inputs 30 16 a) Knowing the input-output matrix A: 20 56 100 80 find X =(1- A)'D where D= 50 8 | 100 80] b) If in 5 years the final demands change to 74 for industry I and 37 for industry II, how much should each industry produce to meet this projected demand? c) What will be the new primary input requirements in 5 years for the 2 industries?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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1. Given interaction between 2 sectors in economy
Industry
Final Demands
Gross Output
I II
Industry
I
20
56
24
100
II
50
22
80
Primary
Inputs
30
16
a) Knowing the input-output matrix A:
20 56
100 80
74
find X =(1- A)'D where D =
F37
50
100 80
b) If in 5 years the final demands change to 74 for industry I and 37 for
industry II, how much should each industry produce to meet this
projected demand?
c) What will be the new primary input requirements in 5 years for the 2
industries?
Transcribed Image Text:1. Given interaction between 2 sectors in economy Industry Final Demands Gross Output I II Industry I 20 56 24 100 II 50 22 80 Primary Inputs 30 16 a) Knowing the input-output matrix A: 20 56 100 80 74 find X =(1- A)'D where D = F37 50 100 80 b) If in 5 years the final demands change to 74 for industry I and 37 for industry II, how much should each industry produce to meet this projected demand? c) What will be the new primary input requirements in 5 years for the 2 industries?
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