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The consumption matrix C for the U.S economy in 1972 has

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald ISBN: 9780321982384 49

Solution for problem 10E Chapter 2.6

Linear Algebra and Its Applications | 5th Edition

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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

Linear Algebra and Its Applications | 5th Edition

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Problem 10E

The consumption matrix C for the U.S economy in 1972 has the property that every entry in the matrix (1 – C)–1 Is nonzero (and positive).1 What does that say about the effect of raising the demand for the output of just one sector of the economy?

Step-by-Step Solution:
Step 1 of 3

Problem 10E

As the Leontief production equation is , which is also written as

Now if  has all entries positive , then since d is the final demand vector so it has positive entries. So by matrix multiplication increase if d any entry in d is increased, that is  increases.

Hence if the demand in any sector increases, then the production in every sector will also increase.

Step 2 of 3

Chapter 2.6, Problem 10E is Solved
Step 3 of 3

Textbook: Linear Algebra and Its Applications
Edition: 5
Author: David C. Lay; Steven R. Lay; Judi J. McDonald
ISBN: 9780321982384

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The consumption matrix C for the U.S economy in 1972 has