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Exercises 1-4 refer to an economy that is divided into

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 1E 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 1E

Exercises 1-4 refer to an economy that is divided into three sectors-manufacturing, agriculture, and services. For each unit of output, manufacturing requires .10 unit from other companies in that sector, .30 unit from agriculture, and .30 unit from services. For each unit of output, agriculture use .20 unit of its own output, .60 unit from manufacturing, and .10 unit from services. For each unit of output, the services sector consumes .10 unit from services, .60 unit from manufacturing, but no agricultural products.

Construct the consumption matrix for this economy and determine what intermediate demands are created if agriculture plans to produce 100 units.

Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

An economy that is divided into three sectors-manufacturing, agriculture, and services. For each unit of output, manufacturing requires .10 unit from other companies in that sector, .30 unit from agriculture, and .30 unit from services. For each unit of output, agriculture use .20 unit of its own output, .60 unit from manufacturing, and .10 unit from services. For each unit of output, the services sector consumes .10 unit from services, .60 unit from manufacturing, but no agricultural products.

Step2

To find

Construct the consumption matrix for this economy and determine what intermediate demands are created if agriculture plans to produce 100 units.

Step3

First column :- unit consumption vector for manufacturing.

Second column :- unit consumption vector for agriculture.

Third column:- unit consumption vector for services.

Consumption matrix

Intermediate demands are calculated  by Cx for given vector x

Cx=

      =

      =

     =

Therefore, the consumption matrix for this economy is intermediate demands are created if agriculture plans to produce 100 units is

Step 2 of 3

Chapter 2.6, Problem 1E 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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Exercises 1-4 refer to an economy that is divided into