Homework Help

# Find the production matrix for the following input-output and demand matrices using the...

Honors

• Up
• 1
• Down

Find the production matrix for the following input-output and demand matrices using the open model.

A =     [.3     .4]                  D = [4]

[.35    .2]                        [6]

Posted by cbromm on July 17, 2013 at 12:16 AM via web and tagged with math, matrix

High School Teacher

(Level 1) Educator Emeritus

• Up
• 1
• Down

Given input-output (technology) matrix `A=[[.3,.4],[.35,.2]]` and demand matrix `D=[[4],[6]]` , find the production matrix X:

`X=(I-A)^(-1)D` where I is the appropriate identity matrix (in this case `I=[[1,0],[0,1]]` ):

`I-A=[[1,0],[0,1]]-[[.3,.4],[.35,.2]]=[[.7,-.4],[-.35,.8]]`

Then `(I-A)^(-1)=1/((.7*.8)-(-.35*-.4))[[.8,.4],[.35,.7]]`

`=1/.42[[.8,.4],[.35,.7]]`

`=[[40/21,20/21],[5/6,5/3]]`

Now `(I-A)^(-1)D=[[40/21,20/21],[5/6,5/3]][[4],[6]]`

`=[[40/3],[40/3]]`

---------------------------------------------------------------

The production matrix (vector) is `[[40/3],[40/3]]`

---------------------------------------------------------------

Posted by embizze on July 17, 2013 at 2:15 AM (Answer #1)