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Given the technology matrix, A, and the production vector, X, below: A = [ .5  0  .2...

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cbromm | Honors

Posted July 21, 2013 at 7:22 PM via web

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Given the technology matrix, A, and the production vector, X, below:

A = [ .5  0  .2 ]                  X = [ 264 ]

      [ .2  .8  .12 ]                      [ 715 ]

      [ 1    .4    0 ]                      [ 585 ]

Compute the demand vector, D.  

    

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 22, 2013 at 12:51 AM (Answer #1)

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We use `X=AX+D` which implies `D=X-AX`

We are given `A=([.5,0,.2],[.2,.8,.12],[1,.4,0])` and `X=([264],[715],[585])`

So `D=([264],[715],[585])-([.5,0,.2],[.2,.8,.12],[1,.4,0])([264],[715],[585])`

`=([264],[715],[585])-([249],[695],[550])`

`=([15],[20],[35])`

The external demand matrix is `D=([15],[20],[35])`

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