# Find the production matrix for the following input-output and demand matrices using the open model. A = [ .4 0 .06 ] D = [ 1 ] [ 0 .8 .02 ] ...

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

A = [ .4 0 .06 ] D = [ 1 ]

[ 0 .8 .02 ] [ 3 ]

[ 0 .2 .88 ] [ 5 ]

### 1 Answer | Add Yours

The production matrix X can be found by X=AX+D or more directly:

`X=(I-A)^(-1)D` where I is the appropriate identity matrix.

We have `A=([.4,0,.06],[0,.8,.02],[0,.2,.88])` and `D=([1],[3],[5])`

`I-A=([.6,0,-.06],[0,.2,-.02],[0,-.2,.12])`

`(I-A)^(-1)=([5/3,1,1],[0,6,1],[0,10,10])`

`(I-A)^(-1)D=([5/3,1,1],[0,6,1],[0,10,10])([1],[3],[5])`

`=([29/3],[23],[80])`

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The production matrix is `([29/3],[23],[80])`

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