Finding a Production Matrix

Finding a Production Matrix


To obtain the production matrix, X, for an open input-output model, follow these steps:

a. Form the n  \times  n input-output matrix, A, by placing in each column the amount of the various commodities required to produce 1 unit of a particular commodity.

b. Calculate I – A, where is the n \times n identity matrix.

c. Find the inverse, (I – A)-1.

d. Multiply the inverse on the right by the demand matrix, A, to obtain X = (I- A)-1 D.

To obtain a production matrix, X, for a closed input-output model, solve the system (I – A) X = 0.


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