**Finding a Production Matrix**

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

**a.** Form the n 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 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.