The Total-Requirements Table

To take into account both the direct and indirect requirements of input by one industry needed for a dollar s worth of output to final demand of another industry, we return to Eq. (4.10), where the set of direct-requirement equations is given by in the vector fonn as follows  

The matrix (I - D) is equal to an infinite series and can be approximated by truncation of term n 

Equation (4.14) can be used to estimate the change in output due to a change in the final demand. 

A simple example will illustrate how the various relationships are applied and indicate some additional uses of input-output analysis. 

Example 4.1. To illustrate the basic concepts without algebraic complexity, we consider a two-industry economy. We shall assume that some central agency like the federal government has collected statistics on suppliers and supplies needed to develop the transaction table shown in Table 4.12. 

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The total-requirements table for the U.S. economy for 1987 is given as Table 4.15 (see Appendix C). The elements of this table are obtained by inverting the I - D matrix, where D is found from Table 4.10. Each column shows the output required both directly and indirectly from the industry named at the left of each row per dollar of delivery to final demand by the industry named at the head of the column. Returning to our automobile example, a 10 million increase in final demand for the products of industry 59A requires an increase of 0.0.3769 X 10,000,000 = 376,900 in total output in both direct and indirect requirements for products of industry 27A. This is about eight times the direct-requirement increase of 45,200 computed by using the direct requirement only. 

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