Alternate input output matrix updating formulations
The principal economic applications, as distinct from engineering and business-management applications, have been made in such fields as economic projections of demand, output, employment, and investment for the individual sectors of entire countries and of smaller economic regions (for example, metropolitan areas); study of technological change and its effect on productivity; analysis of the effect of wage, profit, and tax changes on prices; and study of international and interregional economic relationships, utilization of natural resources, and developmental planning.
Some of these applications require construction of special purpose input-output models.
For purposes of mathematical manipulation, the physical output of sector i is usually represented by x and is called the input coefficient of sector i into sector j.
In a larger table, manufacturing would be represented not by one but by many distinct industrial sectors; its output—and consequently also the inputs of the other sectors—would be described in terms of yards of cotton cloth and tons of paper products, or possibly yards of percale, yards of heavy cotton cloth, tons of newsprint, and tons of writing paper.It equals the total of the income payments (shown in the third row) received by households for services rendered to each sector; it also equals the total value of goods and services (shown in the third column) purchased by households from themselves and from the other sectors.To the extent that the column entries (showing the input structure of each productive sector) cover current expenditures but not purchases made on capital account, the capital expenditures—being paid out of the net income—should be entered in the households’ column.Thus, the values of the total outputs of agriculture, manufacturing, and households are shown in Table 2 as 0 (= 100 x ), 0 (= 50 x ). The last row shows the combined value of all outputs absorbed by eachof the three sectors.Such column totals could not have been shown on Table 1, since the physical quantities of different inputs absorbed by each sector cannot be meaningfully added.