Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according
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Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according to the 3 × 3 consumption matrix
where αjk is the fraction of the output of industry k consumed (purchased) by industry j. Let pj be the price charged by industry j for its total output. A problem is to find prices so that for each industry, total expenditures equal total income. Show that this leads to Ap = p, where p = [p1 p2 p3]T, and find a solution p with non negative p1, p2, p3.
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The condition that total expenditures equal total income for each industry can be expressed as p1 a1...View the full answer
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