Suppose that three industries are interrelated so that their
outputs are used as inputs by themselves, according to the
3x3 consumption matrix
50.1 0.5 07
A = (ajk] = 0.8 0 0.4
[0.1 0.5 0.6
where, ajk is the fraction of the output of industry k consumed
by industry j. Let pibe 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, p3l1, and find a
solution p with nonnegative p1, p2, p3. Also, show that the
consumption matrix A must have column sums 1and always
has eigenvalue 1.
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