This problem refers to Leontiefs input-output model, first discussed in the Exercises

Chapter 3, Problem 78

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This problem refers to Leontiefs input-output model, first discussed in the Exercises 1.1.20 and 1.2.37. Consider three industries I\, I2, h , each of which produces only one good, with unit prices p\ = 2, P2 = 5, = 10 (in U.S. dollars), respectively. Let the three products be labeled good 1, good 2, and good 3. Leta\\ *12 013 "0.3 0.2 O.f A = 021 022 023 = 0.1 0.3 0.3 *31 032 033 0.2 0.2 0.1be the matrix that lists the interindustry demand in terms of dollar amounts. The entry a/y tells us how many dollars worth of good / are required to produce one dollars worth of good j. Alternatively, the interindustry demand can be measured in units of goods by means of the matrixB =b 11 612 ^13 /?21 b22 b23 631 />32 />33where bij tells us how many units of good / are require* to produce one unit of good j. Find the matrix B for the economy discussed here. Also write an equation relatim the three matrices A, By and 5, where5 =2 0 0 0 5 0 0 0 10is the diagonal matrix listing the unit prices on the diagO nal. Justify your answer carefully.