4-7 - 4-7 Leontief Input-Output Analysis TWO-INDUSTRY MODEL...

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4-7 Leontief Input-Output Analysis T WO - INDUSTRY MODEL 2 industries: electric company E and water company W E has electricity (e.) as output W has water (w.) as output E and W both use both water and electricity as input internal demands: \$1 worth of e. uses \$.30 of e. and \$.10 of w. \$1 worth of w. uses \$.20 of e. and \$.40 of w. external demands: \$12 million of e. \$8 million of w. Question : how much w. and e. must W and E produce to satisfy internal and external demands? 4-7 p. 1 E W 10¢ w. / \$e. 20¢ e. / \$w. 30¢ e. / \$e. 40¢ w. / \$w. Outside demand \$12M e. \$8M w.

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Answer : We need to write some equations. Let: x 1 = total output (\$’s worth) of e. needed from E x 2 = total output (\$’s worth) of w. needed from W Internal demands (in \$’s worth): for e.: (used by e.) + (used by w.) = .3x 1 + .2x 2 for w. (used by e.) + (used by w.) = .1x 1 + .4x 2 So: x 1 = 12,000,000 + .3x 1 + .2x 2 (electricity equation) x 2 = 8,000,000 + .1x 1 + .4x 2 (water equation) These equations define the problem. Solve for x 1 and x 2 . We write the system using matrices: +
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