leontief

# leontief - of x What’s left over goes to external demand...

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Leontief’s Input-Output Analysis Math 118 – Finite Mathematics It is easy to mix up the technology matrices when doing Leontief analysis and end out putting down the transpose instead. .. Problem 1. Consider a steel-coal economy: For one unit of steel, it takes 0.3 units of steel and 0.2 units of coal, whereas for one unit of coal, it takes 0.1 units of steel and 0.6 units of coal. Find the technology matrix for this economy. Solution. The technology matrix for a 2-product economy will be of the form A = ± a 11 a 12 a 21 a 22 ² , and the production vector is of the form x = ± x 1 x 2 ² . Together, the product Ax gives the amount of material used in the production
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Unformatted text preview: of x . What’s left over goes to external demand. Thus, we have the Leontief equation x = Ax + d. Since it takes 0.3 units of steel and 0.2 units of coal to produce one unit of steel, we have that ± . 3 . 2 ² = ± a 11 a 12 a 21 a 22 ²± 1 ² = ± a 11 a 21 ² . Similarily, since it takes 0.1 units of steel and 0.6 units of coal to produce one unit of coal, we have that ± . 1 . 6 ² = ± a 11 a 12 a 21 a 22 ²± 1 ² = ± a 12 a 22 ² . Thus, we have that A = ± . 3 0 . 1 . 2 0 . 6 ² ....
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