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# ex26 - MATH 1711 SECTION 2.6 INPUT-OUTPUT ANALYSIS Basic...

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MATH 1711: SECTION 2.6 INPUT-OUTPUT ANALYSIS Basic Idea : Consider an economy consisting of a set of industries, where each industry depends on the other for goods. Inputs are what each industry needs to create a final product. Outputs are the final products. We build an input-output matrix to hold all the information in a given problem. The entry a ij represents the amount of industry i ’s product needed to produced \$1 worth of industry j ’s product (given as percentages). In general, if A is the input-output matrix, X is the variable matrix (how much monetary value each industry should produce), and D is the consumers’ demand for the products, we have the formula X - AX = D, which we solve by factoring out an X : ( I - A ) X = D and multiplying by the inverse of I - A : X = ( I - A ) - 1 D. Here, X = amount produced, AX =amount used in production, or internal demand, and D =amount left for consumers, or external demand. Example : A particular town has a farmer, a butcher, and a baker. To produce \$1 worth of farming products, the farmer requires \$0.20 of his goods, \$0.10 of the butcher’s goods,

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and \$0.40 of the baker’s goods. To produce \$1 of the butcher’s products, the butcher needs
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ex26 - MATH 1711 SECTION 2.6 INPUT-OUTPUT ANALYSIS Basic...

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