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Unformatted text preview: 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....
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This note was uploaded on 02/08/2011 for the course MATH 1711 taught by Professor Evans during the Spring '08 term at Georgia Institute of Technology.
- Spring '08