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MIT11_481Js09_lec19a

# MIT11_481Js09_lec19a - MIT OpenCourseWare http/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 11.481J / 1.284J / ESD.192J Analyzing and Accounting for Regional Economic Growth Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Multipliers in Input-Output Model Presentation to 11.481J Weifeng Li
Introduction z So far, we have learned the relationship between gross output and final demand based on Leontief Inverse Matrix: z We are more interested in assessing the effect on an economy of changes in final demand elements that are exogenous to the model of that economy. 1 ( ) X I A Y = 1 ( ) X I A Y Δ = Δ

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General Structure of Multipliers: Output Multiplier z The simple output multiplier (direct output + indirect output ) direct output z The total output multiplier (direct + indirect + induced output) direct output 1 n j ij i O α = = 1 1 n j i O ij α + = = Direct and indirect impacts on gross output when the final demand for the j th sector changes by one unit, holding All other sectors constant. Leontief coefficient Leontief coefficient with households included in the input coefficient matrix Output Multiplier
Example Simple Output Multiplier Source: Miller and Blair (1985). 1 1 2 .15 .25 .20 .05 1.254 .330 ( ) .264 1.122 1.254 .264 1.518 .330 1.122 1.452 A I A O O = = = + = = + = 1 1 2 .15 .25 .05 .20 .05 .40 .30 .25 .05 1.365 .425 .251 ( ) .527 1.348 .595 .570 .489 1.289 1.365 .527 .570 2.462 .425 1.348 .489 2.262 A I A O O = = = + + = = + + = Total Output Multiplier Household Household

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