Transcription of 7.2 Application to economics: Leontief Model - Mathematics
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economics: LeontiefModelWassilyLeontiefwo ntheNobel prizein economicsin a modelfortheeconomicsof a wholecountryor erent productssuch thattheinputequalstheoutputor,in otherwords, models:openmodel:someproductionconsumedi nternallyby industries,restconsumedby :Findproductionlevel if externaldemandis :entireproductionconsumedby :Findrelative priceof each ,S2,: : :,Sn. Theexchangeof productscanbedescribedby aninput-outputgraphHere,aijdenotesthenum ber of unitsproducedby industrySinecessarytoproduceoneunitby industrySjandbiis thenumber of externallydemandedunitsof :Primitive modelof theeconomy of Kansasin ed:ProductionofTotaloutput=Internalconsu mption+ExternalDemandfarmingindustry(int ons):x=0:05x+ 0:5y+8000horseindustry:y=0:01x+2000(in10 00kmhorserides).
One has 8 p1 = a11p1 +a21 p2 + +aen1 pn p2 = ea12 p1 +ea22 p2 + + an2 p2 pn = ea1n p1 +ean2 pn + +aenn pn since eaij pi is the amount paid by industry Sj for products produced by industry Si. The total income of industry Sj equals the total price Sj has to pay to all other industries. Again, one can write this as a matrix equation: PA = P: This equation can be transformed in the …
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