经济数学和金融数学

作者M.Anthony/等
出版社
出版时间1998-08-01

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片断:WeshallrefertothisasthedemandsetDfortheparticulargood.Ineconomicsyouwilllearnreasonswhyitoughttolookratherlikeitdoesinourdiagram,asmooth,downwardslopingcurve.SupposethedemandsetDcontainsthepoint(30,5).Thismeansthatwhen:thepricep=5isgiven,thenthecorrespondingdemandwillbeforq=30units.Ingeneral.providedDhasthe'right'shape,asinFigure1.1,thenforeachvalueofptherewillbeauniquelydeterminedvalueofq.InthissituationwesaythatDdeterminesademandfunction,qD.ThevaluewrittenqD(p)isthequantitywhichwouldbesoldifthepricewerep,sothatqD(5)=30,forexample.Thereisanotherwayoflookingattherelationshipbetweenqandp.Ifwesupposethatthequantityqisgiven,thenthevalueofpforwhich(q,p)isinthedemandsetDisthepricethatconsumerswouldbepreparedtopayifqisthequantityavailable.Fromthisviewpointweareexpressingpintermsofq,insteadoftheotherwayround.WewritepD(q)forthevalueofpcorrespondingtoagivenq,andwecallpDtheinversedemandfunction.Example(continued)TakingthesamesetDasbefore,wecannowrearrangetheequationofthelineintheformp=(125-6q)/8.SotheinversedemandfunctionisNextweturntothesupplyside.WeassumethatthereisasupplysetSconsistingofthosepairs(q,p)forwhichqwouldbetheamountsuppliedtothemarketifthepncewerep.TherearegoodeconomicreasonsforsupposingthatShasthegeneralformshowninFigure1.2.

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