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經(jīng)濟數(shù)學(xué)和金融數(shù)學(xué)


作者:M.Anthony/等     整理日期:2021-03-03 12:09:44


片斷:
WeshallrefertothisasthedemandsetDfortheparticulargood.Ineconomics
youwilllearnreasonswhyitoughttolookratherlikeitdoesinourdiagram,
asmooth,downwardslopingcurve.
SupposethedemandsetDcontainsthepoint(30,5).Thismeansthatwhen:
thepricep=5isgiven,thenthecorrespondingdemandwillbeforq=30
units.Ingeneral.providedDhasthe'right'shape,asinFigure1.1,thenfor
eachvalueofptherewillbeauniquelydeterminedvalueofq.Inthissituation
wesaythatDdeterminesademandfunction,qD.Theva luewrittenqD(p)is
thequantitywhichwouldbesoldifthepricewerep,sothatqD(5)=30,for
example.
Thereisanotherwayoflookingattherelationshipbetweenqandp.Ifwe
supposethatthequantityqisgiven,thentheva lueofpforwhich(q,p)is
inthedemandsetDisthepricethatconsumerswouldbepreparedtopay
ifqisthequantityavailable.Fromthisviewpointweareexpressingpin
termsofq,insteadoftheotherwayround.WewritepD(q)fortheva lueofp
correspondingtoagivenq,andwecallpDtheinversedemandfunction.
Example(continued)TakingthesamesetDasbefore,wecannowrearrange
theequationofthelineintheformp=(125-6q)/8.Sotheinversedemand
functionis
Nextweturntothesupplyside.WeassumethatthereisasupplysetS
consistingofthosepairs(q,p)forwhichqwouldbetheamountsuppliedto
themarketifthepncewerep.Therearegoodeconomicreasonsforsupposing
thatShasthegeneralformshowninFigure1.2.






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