作者：M.Anthony/等
页数：394
出版社：世界图书出版公司
出版日期：1998
ISBN：9787506239233
电子书格式：pdf/epub/txt
内容简介
片断：
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.ThevaluewrittenqD(p)is
thequantitywhichwouldbesoldifthepricewerep,sothatqD(5)=30,for
example.
Thereisanotherwayoflookingattherelationshipbetweenqandp.Ifwe
supposethatthequantityqisgiven,thenthevalueofpforwhich(q,p)is
inthedemandsetDisthepricethatconsumerswouldbepreparedtopay
ifqisthequantityavailable.Fromthisviewpointweareexpressingpin
termsofq,insteadoftheotherwayround.WewritepD(q)forthevalueofp
correspondingtoagivenq,andwecallpDtheinversedemandfunction.
Example(continued)TakingthesamesetDasbefore,wecannowrearrange
theequationofthelineintheformp=(125-6q)/8.Sotheinversedemand
functionis
Nextweturntothesupplyside.WeassumethatthereisasupplysetS
consistingofthosepairs(q,p)forwhichqwouldbetheamountsuppliedto
themarketifthepncewerep.Therearegoodeconomicreasonsforsupposing
thatShasthegeneralformshowninFigure1.2.
目录
Contents
1.Mathematicalmodelsineconomics
1.1Introduction
1.2Amodelofthemarket
1.3Marketequilibrium
1.4Excisetax
1.5Comments
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
2.Mathematicaltermsandnotations
2.1Sets
2.2Functions
2.3Compositefunctions
2.4Graphsandequations
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
3.Sequences,recurrences,limits
3.1Sequences
3.2Thefirst-orderrecurrence
3.3Limits
3.4Specialcases
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
4.Theelementsoffinance
4.1Interestandcapitalgrowth
4.2Incomegeneration
4.3Theintervalofcompounding
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
5.Thecobwebmodel
5.1Howstableismarketequilibrium?
5.2Anexample
5.3Thegenerallinearcase
5.4Economicimerpretation
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
6.Introductiontocalculus
6.1Therateofchangeofafunction
6.2Rulesforfindingthederivative
6.3Marginalcostasaderivative
6.4Thederivativeofacompositefunction
6.5Thederivativeot’aninversefunction
Workedexamples
Maintopics/Keytermsnotationsandtbrmulae
Exercises
7.Somespecialfunctions
7.1Powers
7.2Theexponentialfunctionanditsproperties
7.3Continuouscompoundingofinterest
7.4Thelogarithmfunction
7.5Trigonometricalt’unctions
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
8.Introductiontooptimisation
8.1Profitmaximisation
8.2Criticalpoints
8.3Optimisationinaninterval
8.4Infiniteintervals.
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
9.Thederivativeineconomics-1
9.1Elasticityofdemand
9.2Profitmaximisationagain
9.3Competitionversusmonopoly
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
10.Thederivativeineconomics–11
10.1Theefficientsmallfirm
10.2Startupandbreakevenpoints
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
11.Partialderivatives
11.1Functionsofseveralvariables
11.2Partialderivatives
11.3Thechainrule
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
12Applicationsofpartialderivatives
12.1Functionsdefinedimplicitly
12.2Thederivativeofanimplicitfunction
12.3Contoursandisoquants
12.4Scaleeffectsandhomogeneousfunctions
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
13Optimisationintwovariables
13.1Profitmaximisationagain
13.2Howpricesarerelatedtoquantities
13.3Criticalpoints
13.4Maxima,minima,andsaddlepoints
13.5Classificationofcriticalpoints-introduction
13.6Theclassificationofcriticalpointsingeneral
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
14.Vectorspreferencesandconvexity
14.1Vectorsandbundles
14.2Pricesandbudgets
14.3Preferences,utility,andindifferencecurves
14.4Linearandconvexcombinations
14.5Choosingoptimalbundles
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
15.Matrixalgebra
15.1Whatisamatrix?
15.2Matrixmultiplication
15.3Howtomakemoneywithmatrices
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
16.Linearequations-1
16.1Atwo-industry’economy
16.2Linearequationsinmatrixform
16.3Solutionsoflinearequationsbyrowoperations
16.4Theechelonformingeneral
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
17.Linearequations-11
17.1Consistentandinconsistentsystems
17.2Therankofaconsistentsystem
17.3Thegeneralsolutioninvectornotation
17.4Arbitrageportfoliosandstateprices
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
18.Inversematrices
18.1Thesquarelinearsystem
18.2Theinverseofasquarematrix
18.3Calculationoftheinverse
18.4Theinverseofa2x2matrix
18.5IS-LManalysis
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
19.Theinput-outputmodel
19.1Aneconomywithmanyindustries
19.2Thetechnologymatrix,
19.3Whyisthereasolution?.
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
20.Determinants
20.1Determinants
20.2Thedeterminantasatestforinvertibility
20.3Cramer’srule
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
21.Constrainedoptimisacion
21.1Theelementarytheoryofthefirm
21.2ThemethodofLagrangemultipliers
21.3Thecostfunction
21.4Theefficientsmallfirmagain
21.5TheCobb-Douglasfirm
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
22.Lagrangeansandtheconsumer
22.1Lagrangeans:amoregeneralformulation
22.2Theelementarytheoryoftheconsumer
22.3Thepriceratioandthetangencycondition
22.4Theconsumer’sdemandfunctions
22.5Theindirectutilityfunction
Workedexamples
Maintopics/Keyterms,notationsandformulae
Exercises
23.Second-orderrecurrenceequations
23.1Asimplifiednationaleconomy
23.2Dynamicsoftheeconomy
23.3Linearhomogeneousrecurrences
23.4Non-homogeneousrecurrences
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
24.Macroeconomicapplications
24.1Recurrenceequationsinpractice
24.2Oscillatorysolutions
24.3Businesscycles
24.4Improvedmodelsoftheeconomy
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
25Areasandintegrals
25.1Theconsumersurplus
25.2Theconceptofarea
25.3Anti-derivativesandintegrals
25.4Definiteintegrals
25.4Standardintegrals
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
26.Techniquesofintegration
26.1Integrationbysubstitution
26.2Definiteintegralsbysubstitution
26.3Integrationbyparts
26.4Partialfractions
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
27.First-orderdifferentialequations
27.1Continuous-timemodels
27.2Sometypesofdifferentialequations
27.3Separabledifferentialequations
27.4Acontinuous-timemodelofpriceadjustment
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
28.Second-orderdifferentialequations
28.1Markettrendsandconsumerdemand
28.2Linearequationswithconstantcoefficients
28.3Solutionofhomogeneousequations
28.4Non-homogeneousequations
28.5Behaviourofsolutions
Workedexamples
Maintopics/Keytermsnotationsandformulae
Exercises
Solutionstoselectedexercises
Index
