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Answer: In Exercises 2124, find an equation of the line

Calculus: Early Transcendental Functions | 6th Edition | ISBN: 9781285774770 | Authors: Ron Larson ISBN: 9781285774770 141

Solution for problem 23 Chapter 1

Calculus: Early Transcendental Functions | 6th Edition

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Calculus: Early Transcendental Functions | 6th Edition | ISBN: 9781285774770 | Authors: Ron Larson

Calculus: Early Transcendental Functions | 6th Edition

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Problem 23

In Exercises 2124, find an equation of the line that passes throug

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AEDE3680Midterm1StudyGuide RegionalEconomics&SustainableGrowth ManyofthesenotesarederivedfromDr.Faggian’sPowerPointslidespostedon Carmen.Ifindthatherslidescontainmuchusefulmaterialthathasaidedinmyunderstanding ofclassconcepts. Lectures1-5areincludedinthisstudymaterial! LECTURE1 Whatisregionaleconomics • Generalregionaleconomicscanbedefinedasthe“subjectconcernedwith understandingandexplainingthegeographicconfigurationoftheeconomy,particularly regardingindustriallocation,regionaldevelopment,urbanization,migration,landuse, etc.”(TheCanadianEncyclopedia,2010) • HooverandGiarrantani(Chapter1)statethatregionaleconomicscanbeseenasthe subjectwhichtriestoanswerthisquestion:”Whatiswhere,andwhy—andsowhat” o What:everytypeofeconomicactivity.Theroleofspaceisfundamental. o Where:locations;involvesproximity,concentration,dispersion,similarityor disparityofspatialpatterns. o Whyandsowhat:economicinterpretationsandpolicyimplications. • Whydifferentpartsofthesameeconomy(regions)behavedifferently. Whatisa“region” • Manydifferentdefinitions • TheUnitedStatescanbedividedintodifferentregions: o Counties o States o Timezones • InEurope,therearethreedifferentlevels: o NUTS1—majorsocioeconomicregions(97current) o NUTS2—basicregionsfortheapplicationofregionalpolicies(271current) o NUTS3—smallregionsforspecificdiagnoses(1,303current) • HOWEVER,thepopulationthresholdsareverydifferentfortheU.S.versusEurope. There’smorevariationwithintheUnitedStates.E.g… o NUTS1minimumis3millionandmaximumis7million o NUTS2minimumis800kandmaximumis3million o NUTS3minimumis150kandmaximumis800k o Therearesomeexceptions LECTURE2 IndustrialLocationAnalysis:TheWeberModel • BasicmodelsproposedbyWeberandMosesarebasedontransportationcosts 1 • TheWebermodel(1909)representsthe“fundamentalbuildingblocksof microeconomicfirmlocationanalysis”(McCann,page3).It’sbasedonafewsimplifying assumptions… o 1.Thefirmisdefinedasapointinspace(therecanbenomultiplelocations); o 2.Theaimofthefirmissimplytomaximizeprofit; o 3.Thefirmproducesoneproductusingonlytwoproductionfactors; o 4.Thereisafixedproductionfactorrelationship,e.g.thereisonlyone“recipe” tocombinethetwofactorstogetthefinalproduct. • TheWeberModelterminology o Inputs—productionfactorswhichafirmusestoproduceagood o Output—finalproductproduced • Thelocationproblemcanbegraphicallyrepresentedbywhathasbecomeknownasthe Webertriangle. o Theequilibriumpointisthefinallocation. o Isodapanescanbeusedtoincorporatecostsoflabororland § Movingiscostly,soafirmrelocationsONLYwhenthefollowingcondition holds:laborcostsavings>extratransportationcosts+relocationcosts § Thegovernmentoffersincentivesforrelocationinmoreperipheralareas tohelpdepressedregions…theindustryrelocatesifthisconditionholds: laborcostsavings+governmentalincentives>extratransportation costs+relocationcosts ClassificationofFirms 1. Resource-oriented—firmswhoselocationdecisionsaredictatedbythelocationof naturalresources.Inasense,theirlocationdecisionsaretheeasiestbecausetheyhave fewchoicesregardingwheretheycanlocate…e.g.coalmineshavetobelocatednear coaldeposits.GoogleInternationalFallsinMinnesota.It’sthe“IceboxoftheNation” becausebusinessesthatneedtotestitemstobeusedincoldweatherlocatethere. 2. Transport-oriented a. Input-oriented—engagedinweight-losingactivities,e.g.wheretheoutputis lighterthanitsinputsandhencelessexpensivetoship…inputsaremorefragile orspoilquickly.E.g.canningfirmstendtolocateneartheinputsource.Fish spoilsquicklybeforebeingcanned. b. Market-oriented—thefirmminimizestotaltransportationcostsbylocatingat themarket.Thesefirmsarenormallyengagedinweight-gainingactivities,e.g. wheretheoutputisheavier,bulkier,moredelicate,perishableormore dangerousthanitsinputsandhencemoreexpensivetoship. 3. Footloose—firmsthatarenottiedtoanyparticularlocation,andforwhich transportationcostsarenotveryimportant.Therefore,theyareneitherresource-nor transport-oriented.Mostservicesarefootloose,buttheystilltendtolocateincentral areaswheretheycanexploitagglomerationeconomies(tobementionedlater). LECTURE3 TheMosesModel(1958) 2 • Takesintoaccountthatinputscanbesubstitutable,whichisimportantbecausein realityfirmshavemorethanoneinput“combination”toproduceanoutput o Inproducingacar,afirmcanuse150kgofsteeland50kgofplastic,or100kgof both,or50kgofsteeland150kgofplastic • OppositeoftheWeberModel.Withoutinputsubstitutability,thefirmwouldhave movedclosertothemoreexpensiveinputtosaveonthehighesttransportationcosts. • TheMosesModelconsidersbothinputcombinationanddistances. o Mosesisabetterapproximation,butWeberisabetterrepresentation PalanderandHotellingModels • Assumesthatmarketsareareas,insteadofapointinspace(y)likeintheMosesand Webermodels. • PalanderModel o TwofirmsAandBarelocatedinareasAandBrespectively.Aone-dimensional marketareaisdefinedbythelineOL. o Differenttransportationcostsarerepresentedbybranchesofthe“tree.” Steeperbranchesmeanhighertransportationcosts. • HotellingModel o Spacegivesyouanadvantage(spatialmonopoly)providesanincentiveforfirms touselocationasa“competitiveweapon”toacquiregreatermonopoly. o There’sanincentiveforfirmstomovetowardseachotheratthecenterofthe market…fortheNashequilibrium(neitherfirmhasanincentivetomovefrom thisequilibrium). o Welfarelossisrepresentedonthegraphic.Thegainisinthemiddle. LECTURE4 Thankstoglobalization,transportationcostshavedecreasedovertime…”Overthetwentieth century,therealcostsofmovingatonamilebyraildeclinedbymorethan90percent” (GlaeserandKohlhase,2004). • Formanufacturingactivities,relocationtomoreperipheralareashasbecomemore common(e.g.toEasternEurope,China,India,etc).DeclineofmanufacturingintheU.K. • Moreperipheral,disadvantageareastrytocompetewiththemore“central”ones acceptinglowerwages. Istheworldbecomingmoreflatorspiky • Flat—activitiesaremoredispersed • Spiky—activitiesaremoreconcentratedinfewerlargecities AgglomerationEconomies • Agglomeration—apointinspacewhereacertainactivityisparticularlydense • Agglomerationeconomies—advantages(savingsoncosts)whichaccruetoallthefirms locatedinthesamearea.Theyarelocation-specificeconomies. o Canmorethancompensateforincreasesinlocalfactorprices. 3 • Threesourcesofagglomerationeconomies: o 1.Localtacitknowledge(spillovers)—Ifmanyfirmsinthesameindustryare allocatedinthesamearea,theemployeesofonefirmhaverelativelyeasyaccess totheonesofanotherfirmsbothviaface-to-facebusinessmeetingsbutalsovia informalcontacts(lunchmeetings,socialoccasions,etc),sotheymightexchange tacitinformationthatisnottradedinthemarket.E.g.thefinancialsectorin London. o 2.Non-tradedlocalspecialistinputs—Ifmanyfirmsinthesamesectorcluster together,thenthereisthepossibilityforcertainspecialistinputstobeprovided. Thesewouldnotbepossibleiftherewasnotenoughdemand.E.g.speciallegal firmsofsoftwarefirmsservingthefinancialsectorinLondon. o 3.Localskilledlaborpool—Thesameistruefor“specializedlabor.”Ifmorefirms ofthesamesectorareco-located,peoplewiththerequiredskillswillbe availableinthelocalarea;hencethefirmwillnotberequiredtospendmoneyin specializedtrainingandwillspendlessinrecruitmentcosts(easiertofind). • Threemaincategoriesofagglomerationeconomies: o 1.Internalreturnstoscale—internaltothefirmandlinkedtothesizeofthe firm.It’sgenerallymoreconvenientforafirmtoproducelargequantitiesthan smallones.Doublingtheinputsmorethandoubletheoutput.Hence,it’sbetter forafirmtohavealargefactorinonelocationratherthantwosmalleronesin twodifferentlocations. o 2.Economiesoflocalization—externaltothefirm,internaltothesector.These arelinkedtothefactthatdifferentfirmsinthesamesectorareco-located, creatingclusters.Theycreateacriticalmasssothatsuppliers,etc,canmoveinas well.Specializedworkersalsomigrateinthearea. o 3.Economiesofurbanization—externaltothefirm,externaltothesector.These accruetofirmsbelongingtodifferentsectorsthatareco-located.Thefactthat lotsofdifferentfirmsareinthesameareameansthatcertainservicescanbe provided,e.g.anairportorcertainmarketingoradvertisingservices,etc. Industrialconcentrationscanbemeasuredbylocationquotients(LQ). • IfLQ>1theregionspecializesinthatparticularsector. • IfLQ<1theregionislowerthanthenationalaverageandtheregionisprobablyan importerofthatgood. • IfLQ=1thenthatregiondoesnotspecializeinthatoutput. LECTURE5 Urbanhierarchiesand“centralplacetheory” • Trends: o Nationstendtobedominatedbyoneortwoprimalcities,generallylocatedin thecenterofthemajorpopulatedregions. o Thelargercitiesproducethelargestvarietyofoutputswhilesmallercities produceasmallerrangeofservicesandgoods. 4 ChristallerModel(1933) • BasedontheobservationsofthespatialdistributionsofcitiesandtownsinSouthern Germanyinthe1930s. • FormulatedbyChristaller,whotriedtoestablishwhethertherewassomekindof regularityinthenumberofcitiesrankedatthedifferentlevelsoftheurbanhierarchy. • Assumptions: o Isotropicspace(flat,identicalinalldirections) o Transportationcostsequalinalldirections o Populationandresourcesequallydistributedinspace o ThereareNdifferentgoods,g,thatcanbeproduced o AhierarchyofNdifferentmarketareaslevelsm o Andahierarchyofdifferenturbancenters • Higherordergoodsprovidehigherorder(larger)marketareas—inotherwords,goods areorderedfromtheonewiththelargestmarkettotheonewiththesmallestmarket o Marketaream=1forgoodg=1 o Marketaream=2forgoodg=2 o Etc… • Becausetherearedifferentcentersproducingthesamerankedgood,thefinalmarket areasareactuallynotcircularbuthexagonal o Foreachcityofrank1,howmanycities,say,rank2arelikelytoexistThereare threepossibleanswers. § 1.TheMarketPrinciple—Eachlowerrankedtowngrowswherethereis morespace(largermarket).Therank2citieswilllocatethemselvesatthe 6vertexesofthishexagon. § 2.TheTransportationPrinciple—Ifyoubelievethatwhatmattersishow centersareconnectedintermsoftransportation(e.g.roads).Therank2 citieswilllocatethemselvesonthestraightlinethatconnectstwolarger cities. § 3.TheAdministrativePrinciple—Ifthesmallerareahastobecontained withinthelargerarea(e.g.citiesinanadministrativeregion),thenthere willbemorerank2citieswithsmallermarketareas. Zipf’sRankSizeRule • Formula:Rankorder=(populationofthedominantmetroarea)(citypopulation) 5

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Chapter 1, Problem 23 is Solved
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Textbook: Calculus: Early Transcendental Functions
Edition: 6
Author: Ron Larson
ISBN: 9781285774770

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Answer: In Exercises 2124, find an equation of the line