land use in a long narrow city

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1、JOURNALOFECONOMICTHEORY3,430-447(1971)LandUseinaLongNarrowCityROBERTM.SOLOWDepartmentofEconomics,MassachusettsInstituteofTechnology,Cambridge,Mass.02139ANDWILLIAMs.VICKREYDepartmentofEconomics,ColumbiaUniversity,NewYork,N.Y.10027ReceivedDecember3,1970Mosttheoreticalmodelsofurbanland

2、useconcentrateonresidentialdensity.Herewetakeupanotherimportantuseofurbanland,forroads,or,moregenerally,fortransportation.Weanalyze,inthesimplestpossiblesetting,theoptimalallocationofagivenurbanlandareabetweenthegenerationoftrafficandthecarryingoftraffic.Weshowthat,exceptinalimiting

3、case,theproportionoflandallocatedtotransportationisadecreasing,concavefunctionofdistancefromthecenterofthecity.Wethenanalyzethecompetitiverentprofilegen-eratedbyanyland-usepattern,ontheassumptionsthattherearenocongestiontollsforroaduse,andthatcommoditiesaresoldatuniformdeliveredpric

4、ewithsellersabsorbingtransportcost.Ontheseassumptions,weshowthatthemarketvalueoflandmaybeaverypoorguidetoland-usedecisions,andwouldleadtooverallocationoflandtotransportation,especiallynearthecenter.Ourmodelisone-dimensionalbecausethatisthebestwecandonow.Wehopeitwillleadontomorereali

5、stictreatmentsoftheproblem.1.ANALLOCATIONPROBLEMImagineabuilt-upareaorcityconfinedtoarectangularstrip.Inthe(x,y)plane,itoccupiesarectangleoflengthLandwidthFKThecityislongandnarrowinthesensethatitswidthWissmallcomparedwithitslengthL.Theoperationalmeaningofthisassumptionisthattranspor

6、ta-tioncostinthebreadthwisedirectionisneglected,buttransportationinthelengthwisedirectionisregardedascostly.TheareaofthecityisWL.ItisalreadydecidedthatanareaA

7、needfor430LANDUSEINALONGNARROWGITY431themovementofgoodsfromplacetoplaceaccordingtorulestobelaidownsoon.Therestofthecityarea,WL-A,istobedevotedtoaroadwhichcarriesthetrafficgeneratedbythebusinessdistrict.Theproblemnowarises:Howshouldtheroadbelaidouttominimizetheaggregatetransportcosti

8、ncurredinthecityper