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1、Chapter10ApplicationstoNaturalResourcesTherapidincreaseofworldpopulationiscausingacorrespondingin•creaseinthedemandforconsumptionofnaturalresources.Asaconse•quencetheoptimalmanagementandutilizationofnaturalresourcesisbecomingincreasinglyimportant.Therearetwomainkind
2、sofnaturalresourcemodels,thoseinvolvingrenewableresoiu'cessuchasfish,food,timber,etc.,andthoseinvolvingnonrenewableorexhaustibleresourcessuchaspetroleum,minerals,etc.InSection10.1wedealwithafisheryresourcemodel,thesoleownerofwhichisconsideredtobearegulatoryagency.Th
3、emanagementprob•lemoftheagencyistocontroltherateoffishingovertimesothatanappropriateobjectivefimctionismaximizedoveraninfinitehorizon.Adifferentialgameextensionknownasthecommonpropertyfisheryre•sourcemodelisdiscussedinSection12.1.3.Forotherapplicationsofoptimalcontr
4、oltheorytorenewableresourcemodelsincludingthosein•volvingpredator-preyrelationships,seeClark(1976),Goh,Leitmann,andVincent(1974),andJ0rgensenandKort(1997).Section10.2dealswithanoptimalforestthinningmodel,wherethin•ningistheprocessofremovingsometreesfromtheforesttoim
5、proveitsgrowthrateandquality.AnextensiontoachainofforestsmodelispresentedinSection10.2.3.ThefinalmodelpresentedinSection10.3dealswithanexhaustibleresourcesuchaspetroleum,whichmustbeutilizedoptimallyoveragivenhorizonundertheassumptionthatasubstitutewiUtaketheplaceoft
6、heresourcewhenthelatter'spricebecomestoohigh.Therefore,the26810.ApplicationstoNaturalResourcesanalysisofthissectioncanalsobeviewedasaproblemoftheoptimalphasinginoftheexpensivesubstitute.10.1TheSoleOwnerFisheryResourceModelWiththeestablishmentof200-mileterritorialzon
7、esintheoceanformostcountrieshavingcoastlines,thecontroloffishinginthesezoneshasbecomehighlyregulatedbythesecountries.Inthissense,fishinginterritorialwaterscanbeconsideredasasoleownerfisheryproblem.Ontheotherhand,ifthecitizensandcommercialfishermenofagivencountryarep
8、ermittedtofishfreelyintheirterritorialwaters,theprob•lembecomesthatofanopenaccessfishery.Thesolutionsofthesetwoextremeproblemsarequitediff
