资源描述：
《economic applications》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、Chapter11EconomicApplicationsOptimalcontroltheoryhasbeenextensivelyappliedtothesolutionofeconomicproblemssincetheearlypapersthatappearedinShell(1967)andtheworksofArrow(1968)andShell(1969).Thefieldistoovasttobesm-veyedindetailhere,however.Severalbooksintheareaare:Arrowa
2、ndKnrz(1970),HadleyandKemp(1971),Takayama(1974),LesourneandLeban(1982),SeierstadandSydsaeter(1987),Feichtinger(1988),LeonardandLong(1992),VanHilten,Kort,andVanLoon(1993),KamienandSchwartz(1998),andDockner,J0rgensen,Long,andSorger(2000).Wecontentom-selveswiththediscussi
3、onofthreesimplekindsofmodels.InSection11.1,twocapitalaccumulationoreconomicgrowthmod•elsarepresented.InSection11.2,weformulateandsolveanepidemiccontrolmodel.FinallywediscussinSection11.3,apollutioncontrolmodel.11.1ModelsofOptimalEconomicGrowthInthissectionwedeveloptwos
4、implemodelsofeconomicgrowthorcapitalaccumulation.TheearliestsuchmodelwasdevelopedbyRamsey(1928)foraneconomyhavingstationarypopulation;seeExercise11.8foroneofhismodels.ThefirstmodeltreatedinSection11.1.1isafinitehorizonfixed-end-pointmodelwithstationarypopulation.Thepro
5、blemisthatofmaximizingthepresentvalueofutilityofconsumptionforsociety,andalsoaccumulateaspecifiedcapitalstockbytheendofthehorizon.Thesecondmodelincorporatesanexogenouslyandexponentially29011.EconomicApplicationsgrowingpopulationintheinfinitehorizonsetting.Themethodofph
6、asediagramsisusedtoanalyzethemodel.Forrelateddiscussionandextensionsofthesemodels,seeArrowandKurz(1970),BurmeisterandDobell(1970),andIntriligator(1971).11.1.1AnOptimalCapitalAccumulationModelConsideraone-sectoreconomyinwhichthestockofcapital,denotedbyK{t),istheonlyfact
7、orofproduction.LetF{K)betheoutputrateoftheeconomywhenKisthecapitalstock.AssumeF(0)=0,F{K)>0,P{K)>0,andF"(ir)<0,forK>0,ThelatterimpUesthediminishingmarginalproductivityofcapital.Thisoutputcaneitherbeconsimiedorbereinvestedforfurtheraccumulationofcapitalstock.LetC(t)beth
8、eamoimtofoutputallocatedtoconsumption,andletI{t)=F[K{t)]—C{t)betheamountinvested.Let8betheconstantrateofdepreciationo
