美国生数学建模竞赛奖题篇

精品数淘精品数淘宝店铺：闵大荒工科男的杂货Understandingthesocioeconomicprocessesandtensionsunderlyingpopulationstabilityisim-perativeforestablishingapopulationofhumansonMars.Theobjectiveofourteamwastodevelopgovernmentalandwelfarepoliciesthatwouldallowforapopulationof10,000newresidentsonMarstodevelopanegalitariancivilizationthatsurpassessimilarcivilizationsonEarth.Toaccomplishthisgoal,ourteamwastaskedwithbuildingamodelthatevaluatestheparametersrelatedtoincome,education,andequalityforthenewpopulation.Wedevelopedanagent-basedmodelthatsimulatesapopulationof10,000agentsonMarsusingrealworlddatagivenbytheUSCensus’dataonoccupationalincome.Inourmodel,eachagent,orMartiancitizen,progressesthroughtheirlifecyclebyattendingcollege,searchingforjobs,andearningincome.Thegovernmentthenprotectstheseindividualagentsfromeconomicharmusingprogramssuchaswelfareandminimumwage.Tomaximizebothsocialwelfareandproductivity,wechosetomonitorthestateoftheeconomyandcreatemetricsthatwouldmeasuretheeffectofagent-basedfactorsonthecommunity’swell-being.Wemeasuredmultipleparametersofthecom-munitygeneratedbytheseagents,whichallowedustoevaluatetheconditionoftheeconomy.Fromtheseparameters,wegeneratedthreemetrics:theIncomeMetricI,theEducationMetricE,andishesawagegapbetweentherichandthepoorthatiseithertoolargeortoosmall.Theeducationmetricmeasurestheamountofunemploymentasaneconomicalfactorandthestudent-to-facultyratioasasocialwelfarefactorsoastoevaluateeducationthroughboththelensofproductivityandwell-being.Finally,theEqualityMetriccomparestheproportionofwomeninoccupationsonMarstotheirproportioninjobsonEarthtoillustratethedynamicsocialequalitypresentinPopulationZero.Additionally,ourmodelincludesseveraleconomicindicatorsandpropertiesliketheinflationrate,aprogressivetaxsystem,totalinvestment,andgovernmentdebttoaddfurthertothedynamicequilibriumoftheeconomy.Usingourmodel,wefoundthatthebestinitialpopulationhadameanageof37andaratioof1:10ofinnovatorstoproducers.AnalysisofourmetricssuggeststhattheMartiansocietycansupportmorethan10,000peopleincaseofanemergencymigrationfromEarth,assumingthatinfrastructureispresent.Wefoundthataminimumwageof$70,000providedthegreatestbenefittosociety.AsmaternityandpaternityleavelengthsdidnothaveagreatimpactonGDP,wedeterminedthatamaternityleavelengthof10monthsandapaternityleavelengthof3months.Governmentcontrolofinflationprovedtobecriticaltomaintainingthepurchasingpowerofthepeople.Aprogressivetaxsystemservedtoincreaseincomeinequalitywhilekeepinginvestmenthighandgovernmentdebtlow,allowingthegovernmenttoprovideforincreasededucationandinfrastructureneedsinthefuture.Mostimportantly,ahappinesssurveycanbeutilizedtocreateaastrong,collaborativesocietyworkingtoreachcommongoals.精品数淘宝店铺：闵大荒工科男的杂精品数淘宝店铺：闵大荒工科男的杂货January24,Dr.IsabelleC.MossDirectorofLIFEQuaiGustave-DearDr.ThankyouforworkingwithustodesignaplantocolonizeMars!Weareexcitedtobeapartofhuman-ity’sgreatestadvancementsincetheMoonLanding–UTOPIA:2100.WehavedevelopedamodeltoaddressyourconcernsaboutthesocialandeconomicequalityinUTOPIA:2100.Weaimedtoproducepolicymeasuresthatwouldmaximizeincomeequality,genderequality,andeducationaladvancementinthesociety.Consideringthecomplexityofdescribinggovernmentalpolicyforasocietyonanentirelynewplanet,wedevelopedanintricate,agent-basedmodelthatsuggestedthattheinitialpopulationshouldbecom-posedofa50:50ratioofmales:femalestooptimizetheequalitymetric.Wealsodeterminedthattheoccupationsofeachpersonshouldbechosensothattheproportionofpeopleineachjob(asdefinedbytheBureauofLaborStatistics)isconserved.Wefoundthatchoosingapopulationwithameanageof37,andwhichconsistedofmoreteenagersandchildrenthanolderpeople,resultedinhighGDPvaluesandoptimizedtheeducationandincomemetrics(seeimagebelow).Selectingapopulationwitha10%proportionofinnovators(thoseindividualswithjobsinmanagementandsciencewhoaremorelikelytoinvestintechnologicaladvancement)producedoptimalunemploymentrates.Otherfactorssuchasmaritalstatusandethnicityarelessinfluentialontheoveralldevelopmentofthecolony,soensuringthatthesedemographicsareequallyrepresentedisadequate.Theuseofunskilledlaborhasbecomesubstantiallylowerwhencomparedtothe21stcenturyduetotheriseofautomationandinnovationsintheroboticsindustry.Therefore,wesuggestthatthegovernmentrequireandfundthetwo-yearcol-legeeducationofallpeople,eliminating"unskilledlabor"fromUTOPIA:2100.Whenwetestedvariouspopulationdistributions,wenoticedsomeoscillationsineducationdemand.Inparticular,afterafewyearsintothemodel,thedemandforeducationslowlyfellovertime.However,asthenewgenerationcameintothecollegeeducationsystem,ahugespikeintheeducationdemandoccurred.Tomitigatetheeffectsofthisinflux,theMartiangovernmentshouldbepreparedtoprovidefundsduringthesuddeninfluxofstudents.POLICYADVISORY精品数淘宝店铺：闵大荒工科男的杂货精品数淘宝店铺：闵大荒工科男的杂货ThefirstthingtobedoneinthenewMartiancivilizationissocialwelfare.Inordertocorrectlyimple-mentthis,thecivilization’sgovernmentmustbeabletoprovideuniversalhealthcare,collegetuition,socialsecurity,andwelfare.Wealsotestedvarioussocialbenefitslikeminimumwage.Accordingtoourincomemetrics,aminimumwagevalueof$70000(adjustedforprojectedinflationin2100)willprovidetheoptimalbenefittosociety.Ontheotherhand,maternityandpaternityleaveappeartohaveaninsignificanteconomiceffect.Settingthesetwolengthsto10monthsand3monthsrespectivelymayhelpincreasethehappinessandwell-beingofourpopulation.Thegovernmentisalsoresponsibleforthesocialandeconomicwell-beingofallcitizensofUTOPIA:2100.Asaresult,thecentralbankinginstitutionmustensurethatinflationratesstaybelowincomegrowthratestopreventlossofpurchasingpowerandkeepinvestmentlevelshigh.Weproposeapro-gressivetaxsystemtohelpfundgovernmentspendingwhilereducingincomeinequalities.Thetaxrateshouldbemaintainedsothatthegovernmentisnotearninglargesumsofmoneyandsothatthepeoplearenotlosingmuchoftheirhard-earnedincomeduetothegovernment.Strictnon-discriminatorypoli-ciesshouldbeimplementedinthejobsectortoincreasegenderequality;peopleshouldnotbedeniedjobsduetotheirgender,race,andothercharacteristics.AnextremelyefficientandreliablemethodtomeasuretheprogressofUTOPIA:2100isthehappinessindex,whichcanbemeasuredbyimplementingasurveyinwhichcitizensreporttheirsatisfactionaboutgovernmentalpolicies(suchasmaternity/paternityleavelength,unemployment,andinflation).Byincreasingtheoverallhappinessofthepeoplethroughthissurvey,thegovernmentcangainthepeople’strust,andformastrong,collaborativesocietyworkingtoreachcommongoals.Byfollowingthesepolicies,wehopetoachievethe•Thedevelopmentofalargemiddleclassthatcomposesthevastmajorityofthepopulation.Wealsohopetominimizethenumberofminimumwageworkersandhaveonlyasmallnumberofextremelywealthypeople.Theunemploymentrateisstableandlow,andoureducationsystemscanadequatelyaccommo-dateandteachthepopulation.Wehopetoeventuallyhavegovernmentsubsidisationof4-yearcollegeeducationsforallstudents.Thereisanequalproportionofwomentomenineachjob••Withthesepoliciesinplace,thegovernmentneedonlydevelopphysicalinfrastructure(livingquarters,foodproductionfacilities,etc.)aspopulationsizegrows.Giventheinitialpopulationsizeandcharac-teristics,keepingupwiththepopulationgrowthshouldnotbedifficult.IntheeventofadisasteronEarthresultinginaneedforlargescalemigrations,thegovernmentonMarsneedstoimproveitsphysicalinfrastructuretoaccommodatethelargeinfluxofimmigrants.However,noneofthepoliciesneedtobealteredsubstantially.WethankyouforyourcooperationinthisgrandendeavorandwewishthebestforUTOPIA:MatthewC.McConaugheySeniorPolicyAdvisorMathematicalAnalystLABORATORYOFINTERSTELLAR,FINANCIAL,ANDEXPLORATIONE:mcconaughey@M:(555)555-5555精品数Houston,wehaveaproblem!TheLaboratoryofInterstellar,Financial,andExplorationPolicy(LIFE)hasconductedmultiplestudies,designedtheinfrastructure,andconductedscientificexperi-mentstoallowforthefirsthumanpopulationtoliveonMars.Thisfirstpopulation,calledPopulationZero,willinclude10,000people.ThemissionofPopulationZeroistocreateasustainablesocietybymaximizingbotheconomicoutputandhappinessintheworkplaceforitscitizens.Thisproject,termedUTOPIA:2100,outlinesthegoalofcreatinganoptimalworkforceforcenturytogiveallpeoplethegreatestqualityoflifewithavisionofsustainabilityforthe100yearsonMars.Thismartiancommunitywillbedrivenbyegalitarianprinciplesineconomics,government,workforce,andjusticesystems.Intheprocessofdevelopinganeconomic-workforce-educationsystemforPopulationZero,LIFEhastaskedourgroupofmathematicalmodelersandpolicyadvisorstodevelopasetofpoliciestofacilitatethemigrationtoMars.Thegoalofourteamistoconsiderincome,education,andequalityastheyrelatetothegoalsofPopulationZeroandprovidepolicyrecommendationsthatwillaccommodatesuchinterplanetarycommunityprojects.RestatementofOurgroupistaskedwithdevelopingpolicyrecommendationsthatwillallowPopulationZerotomaximizebotheconomicoutputandhappinessintheworkplacefortheircitizens.ThevisionoftheUTOPIA:2100projectistoproduceasustainablepopulationonMars.TheInternationalCoalitiononMars(ICM)hasprovideddirectivesforourgrouptodeveloptheserecommendations.ParametrizationofWearetaskedwithdefiningparametersrelatedtoincome,education,andsocialequalityforPopu-lationZero.Thisinvolvestheconsiderationofworkforcedemographics,educationaldemographics,governmentalinfrastructurethatfacilitatestheseparameters,andpoliciesthatwillensurethatsuchparametersaremaximized.Incompletingthisdirective,weareaskedtoidentifyspecificoutcomesthatwouldindicatepos-itiveoutcomesforthesethreefactorsforthenextdecade.WearealsoaskedtosuggestpossibledemographicsofPopulationZerothatwouldleadtopositiveresults.Furthermore,metricsaretobecreatedthatcanmeasuretheseparameters.SampleWearetaskedwithsynthesizingasamplepopulationof10,000thatwouldensurethegoalsofUTOPIA:2100.Indoingso,wemustconsiderthedemographicsofage,sex,andeducation.Fur-thermore,thispopulationmustbecapableoffacilitatingthegoalsofUTOPIA:2100.Finally,wearetaskedwithbuildingamodelthatcandescribethepopulationdynamicsforthenexttenyears.Indoingso,wemustdeterminethesalarydistributionthatwillbalanceproductivityand精品数wellbeing.Wearealsoaskedtocharacterizeinnovationsthatcouldimproveourmodel.Inaddition,weconductsensitivityanalysisfora100-yearplanandconsideremergencyevacuationmigrationpatternsfromEarthtoMars.DefinitionsandSinceitischallengingtopredictallvariablesandfactorsthatmayaffectourmodel,wemadecertainassumptionstoproduceaworkingmodel.•EveryMartiangoestocollegetoobtainatleastanAssociate’s–DuetothehighleveloftechnicalskillsrequiredtosurvivethenewlifeonMarsasasthepredictedhighdemandforeducationinthecitizensbecomewell-educated.century[1],wemandatethat•EducationDiplomasareissuedat2-,4-,6-,and8-year–WeassumeeverycollegestudentfollowsthetraditionalpatternofAssociate’sin2years,Bachelor’sin4years,Master’sin6years,andPh.Din8years.Otherdegreeoptionsthatrequiremorethan8yearsarenotcoveredinourmodel.Everyindividualisactivelypursuingajobgiventhattheyareofworkingageandarenotapermanentstay-at-homemomordad.–Inourmodel,pursuingajobandbecomingaproductivecitizenismoreimportantthanholdingdegreesthatrequirehigherlevelsofeducation.Inanegalitariansociety,thesocialwelfareoftheMartiancitizensshouldnotdependontheeducationtowhichtheyareprivy.MembersofthepopulationonMarswillretireattheageof70,andtheirlifeexpectancywillbe100years.••–AccordingtotheUNPopulationBureau,thelifeexpectancyincenturywill100[2].Inaddition,fromhistoricalcharts[3],itcanbeseenthataverageretirementhasincreasedfrom57in1991to60in2012.Thisisroughlyanincreaseof1yearinretirementper7yearspassed.Extrapolatedtotheyear2100,aretirementageof70isareasonableestimate.•Race,ethnicity,orreligionhavenoimpactonapopulation’sabilitytoprogresson–Theculturalvaluesbornefromrace,ethnicity,andreligionaredifficulttoquantifyorexpressinamodel.Incomes,thenumberofworkersineachoccupation,andgeneralpriceswillincreaseatthesameannualrateastheycurrentlydo.•–Usingthesameannualrateofincreaseisareasonablewaytoextrapolateincomes,prices,andjoboccupationsfromcurrentones.•Thenecessaryinfrastructure(ex.homesandotheressentials)isalreadypresentonMarsbeforePopulationZero.ItisreasonabletoassumethatLIFEhasalreadybuiltinfrastructuretosupportPopulationThefamilialrelationshipsbetweenindividualsagentsarenotRepresentingfamilialunitsinanagent-basedmodelrequiresanunderlyingnetwork.Suchanetworkiscomputationallyintensiveanddifficulttoevaluateover10,000nodes.ThetimeofdeathisnotcontingentupontheeventsthattakeplaceinyourOurmodeldoesnottakeintoaccountthehard-to-quantifyrelationshipsbetweenincomeandoccupationonhealth.••精品数Otherthanmaternityandpaternityleave,ourmodeldoesnotconsideranyotherformsof–Itischallengingtoquantifyeventsinthelifeofanagentinourmodelthatwouldresultinunpaidleave.AnalysisofThetwoimportantthemesinthisproblemarethemaximizationofsocialwelfareandproductivity.ThenewsocietyinMarsisbaseduponegalitarianprinciplesandmustbeabletoprovideforthewellbeingofitscitizenswhilstproducinganunparalleledeconomy.Sincewearecreatinganentirelyindependentandself-sustainingcivilization,wecanincorporateseveraldesirablecharacteristicsthatmayormaynotbepresentonEarth.Thefirstsuchcharac-teristicforourMartiancivilizationispersonalinitiative:everyindividualshouldbemotivatedtoincreasethewell-beingofhisorherself.Thismotivationusuallycomesintheformofhigherwagesfortheindividual.Althoughasimpleconcept,thelackofpersonalinitiativewasamaincontributortothedownfallofCommunism[4].Ratherthanreducingthebehaviorofmembersofthepopulationtoasetofvariables,itisimportanttomaintainthecharacteristicsofeachindividualagentsoastoaccountforthispersonalinitiativeinourmodel.Thesecondessentialcharacteristicofouradvancedcivilizationissocialwelfare.Inparticular,theMartiangovernmentshouldbeabletoprovidefundstoaccommodatehealthcare,collegeeducation,maternity/paternityleave,andothersociallyusefulpublicgoods.HavingthiswouldallowourMar-tiancivilizationtopotentiallysurpasstheUnitedStatesinsocialwelfareprograms.Ourplantoapproachthisproblemistodevelopanagent-basedmodel,whereagentsrepresentPopulationZeroonMars.Althoughweconsideredmodelsbasedondifferentialmathematics,tradi-tionaldifferentialequationmodelsdonotaccountforpersonalinitiative.Furthermore,suchsystemsoftenoverlookcomplexinteractionsthatoccurduetothebehaviorofdiscreetagentsratherthancontinuousvariables.Therefore,wechosetouseanagent-basedmodel,asitaccuratelyrepresentsaperson’simpactonsocietyaswellastheinteractionsbetweenandwithincitizens.Tocharacterizeourcivilization,wecreatedthemodelinNetLogo.ModelDesignandTobetterunderstandthemechanicsandinteractionsinthesystem,wewilldescribeourmodelbyanalyzingthelifeofBob,apersonbornonMars.Ourmodelcategorizespeopleinto4lifestages(0,1,2,3,and4)basedontheirageandoccupation.WhenBobisborn,hislifestageis0.OnceBobbecomes5yearsold,hestartsattendingprimaryschool,andhislifestageissetto1.Bobcontinuesthroughhiseducationuntilhegraduateshighschool.BobreceivesanAssociate’sdegreebecausecollegeeducationispaidforandrequiredbytheAftergettinghisAssociate’sdegree,Boblooksforajob.However,hecanonlysearchforjobswhichhaveaneducationrequirementof2yearsorless.IfBobfindssuchajobonhisfirsttry,hetakesit;otherwise,hecaneithercontinuetosearchforajob(andisclassifiedasunemployed)witha精品数probabilityp2orgobacktoschoolwithaprobability(1−p2).Ifhegoesbacktoschool,hecontinueshiseducationandobtainsaBachelor’sdegree.Onceagain,hesearchesforajob,butthistime,heandgoesbacktoschool(nowwithaprobability(1−p4)),hegetshisMaster’sdegreeandsearchesforajobagain(thistimesearchingthroughjobswithaneducationrequirementof6yearsorless).Ifhestilldoesnotgetajobandgoesbacktoschooloncemore(withprobability(1−p6)),heobtainsaPh.D.Then,heleavescollegewithprobabilityp8=1andcontinuestosearchforajob(withanyeducationrequirement)untilhefindsone.IfBobhasaBachelor’s,Master’s,oraDoctorate,thereisachancethathewillgetajobwithalowereducationrequirementthanhiseducationalattainment.Forexample,letusassumethatBobhasaMaster’sdegreeandissearchingforajob.Althoughtherearenoavailablepositionsforjobswithaneducationalrequirementof6or4years,thereisanavailabilityforajobwithaneducationalrequirementof2years.Bobthentakesthisjob,andisclassifiedasunderemployedsinceheis”overqualified”forhisjob.Peoplewhoareunderemployedcontinuetosearchforjobswhiletheywork.Inthiscase,Bobwillseeifthereareanyjobavailabilitieswitheducationrequirementsof4or6years.Ifhefindsone,hewillquithiscurrentjobandtakethenewjob.Ifhefindsmorethanonejobwithdifferenteducationalrequirements(bothhigherthanthatofhiscurrentjob),hewilltakethejobwiththehighesteducationalrequirementthathesatisfies.OnceBobhasajobwhoseeducationalrequirementmatcheshislevelofeducation,heisnolongerclassifiedasunderemployed.TheCensusTodeterminethesetofavailablejobsateverystepinourmodel,weneeddatathatindicatesthelikelydistributionofjobsthatwillbeavailableonMars.Todothis,weusetheUnitedStatesBureauofLaborStatistics’(BLS)datafrom2011to2015.TheBLScategorizesthesetofalloccupationsintheUSinto22primarycategories.Eachcategorycontainsthenumberofpeopleinthatcategory,meanincome,medianincome,percentile10income,percentile25income,percentile75income,andpercentile90income1.Toextrapolatethedatafortheyear2100foreachindividualoccupation,webothincomeandnumberofworkers.Giventhesegrowthrates,wescalecurrentUSemploymentandincomevaluestothatof2100US.Thelastthingweneedforeachoccupationtypeistheminimumeducationnecessaryforthatoccupation.TheBLSdoesnotprovideeachofthe22occupationswithaminimumeducationlevel.Instead,wereferencedindependentsourcestodeterminethesevalues.OurcalculationscanbearesummarizedinTable1andTable2intheAppendix.Ateverytickinthemodel,an“IncomeFile”and“JobDistribution”areevaluated.The“IncomeFile”containsdataaboutthemeanincomeandpercentileincomesforagentsinthemodel,whilstthe“JobDistribution”containsthedistributionsofjobsinthemodel.Bothvariablesinitiallystartrates).However,sincethepopulationofMarsisnotthesameasthepopulationoftheUS,itisnot1Twodatapointsweregivenavalueof#onthedata-setsincetheywereover187200.Wereplacedthemwith精品数精品数thenumberofworkersineachoccupationthatcarriesmeaningbutrathertheratiooftheworkersineachoccupationtothecompletelaborforce.Thus,wereplaceeveryvalueviforoccupationiwith itoobtainthefractionoftotaljobsthatareofoccupationi.TocalculatethenumberofactualjobsonMars,weneedtomultiplybythesizeofthejobmarket(i.e.thenumberofpeopledemandingjobs).Thisisequaltothenumberofpeopleworking,thenumberofunemployedindividuals,andthesubsetofstudentsincollegethatareactivelyrequestingjobsatthetime.However,intherealworld,jobcreationandjobeliminationarenotinstantaneous:thereissomeinflexibilityinchangingthenumberofjobs.Toaccountforthis,thesetofavailablejobsisresetaccordingtothesizeofthejobmarketonceayearinsteadofonceatick.Notethatinourmodel,ticksareevaluated6timesperyear.Todeterminetheincomeforeachpersonwhoishired,eachworkerisgivena“percentile.”Ifthispercentileis10,thenthatworkerreceivesthepercentile10incomefromourjobratios.Ifthepercentileis25,thenthatworkerreceivesthepercentile25income.Ifaworkerisgivenapercentilebetween10and25,thenthatworkerreceivesaweightedaverageoftheknownvaluesofthepercentile10andpercentile25incomes.Inotherwords,iftheworkerisgivenapercentileofx,thenhisorherincomeis(25−x)×(percentile10)+(x−10)×(percentileIfaworker’spercentileisbelow10,heorshereceivesminimum-wage(whichwillbedescribedindetaillater).Ifaworker’spercentileisabove90,wecannotinterpolateduetoalackofdata,andthereforesetittobethepercentile90income.Ofcourse,theremustalsoberoomforgrowthfortheworker’sincome.Toaccountforthisgrowth,theworker’sincomeincreasesbysomefixedamountgivenbyhisorherjob’sgrowthrateeveryyear.Whenaworkerreceivesajob,heorsheisrandomlyassignedapercentilefrom10to50asastartingsalary.WhenPopulationZeroarrivesonMars,theirsalarybeginsatthepercentileappro-priatefortheirageandeducation,giventhattheystartedfreshoutofcollege.Whencalculatingthefoundthemediantenuretobe4.3years[42],sowesetthepercentilegrowthrate =Thereisa2%chancethatagivenworkerwilllosehisjobeveryyear[43].Ifaworkerloseshisjob,hewilllookforanewoneinthejobmarketandwillremainunemployeduntilhefindsone.Thereisalsoaprobabilitythataworkerwillquithis/herjobandbecomeastay-at-homeparent.Inthiscase,theworkerisremovedfromthelaborforceandhis/herlifestageissetto4,thoughtheydonotreceivesocialsecurityuntiltheyreach70yearsofage.Theprobabilitythataworkerbecomesastay-at-homeparentdependsuponhis/hergenderandisinverselyproportionaltohis/herlevelofeducation[50,51,52].LevelofPh.精品数Theprobabilitiesp2,p4,p6,andp8aresetusingthe2015USCensusBureaudataonEducationalAttainment:[28]: Bachelor Ph.Toillustratethis,considerp4.ItisdefinedtobethenumberofpeoplewholeavecollegewithBachelor’sdegreeoverthenumberpeoplewholeavecollegewithaBachelor’sdegreeorhigher. =0.49p446515+18683+BirthandNow,letusconsideranotheragentinourmodel,Alice.Aliceisapproximately26yearsold,hasajob,andismarriedtoBob2.AsAliceisafemalebetweentheagesof18and50,thereisachancethatshewillhaveachild.Thisprobabilitypbabyisgivenasafunctionofage(a)andthenumberofbabiespreviouslyconceived(b).Theprobabilityisinverselyproportionaltothenumberofbabiespreviouslyconceivedsinceoneislesslikelytogivebirthifonealreadyhasalotofchildren.Theprobabilitypeaksat26yearsofage(asshownby[38])andislowerattheboundariesof18and50yearsofage.Thus:1a−6(1a−4)2+pbaby=k× b+Noticethatthismetricisproportionaltoaconstantk.Tosimulatetheworldbirthrateof2.4[39],weusetheconstantk=0.2653(asdeterminedbytrial-and-error).IfAliceisgoingtohaveachild,atimerstartsforher.Oncethattimerreaches9months,thebabyisborn.Afterthebabyisborn,Alicecannothaveachildforatleastanother15months.WhenAlice’sbabytimerreaches7months,shegoesonmaternityleave(ifshehasajob).Thematernityleave’slengthisvariedduringmodeltestingtodetermineitseffectondifferentmetricsdiscussedlater.WagesthatAlicereceivesduringhermaternityleavearenotcountedinanyoftheincomemetricsasthesearetransferpaymentssubsidizedbythegovernment.WhenAlice’smaternityleaveends,Bob’spaternityleavebegins.Thepaternityleavelengthisalsovaried.4LetusonceagainconsiderBob,whoisnow70yearsold.BobnowretiresandbeginsreceivingSo-forsometime.Whenpeopleareborn,theirlifespanispredeterminedusingagammadistribution.Themeanlifespanis100years,withavariationof10years.OnceBob’sageequalshislifespan,he2Notethattherearenofamilystructuresbuiltintothemodel;weareassumingonehereforthesakeofexplanation3WhenPopulationZeroisinitializedonthemodel,thisconstantisincrementedtoitsfinalvalueover20yearstopreventlargebabybooms-thisalsosimulatesthefactthatpeoplewouldnotimmediatelyreproduceathighonceon4Intheactualmodel,whenAlice’smaternityleaveends,thepaternityleaveofarandom,workingmalewhoisnotalreadyonleavewillbegin.精品数dies.ThisisthelifecycleofapersonlivinginourmodelofUTOPIA:Toillustratethelifecycle,weprovidethefollowingFigure1:AFlowchartillustratingthelifeofindividualagentsintheGlobalAswebegintoconsidermonetarycostsandthebureaucracy,itisimportanttoconsidertheglobalinflationthatoccursbetweentodayandthe22ndcentury.USinflationfrom1923to2012isillustratedbelow[37]:Duetotheseeminglyrandombehaviorofworldinflation,wecannotreasonablyextrapolate精品数tionforthe精品数tionfortheremainderofcentury.Toavoidthispitfall,weconsiderCanada’sinflationFromthefollowingfigure,weseethatCanadahasaverystableinflationrateAsCanadatendstofavoreconomicstabilityoverrapideconomicgrowth,wewillmodeloureconomyafterCanada’seconomy,sinceourgoalistomaximizebothproductivityandsocialwelfare.CurrentCanadianinflationisaround1.3%[41],sothiswillbetheworldinflationrateusedtoconvertfromthe21stcenturyto22ndcenturymonetaryvalues.EconomicIndicators&ThegoalofPopulationZeroistocreateasocietythatfarexceedstheeconomicstrengthofsimilarsocietiesonEarth,yetachievesasocietalequilibriumacrossincome,equalityinworkspace,andedu-cation.Assuch,itisimportanttomonitortheconditionoftheeconomyinducedbyouragent-basedmodel.WecalculatevariouseconomicindicatorsthatallowustotrackthedevelopmentandprogressofUTOPIA:2100.Topreserveincomeequality,wehaveimplementedaprogressivetaxsystemwith5taxbrackets.Alltaxesaredeductedfromeachconsumer’sincome.Thesetaxesprimarilyrepresentincometaxrates,butcanbeadjustedtoincludesalestax,propertytax,etc.Thetaxrateforeachbracketisafractionofthe“overalltaxrate”(OTR),whichisvariedduringmodeltesting.WecanvarythetaxratetodeterminetheeffectonGDP,governmentdebt,andourincomemetric.Thefollowingarethetaxbracketsandtheircorrespondingrates:TaxTax≤MinimumMinimumWage–(MinimumWage+IncomeMean2(MinimumWage+IncomeMean)–Income2IncomeMean–75thIncome475thIncomePercentile–90thIncome3≥ IncomeGovernmentSpendingandusingratiosfromtheU.S.governmentwiththeexceptionofhealthcar