一类宏观动态经济系统的动力学模型

20001111:100026788(2000)1120072206,(,610065):,:,;;,L,,L:;;:N941.3aAKindofDynamicalModelsonDynamicalMacro2economicSystemTANGJian2ping,XUJiu2ping(InstituteofInformationandDecisionMaking,SichuanUniversity,Chengdu610065)Abstract:Inthispaper,thecorrespondingeconomicanalysesaregiventotheeconomicdynamicalmodelofconsumption,capitalandmoneyandtoitsdynamicalproperties.Manyconclusionswithpracticalsignificanceareobtainedasfollows:Itisnecessaryforensuringtheeconomicrunningstabilitythatthemonetarygrowthrateiskeptalowerlevel.Thelowerpercapitaconsumptionlevelisunfavorabletotheeconomicstabilityanddevelopmentwithahighspeed.Somemeasuressuchascultivatingthegroupinvestors,establishinginverstmentfundshouldbetakenforensuringthestabilityanddevelopmentofthecapitalmarketinChina.Moreover,adynamicalmodelonpercapitamoneyholdingisbuilt,andthepossibledynamicalpropertiesofpercapitamoneyholdingarediscussed.Keywords:dynamicalmodel;economicanalyses;moneyholding1Keynes30,[1],,[2]L,(Clower),LSidrauski60,(Ramsey),cm,[3]:a:1999204207:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.dKödtK=n+H-f’(k)dkdt=f(k)-nk-cdmödtm=R-n-P(1.1)KkcmPHnR;f(k)=F(KöN,1)ZZ,u(c,m),Kc,mZ,,ckmZ,,:(MI)dcdt=e(f’(k)-n-H)cdkdt=f(k)-nk-cdmdt=Rm-nm-Pm(1.2)e=-dVödccõd2Vödc2(1.3)V,(111)Z,Z[13,518]Z(MI),,,,,Z2(MI),:f’(k0)=r=H+n,c0=f(k0)-nk0ZZ,n+HZ,c0=f(k0)-nk0ZZ,ZZZ,0ZWm=(P+r)K,Wm=0,P+r=0,ZRouth2Hurwiz:211(112)X0=(c0,k0,m0)T:1)n+P+Pmm0-H-R02)n2+nP+nPmm0-nR+f(k0)c0e03)f(k0)c0e(n+P+Pmm-R)04)nd2+n2d-f(k0)nd+nf(k0)c0e-f(k0)f(k0)c0e0211,,RZ,H,R0,RR03711©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,n+P+Pmm0-H0,Z,Z,,,Z1992,1993,,,Z,,1996GDP917%,611%,L,,L211n2+nP+nPmm0-nR+f(k0)c0e0,,f(k)=akn(nE2),a,Z,,,90,,,,,,,Z,,,,,Z212R3(MI)R2Xa=BX,X=(k,m)T,B,D=detB=(f(k0)-n)[(R-n)-Pmm0-P],S=traceB=f(k0)-n+(R-n)-Pmm0-P,:1)D0,(MI)(k,m);2)D0,S2-4DE0,(MI)(k,m)ZS0,;S0,Z212,D=(f(KS)-n)[(R-n)-Pmm0-P],f(k0)=r=n+H,D=H[(R-n)-Pmm0-P]ZH0,n,P,Rk-m(k0,m0)Z:S=H+(R-n)-Pmm0-P=(H-Pmm0)+(R-P)-n,Pm0,H-Pmm00Z,D0,RS00,(k0,m0)ZZ,f(k)=ak,a(0,0)Za,(0,0)Zf(k)=ak2,ZZc,kZf(k)=ak3,kZ,[20]ZZ,,,,,,Z,,,;,,Z,Z19491415à198841à,Z,,,Z,,Z,,,,Z,Z,,Z,,,,Z,,,ZZ,,n=0Z47200011©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.yZP,ZZZ,m0ZHs:maxHs=s[V(c)+W(m)]exp[-H(t-s)]dt(2.1),cmHZV(c)W(m)cmZ:c+dmdt=y-Pm+z(2.2)KmZHamilton:H=[V(c)+W(m)+K(y-Pm+z-c)]exp(-Ht)(2.3)[1315],Hamilton:dVdc=KdKdt-HK=PK-dWdm(2.4)(214):dKödtK=H+P-dWödmK(2.5)c=y,(214)KZy,,K=1Z:dWdm=H+P(2.6)R,:dmdt=(R-P)m(2.7)(216)(217)(MII)dmdt=(H+R)m-dWdmm(2.8),Z(MII),m0,:Wm(m0)=H+RZWmm(m)0,dmdtm0,m0Z2.1.211m0,m0m0Z(MII)ZZmm0,m0ZmHZlimmWm(m)=0,R0,limmdmödtm=H+RH,Z,,Z,ZZ,Zm0ZZ212,limm0mWm(m)0,213,limm0mWm(m)=0Z213,m=0,dmdt=05711©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Zm0,212,m=0,dmdt0Z212,Z213Z,,0Zlimm0mWm(m)=0,ZZ212213?Z:,Z:,,,Z,Z:,Z,:R=Wm(m)-amZdmdt=Hm-aZ,,,0,Z213212Z,Z,,Z3,:,;;,Z,,Z(MI),,L,,L:[1]KeynesJohnM.Thegeneraltheoryofemployment[J].InterestandMoney,1936:358359.[2]1[J]1,1993,(1):1824.[3]SidrauskiMiguel.Rationalchoiceandpatternsofgrowthinamonetaryeconomy[J].AmericanEconomicReview,1967a,57(2):534544.[4]AumannRJ.SubjectiveProgramming[A].ShellyMWandBryanGL.HumanJudgmentsandOptimality[C].JohnWileyandSons,NewYork,1964.67200011©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.[5]Tversly,A.Ageneraltheoryofpolynomialconjointmeasurement[J].JournalofMathematicalPsychology,1967,4:120.[6]SimonHA.Theoriesofdecisionmakingineconomicsandbehavioralscience[J].AmericanEconomicReivew,1959,49:253283.[7]FishburnPC.Independentinutilitytheorywithwholeproductsets[J].OprationsResearch,1965,13:2845.[8]FishburnPC.Advitivityinutilitytheorywithdenumerableproductsets[J].Econometrica,1966,34:500503.[9]FishburnPC.Additiverepresentationofreal2valuedfunctionsonsubsetsofproductsets[J].JournalofMathematicalPsychology,1971,8:382388.[10]PollakRA.Additivevonneumann2morgensternutilityfunctions[J].Econometrics,1967,35:485495.[11]MegerRF.OntheRelationshipamongtheUtilityofAssets[A].theUtilityofConsumption,andInvestmentStrategyinanUncertainbutTimeInvariantWorld[C].ProcFourthIFORSConferrence,Venice,Italy,1969.[12]1[M]1:,19871[13]IntriligatorMichaelD.MathematicalOptimizationandEconomicTheory[M].Pretice2Hall,1971.[14]ShellKarl.ApplicationsofPontryagin’sMaximumPrincipletoEconomics[S].KuhnHW,SzegoGP.MathematicalSystemsTheoryandEconomics[C].Springer2Verlag,Berlin,1969,1.[15]BenvenisteLM,Jos’eA.Seheinkmandualitytheoryfordynamicoptimizatonmodelsofeconomics[J].TheContinuousTimeCaseJournalofEconomicTheory,1982,27(1):119.[16]ZHANGWei2bin.synergeticEconomics[M].Springer2Verlag,BerlinHeidelberg,1990.[17]1[M]1:,19921[18]LawrencePerko.DifferentialEquationsandDynamicalSystems[M].Springer2Verlag,1991.[19]1[M]1:,1995.[20]1[J].,1998,(7):24291(56):[1].[M].:,1990.[2].[M].:,1995.[3].(ODBC)[M].:,1997.[4].PowerBuilder6.0[M].:,1998.[5]OlugbengaMejabiandNanuaSingh.AFrameworkofEnterprise2WideIntegration[J].ComputerIntegratedManufacturing,1997,10(4):212220.[6]LimHS,JusterN,PenningtonA.Enterprisemodelingandintegration:ataxonomyofsevenkeyaspects[J].Co