有政府行为的货币经济动力学模型

199955a(,610065),.,,,.DynamicModelofMonetaryEconomicswithGovernmentActionsXUJiupingHUZhineng(Inst.ofInfoandDecisionMaking,SichuanUnionUniversity,Chengdu610065)AbstractInthispaper,consideringtheproblemsoffinancialdeficitsandsurpluseswithgovernmentactions,weconstructadynamicmodelofmonetaryeconomic,obtainsomeeconomicdynamicproperties,discussdifferenteffectswhenthesystemsareine2quilibrium,andexplainthecauseofbusinesscycle.Finallyweshowtheimportanceandnecessityofcontrollinginflation.Keywordsgovernmentactions,monetaryeconomic,dynamicalsystems,economice2quilibrium.1Keynes,[1].[2],.,AA=B+M(1.1),B,M,p=p(t),t.y=y(t),y.(G),,:(1),Z=pz,z.(2),,,D=pd,d.(3),,M=pm,m,.d,y.,LM.L=MaöM=dM(t)ödtöM(t)=maöm+paöp(1.2)a:1997210208:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.g=z+d+Lm(1.3)zy,,[3],D=d+Lm=g-z(1.4)L=(D-d)öm(1.5)[4],,,DeutscheBundesbank2à.P=paöp=dp(t)ödtöp(t)=¥((c+g)öy-1)+H+L=¥((c+g)öy-1)+H+(D-d)öm(1.6),¥()0,¥(0)=0,H0.Aa=dA(t)ödt=eR(A-M)-pc-Z(1.7),,R(A-M),,e,0e1,pc,(1.7)aa=da(t)ödt=(eR-P)a-eRm-c-z=ra-eRm-c-z-(1-e)Ra(1.8),r=R-P.[5],,(),(,,),u(c)+v(m)=u(c(t))+v(m(t))(1.9)[6],()()0[u(c)+v(m)]exp(-Qt)dt(1.10),HamiltonH=H(m,c,K)=u(c)+v(m)+K(ra-eRm-c-z-(1-e)Ra)(1.11)c,mu(c)=K(1.12)v(m)=KeR(1.13)Ka=K(Q-r+(1-e)R)(1.14)(1112)(1114)Gccaöc=eR-Q-P(1.15),Gc=-u(c)cöu(c)0,,(1112)(1115)RaöR=eR-Q-P+m(RaöR-Gccaöc)maöm(1.16)(MI)ma=-(H+¥((c+g)öy-1))mca=(eR-Q-P)cöGcRa=(eR-Q-P)R(1.17),P=¥((c+g)öy-1)+H+(D-d)öm.2(1117)dxödt=f(x,g,d)(2.1)x=(m,c,R)T,f(x0,g0,0)=0,g=g0,1[1].d,d0,,g=gLg0,gL,1.219995©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(a)Subcritical(b)Transcritical(c)Supercrical1211[7](211),f(x0,g0)=0,A=Df(x0,g0)K=0v,ATK=0w,Ak,(n-k-1).i)wTfg(x0,g0)0,wT[(D2f(x0,g0))(v,v)]0(2.2)RnR(211)(x0,g0)Rn{g0},(211)gg0,(Saddle2node).ii)wTfg(x0,g0)0,wT[(Dfg(x0,g0))v]0,wT[(D2fg(x0,g0)(v,v)]0(2.3)RnR(211)(x0,g0)Rn{g0},(211)gg0,(Transcritical).(iii)wTfg(x0,g0)=0,wT[Dfg(x0,g0)v]0,wT[D2f(x0,g0)(v,v)]=0,wT[D3f(x0,g0)(v,v,v)]0(2.4)RnR(211)(x0,g0)Rn{g0}.(211)gg0,(pitchfork).212,d=0,,D0,(211)(transcriticalbifurcation).d0,(211);.Dd,(211).(1117)H+¥((c+g)öy-1)=0eR-Q-P=0(2.5)(m,c,R),x0=(m0,c0,R0).ma=-(H+¥(c+c0+g)öy-1))(m+m0)ca=(eR+eR0-Q-¥((c+c0+g)y-1)-(D-d)ö(m+m0)-H)(c+c0)öGcRa=(eR+eR0-Q-¥((c+c0+g)öy-1)-(D-d)ö(m+m0)-H)(R+R0)(2.6),A=0m0¥öy0(D-d)c0öGcm20-c0¥2öGcyec0öGc(D-d)R0öm20-R0¥öyeR0(2.7)(KI-A)=0K1=0;K2,3=12[Q+(D-d)öm0-c0¥öGcy(c0¥öGcy-Q-(D-d)öm0)2-4c0(D-d)¥öGcym0](2.8)(KI-A)v=0(KI-A)Tw=035©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.v=(1,0,-(D-d)öem20)T(2.9)w=(0,-GcR0öc0,1)T(2.10)fg(x0,g0)=fg(x,g)ûx=x0,g=g0=(-m0¥öy,-c0¥öGcy,-R0¥öy)T(2.11)wTfg(x0,g0)=0(2.12)Dfg(x0,g0)=Dfg(x,g)ûx=x0,g=g0=-¥öy-m0¥öy200-¥öGcy-c0¥öGcy200-R0¥öy2-¥y(2.13)wT[Dfg(x0,g0)v]=(D-d)¥öem20y(2.14)wT[D2f(x0,g0)(v,v)]=(0,-GcR0öc0,1)(0,-2(D-d)c0öGcm30,-2(D-d)R0öm30+2(D-d)2öm40)T=2(D-d)2öm40(2.15)wT[D3f(x0,g0)(v,v,v)]=(0,-GcR0öc0,1)(0,6(D-d)c0öGcm40,(6(D-d)R0öm40)T0(2.16)213g.g,gi,i=1,2,,D-d0,(211)gi.H+¥=0,m,g,211,213.213(211),,,..cR,.214[1](211),gg0Jacobian,E(E)v(E)(v(0)=0).215(1117)W(c,R)=C(1117)dt1=dm-(H+¥)m=GcdceR-Q-P=RdReR-Q-P(2.17)Gcc=aR2ö2(2.18)A,¥(2117),w(m.c.R)=B(2.19)B.,(1117)W(m,c,R)=C(2.20),C216(211)W(m,c,R)=C,x0=(m0,c0,R0)R3(211)W(m,c,R)=C,(211)x0,(211)W=Cx0.x0,cRW=Cx0,,(211)Ma=F1(m,c,R)ca=F2(m,c,R)Ra=F3(m,c,R)(2.21)(0,0,0),Fi(0)=0,(i=1,2,3)W(2,21),WmF1+WcF2+WRF3=0(2.22)W=CcR,Wc(0)=WR(0)=0,Wm(0)0(2.23),F1=-WcF2öWm-WRF3öWm(2.24)419995©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(2124)(2121)DF(0)=000F2mF2cF2RF3mF3cF3R(2.25)ûDF(0)-KIû=0K1=0,K2K3(2126).F2cF2RF3cF3R-KI=0(2.26)W=CW(0,0,0)-C0=0,(2123)W=C0(0,0,0)m=m(c,R)m(0,0)=0,5mö5cû(0,0)=-WcöWmû(0,0,0)=0,5mö5Rû(0,0)=-WRöWmû(0,0,0)=0(2.27)x0,W=C0(c-R)f=(f2(c,R),f3(c,R))=(F2(c,R,m(c,R)),F3(c,R,m(c,R)))(2.28)(c,R)W=C0,W=C0ca=f1(c,R)Ra=f2(c,R)(2.29),(0,0),(2127)(0,0)Df(0,0)=F2cF2RF3cF3R(0,0,0)(2.30).217(218),(c0¥öGcy-Q-(D-d)öm0)2-4c0(D-d)¥öGcym00,d=0i)Q+(D-d)öm0-c0¥öGcy0,(211),2a);ii)Q+(D-d)öm0-c0¥öGcy0,(211),2b);iii)Q+(D-d)öm0-c0¥öGcy=0,(211),2c)(a)(b)(c)2215c-R,214(c,R).d0,(c,R),,d,.218d,m,c-R,(211).2.3,2.4,2.6(211)c-R,(218),[7].(211)D=d,Q=c0¥öGcy,ûAû=0,(m0,c0,R0)=x0(211),(211)55©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.ma=P2(m,c,R)+¥(m,c,R)ca=Q2(m,c,R)+W(m,c,R)Ra=S2(m,c,R)+F(m,c,R)(2.31),P2,Q2,S2m,c,R,¥,W,F(m,c,R)3.,.3,g,d.d=0,,m,m,Q+Döm0=c0¥öGcy,(c,R).g,P,R,,c,P,c,c,R,,,R.[9],Ukraine,Russia,,,,1720%,,.R,R,c,,,,,,.H+¥=0g,,,,[3],.R=(Q+Döm)öe,gR.d0,R=(Q+(D-d)öm)öe,,,m,.,,,,,.g,,,.,,,,,,,,,,.,¥+H=0c=y[1+¥-1(H)]-g,¥0,¥(0)=0,,,,.[10],,19901994,,19921993,,,.Estovia,Latvia,Lithuania,PolandSloveria,,,,1994,.4,,d,,,M1;,M2,d,.Z,zc,Mz,,,.(60)619995©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,.,(onedayahead)..5A(0042)1AkaikeH.Markovianrepresentationofstochasticprocessbycanonicalvariables.SIAMJ.ControlandOptimization,1975,13:1621722MehraRK.Kalmanfiltersandtheirapplicationstoforecasting.TIMSStudiesinManagementSci2ences,1979:75943Aoki,M.StateSpaceModelingofTimeSeries.Berlin:Spring2Verlag,19904Cerchi,MandHavennerA.Cointegrationandstockprice: