The Soft Engine for Economic Growth in a Long-Time: The Economic Development Power, Conversion and Conservation for economic Energy

Transcription

1 Th Third of Working paprs for Rsarchs abou Dlopmn Powr DP Vrsion. Th Compld Tim: 4--4 Th Sof Engin for Economic Growh in a Long-Tim: Th Economic Dlopmn Powr, Conrsion and Consraion for conomic Enrgy Fng DAI Dparmn of Managmn Scinc, Zhngzhou Informaion Enginring Unirsiy P.O.Bo, Zhngzhou, Hnan, 45, P.R.China fngdai@public.zz.ha.cn; fngdai@6.com Absrac Basd on h horis of Dlopmn Powr [8]-[] and Parial Disribuion []-[4], and combining wih h acual conomic dlopmn, his papr discusss h main ways how h Dlopmn Powr DP is accumulad or rlasd, sablishs h analyic modls of DP and h modl of rlaion bwn DP and produciiy; classifis conomic dlopmn ino h hr sas in nrgy h sa of normal nrgy, srong nrgy and supr nrgy; gis h mhod of calculaing h criical im of srong nrgy and supr nrgy and h approach o dscrib h oling procss of hs hr sas; pus forward h laws of conrsion and consraion bwn mass and nrgy in conomic dloping. According o ha DP is accumulad and rlasd on afr anohr, his papr poins ou, a sign ha accumulaion of DP is compld is h mos of conomic facors ar in ordr, and h sign ha rlas of DP is compld is h mos of conomic facors ar in chaos, and also gis h ways o calcula h mos possibl im ha h DP sars accumulaing or rlasing. Finally, h auhor mak a comprhnsi mpirical analysis on all of rsuls in his papr by mans of h US GDP daa from 94 o 3, h oucoms ar saisfid. Th conclusions in his papr mak clar ha h conomic Dlopmn Powr, namly conomic dlopmn nrgy, is h ngin for h conomic growh. Ky words Dlopmn Powr DP, Parial Disribuion, conomic growh, nrgy sas of conomic dlopmn, conrsion and consraion on conomic nrgy, analyic modl Inroducion Up o now, hr ar many of h imporan sudis in h conomic hory, such as R. E. Lucas s businss cycl hory [98], Prsco s ral businss cycl hory [98], P. M. Romr s nw growh hory [986], and D. Kahnman s prospc hory [979], c. Ths horis has aailably propld forward h conomic dlopmn of world. Bu, hr ar many conomic problms which ha no y bn sold horoughly. Such as, Wha is h rason ha caus h cycl in conomic dlopmn? Which is h h dominan causaion ha aros h flucuaion of conomic mark Whhr hr ar h mass and h nrgy momn in h procss of conomic dlopmning or no? how can w dscrib and masur hm if hr ar mass and h nrgy momn? Thr is h diffrnc bwn h diffrn counris in h ra of conomic growh and h ll of

2 produciiy, wha is h rasons of i? In ordr o sol h problms mniond abo, h concp of Dlopmn Powr DP has bn gin and discussd firs in h rfrncs [8-]. Th hory of DP indicas: Th produciiy is h isibl bhaior abiliy for mankind o impro h sociy and naur, and h DP is h inisibl bhaior moiiy for mankind o impro h sociy and naur. In h conomic sociy, DP is h bhaior moiiy o dlop conomy, and w also call i h conomic DP EDP for shor. EDP is also h nrgy of conomic dlopmn. Th produciiy is h hardwar of conomic dlopmn; and EDP is h sofwar of conomic dlopmn. Boh of hm ar of symmry, and h mos basic facors in conomic dlopmn. Th momn of EDP will influnc h ll of produciiy, and ic rs. EDP is jus h conomic dloping nrgy. Th accumulaion and rlas of EDP bring on h flucuaions of i, namly h flucuaions of conomic dloping nrgy EDE. Jus h momn of EDP or EDE rsuls in h flucuaion of conomic produciiy, so i is h moi forc of conomy. Th EDP is scald by conomic dlopmn nrgy, and masurd by flucuaion ra of ll of produciiy. Tha larg or small in EDP or EDE will dcids ha h ponials of conomic growh is larg or small, and h duraion of conomic growh is long or shor. If w dscrib h basic ll of produciiy wih Gross Naion Produc GDP, hn h flucuaion ra of produciiy could dscribs EDP. A his im, w could masur EDP by mans of arianc of produciiy ll. And assum ha h acual ll of produciiy follows h Parial Disribuion []-[3]. I is worh o say, h flucuaion is gnrally a dscripion of risk in mainsram of h conomic docrin, bu i is h dloping nrgy in DP hory. Th following discussion will do no disinguish DP, EDP and EDE. Basd on h hory of DP and combing wih ral conomic dloping, his papr will: discusss h main way and basic modl of DP in is accumulaion and rlas. adancs hr kind of nrgy sa of conomic growh, i.., h sa of normal nrgy, srong nrgy and supr nrgy, and gis h approachs o calcula h criical ims of srong nrgy and supr nrgy. pus forward h laws of conrsion and consraion bwn mass and nrgy in conomic dloping according o h modl of rlaion bwn DP and produciiy. poins ou h sign ha accumulaion of DP is compld is h mos of conomic facors ar in ordr, and h sign ha rlas of DP is compld is h mos of conomic facors ar in chaos, and gis h ways o calcula h mos possibl im ha h DP sars accumulaing or rlasing. indicas h rason why h flucuaion of conomic producion and mark occur. Th basic rason is hr ar many ioln bifurcaions bwn h produciiy and DP, such as DP is oo small o suppor h conomic growh, or DP is so largr o rrs h original rnd of conomic rcssion quickly. plains ha h ral rason of h conomic diffrncs is h diffrncs in hir abiliy of DP accumulaing and rlasing bwn dlopd counris or rgions and undlopd counris or rgions. Only h DP is h durai moiiy for conomic growh. Finally, w shall mak a comprhnsi mpirical analysis on all of rsuls in his papr by mans of h US GDP daa from 94 o 3. Th Main Approachs for DP Accumulaing and Rlasing

3 Th rfrncs [8]-[] indica: Th produciiy is h isibl abiliy for mankind o push forward conomy, and h DP is h inisibl moi forc for mankind o push forward conomy. DP includs h inisibl conomic facors such as policy, scinc and chnology, ducaion, knowldg, managmn, law, culur, ida, c. so w could say ha DP is h sof ngin for conomic dlopmn. Th way of DP accumulaing or rlasing is complicad and dirs. Hr, w gi a brif dscripion abou h basic ways for DP accumulaing and rlasing, in ordr o mphasiz ha DP is ry imporan and of ubiquiy in naional conomic dlopmns.. Th main approachs for accumulaing DP Th posii innoaion o naional conomic sysm. Th naional conomic sysm plays an normously imporan funcion o conrol h conomic dlopmn. This funcion is radically producd from h sysm dlopmn powr SDP. Making a coninuous innoaion on conomic sysm, and insuring h conomic sysm bing rasonabl and fficin, will allow SDP o b accumulad coninuously, and nabl h diffrn branchs of conomic sociy o b coordinad on anohr always, so ha h conomy could kp on growing. Prfcing coninuously h conomic policis and conomic laws. Th prfcion of conomic policis and laws can urg, conrol and guid h conomy o dlop in righ dircion. This kind of funcion of conomic policis and laws is h policy dlopmn powr PDP. Thrfor, w could acquir h PDP o acclra conomic growh if rnwing and prfcing h naional policy and laws sysm coninuously. 3 Esablishing ffcily h innoaing mchanism in scinc and chnology. Th dloping ialiy of conomy coms from many of nw conomic producs going ino opraion, and nw conomic producs ar h rsuls of h applicaion of arious nw scinc and chnology. Jus h kind of forc for scinc and chnology o impl conomic dlopmn is h dlopmn powr of scinc and chnology, STDP for shor. So w mus sablish h innoaing mchanism in scinc and chnology, promo scinc h chnical o progrss, and ransla h rsuls of nw scinc and chnology o nw conomic producs, namly accumula h STDP coninuously, in ordr o g h inhausibl forc of scinc and chnology for conomic dlopmn. 4 Dloping complly h sysm of conomic ducaion. Th good ducaion sysm and h pracic nironmn in conomy can mak popls who ar ngagd in h conomic aciiis larning h ncssary knowldg, and g h worhy princ. Thos popls can us hir knowldg and h princ in conomy o promo h naional conomic dlopmn. So h knowldg and princ ar a kind of forc, is calld h knowldg dlopmn powr KDP. Thrfor, sablishing complly a sysm of conomic ducaion is ry imporan for improing h naional conomic nironmn, accumulaing h KDP ffcily, and proiding a good foundaion for h conomic dlopmn. 5 Sandardizing parn and opimizing srucur in h conomic managmn. Sandardizing managmn in ry ll of conomic dparmns plays an imporan and non-rplacabl rol in promoing conomy o dlop ordrly and ffcily. W could rgard his funcion of Sandardizing managmn as h managmn dlopmn powr MDP. Thrfor, h MDP will b accumulad ffcily if w mak a posii innoaion in sandardizing h conomic managmn and in opimizing h hirarchical srucur of conomic dparmns, so ha h dloping forc in managmn will b obaind o push forward h conomic progrss. 6 Dsigning and achiing h larg scal and synhic projcs. Dsigning and achiing a larg scal and 3

4 synhic projc usually affc h siuaion of naional consrucion and h conomic dlopmn as a whol. Jus h forc of larg scal projc push conomy forward is a projc dlopmn powr PDP,.g. boh h succss in applicaion o hold h Olympic Gam 8 and h succsss in launching and rurning of spacfligh airship wih prson a 3 ar all h br ways o accumula PDP for Chins conomic dlopmn. Jus h procss of launching h full of ims mniond abo complly is h accumulaing procss for naional conomy DP.. Th main approachs for rlasing DP Afr all of h works mniond in. ha bn don, w ha h nw or improd sysms of conomy, nw conomic policis and laws, nw innoaing mchanism in scinc and chnology, nw or improd sysm of conomic ducaion, sandard and opimal managmn in conomy, and ohr hings in ha DP ar accumulad. A his im, sysms and nironmns of conomy ar br and ordrd, conomy sars dloping in a good procss, and h DP which had bn accumulad sars rlasing. In h rlasing procss of DP, h conomy will ha a sabl and ordr dlopmn unil DP is rlasd sufficinly, and hn a nw procss of DP accumulaing sars..3 A brif summary In figur, w dscrib h approachs and procss of accumulaing and rlasing DP. To say in shor, h DP is accumulad by h group innoaions, and h DP is rlasd by h applicaions of h group innoaions. Th DP momns of accumulaion and rlas ar shown as h flucuaions of conomic nrgy, and hos flucuaions influnc h conomic growh or conomic rcssion. So w s ha DP should b h ngin for conomic growh. Figur Th ways and procss of accumulaing and rlasing DP. DP is h bhaior moiiy and h sof ngin o dlop conomy, i is h inisibl forc, and includ policy, scinc and chnology, ducaion, knowldg, managmn, sysms and laws, culur, ida, c. Th Analyic Modls of DP and Produciiy. Noaions and dscripions of modls If no: µ h basic ll of conomy, namly a masuring ind for basic produciiy, is ral alu is gnrally h producion alu.g. GDP, Gross Domsic Produc, h basic produciiy for shor, µ. Bcaus h conomic growh is ssnially h incras for ll of produciiy, and h conomic rcssion is 4

5 5 ssnially h dclin for ll of produciiy, w do no disinguish h ll of conomy from produciiy in h following discussion, i.. rgard hm as h sam. σ h flucuaion rang of h basic produciiy, i.., h sandard arianc of h basic h basic produciiy ll, σ>. σ can dscrib h absolu nrgy of conomic dlopmn. =σ µ h flucuaion ra of h basic produciiy, is a masuring ind of DP Economic Dlopmn Powr. can dscrib h dloping nrgy of conomy, gnrally <<. In h following discussion, w do no disinguish DP from h dloping nrgy of conomy, i.. rgard hm as h sam. X h acual produciiy. X is a non-ngai random ariabl. According o assumpion in [8]-[], h acual produciiy follows h disribuion of dnsiy as < = d f µ µ A his im, w call X follow h parial disribuion []-[5], and dno: X Pµ,. Thus, w ha Thorm For any [, ], h following quaions com approimaly ino isnc + = d µ π µ π. = d π µ + µ π sgn µ π µ. whr, < = > = sgn. If µ,, X ar all im-arian, and noing rspcily as µ,, X, hus w ha a parial procss X Pµ,. Espcially, if X Pµ,, w call X follow a DF procss [6].. Som basic rsuls According o assumpions in rfrncs [8]-[], if h acual produciiy X Pµ,, hn w ha []-[5] Th arag alu of acual produciiy: EX = µ + + µ π µ π whr, RX= + µ π µ π can prsss ha h arag incrmn of acual ll of produciiy is cding h basic ll of i. Th arag of ral DP dlopmn nrgy: X D X = whr, ] [ X E X E X D + = µ. Bcaus RX>, w ha EX>µ, and DX <. EX>µ mans h arag alu of ral produciiy is

6 largr han h basic ll of produciiy, his also mans h ral produciiy is gnrally in a growing rnd; and DX< mans DP usually is rlasing coninuously unil i rachs a lowr ll, a his im DP will rlas again afr i has bn accumulad. 3 Th Analyic Modl of DP 3. Th basic modl of DP Gnrally spaking, h diffrnial raio of alu of DP o µ alu of produciiy should ha somhing o do wih currn sa of DP, i.., d = dµ g whr, g is a coninuous funcion. If produciiy is of growh coninuously, g> mans DP is accumulaing, g< mans DP is rlasing, and g= mans DP is sabl, and if produciiy is of rcssion coninuously, h manings is rrs. Spcially, if g= γ, γ is a consan. Thn w obain = α whr, h consan α>. If DP and produciiy ar im-arian, from quaion, w know =α. so h quaion can b prssd as γ [ µ µ ] = whr, and µ ar h original alus of DP and produciiy rspcily; h consan γ, is calld h characrisic ind of DP, could dscribs whhr DP is largr or smallr, and has h following maning: In h procss of conomic growh, i.. h produciiy µ is incrasing by dgr, >, DP is accumulaing γ = =, DP is sabl <, DP is rlasing In h procss of conomic rcssion, i.. h produciiy µ is of dscnding >, DP is rlasing γ = =, DP is sabl <, DP is accumulaing According o modl, if = >, w obain µ = µ + ln. This quaion prsss how DP, γ i.. conomic dloping nrgy, influncs produciiy µ, so w could hink ha DP is h ngin for conomic growh. 3. Th im-arian modls of DP and produciiy Th quaion can also b prssd as 6

7 = ± δ δ 3 whr, h maning of + is incrasing in produciiy growh, and - is conomic rcssion; δ> is a consan. L Thn, w obain dµ d ± δ = 4 µ = ln m 5 γ whr, δ is calld h paramr in scal, and h quaion 4 could b fid furhs wih h conomic raliy by us of paramr δ. 3.. Th im-arian modls of DP and produciiy in conomic growh. From 3 and 5, and w can prss produciiy µ for conomic growh as µ = ln γ 6 and DP can b prssd as = 7 In h prssion 6 and 7, γ> and < ar adap o h conomic growh wih DP accumulaing; and γ< and > ar adap o h conomic growh wih DP rlasing. Thn, h prssion 7 can b prssd as =. 3.. Th im-arian modls of DP and produciiy in conomic rcssion. Similarly, from 3 and 5, produciiy µ can b prssd for conomic rcssion as µ = ln γ + 8 and DP can b prssd as = + 9 7

8 In h prssion 8 and 9, γ< and < ar adap o h conomic rcssion wih DP δ γ accumulaing; and γ> and < ar adap o h conomic growh wih DP rlasing. Thn, h prssion 9 can b prssd as = Th approach of calculaing h paramr δ. For h procss of conomic growh, and according o 6, w ha µ = ln. Th paramr δ can b simad as h following formula : γ δ = γ Similarly, for h procss of conomic rcssion, and according o 8, w ha µ = ln +. γ Th paramr δ can b simad as h following formula : δ = γ Of cours, hr ar som ohr approachs for simaing δ. 4 Th Analysis for Economic Dlopmn Enrgy and Is Modls 4. Th dloping nrgy analysis in conomic growh In h procss of conomic growh wih DP accumulaing, i.. µ is incrasing and r>,if l = =, w ha ε = Thus, whn > ε, >. And l =, w obain 8

9 τ = 3 Thus, whn = τ, =. Dfiniion Suppos ha conomy is growing, and DP is accumulaing. ε and τ ar rspcily drmind by and 3, hn Whn << ε, and a his im, <<, w call h sa of conomy h normal sa in nrgy, and h normal sa of conomy for shor. Whn ε < τ, and a his im, <<, i.. DP>, w call h sa of conomy h srong sa in nrgy, and h ε τ srong sa of conomy for shor. ε is h criical im of Figur Th oling procss of h normal sa, h srong sa. srong sa and h supr sa of conomy. Whn 3 Whn = τ, and a his im, =, i.. DP=, w call << ε, hn DP,, h conomic sa is normal sa in nrgy. Whn h sa of conomy h supr sa in nrgy, and h ε < τ, hn DP,, h conomic sa is srong sa in supr sa of conomy for shor. τ is h criical im of nrgy. ε is h criical im. Whn = τ, hn, DP supr sa. =, h conomic sa is supr sa in nrgy, τ Th oling procss of h normal sa, h srong is h criical im of supr sa sa and h supr sa of conomy is shown in figur. Basd on dfiniion, wha w nd o plain ar: For h srong sa in conomy, DP. In fac, ha circumsanc could b happnd. I dos no man ha DP i.., dloping nrgy of on indusry is largr han, whr h producion alu of on indusry is compud as a whol; i mans ha DP of on indusry w call i undrlying DP diffus o many of ohr indusry, and mak hir DP w call h driai DP accumula rspcily, so ha h sum of all h undrlying DP and h driai DP is largr han. For ampl, h dlopmn of h compur indusry maks h compurs bing usd widly, and h usag of compur causs ohr indusris o dlop, such h indusris as manufacuring conrol, wahr analysis, spacfligh nginring, scinific simulaion, c. As for manufacuring conrol, h applicaion of compurs can bring abou an adanc in chniqu abiliy of manufacuring conrol, i.. DP of manufacuring conrol bing accumulad fficinly, so ha h produciiy of manufacuring conrol is proplld forward; and if h producs of manufacuring conrol basd on compur ar applid o producing procss, and achi a good acual rsuls, hus DP of manufacuring conrol sars rlasing. Furhr mor, h dlopmn of manufacuring conrol will propl h is downsram indusris forward, such as spin and wa, papr making, sl indusry, machin and lcronics, c. On h ohr hand, h highr rqus o compur from manufacuring conrol will accumula h DP of compur indusry. All of ha ar h diffusing procss of DP, and can b dscribd by figur 3. For h supr sa in conomy, DP =. Tha is an rm cas of srong sa in conomy; h sum of undrlying DP and is driai DPs is so larg ha w can no alua DP of h indusry by a fini way. W ha a similar planaion o µ= produciiy ll is of infiniyundr h supr sa in conomy. DP = mans, according o h dfiniion of in scion., ha h arianc of h produciiy 9

10 ll is of infiniy. As w know, h arianc of Ly disribuion is characrisic funcion is ˆ α a k l α a, k = is of infiniy, i.. < >= <α<. So i migh b adapi o dscrib h bhaior of supr sa in conomy by Ly disribuion; if lik his, h supr sa in conomic nrgy migh b in accordanc wih h hory of fracal conomy [8] in som dgr. Figur 3 DP momn and diffusion procss in compur indusry. DP of compur indusry, as an undrlying DP, could b diffusd o ohr indusris, and h DP of hos ohr indusris migh b accumulad along wih undrlying DP accumulaing. Th srong or supr sa in conomy migh occur afr bcaus h undrlying DP and is driai DP wr accumulad. 3 For h conomic growh wih DP accumulaing, in gnral, h DP <; if, h durai im of his conomic procss, is largr han ε, h criical im of srong sa, i.. > ε and >, h diffusion of DP may occur, h indusrial conomy prsns a srong sa in nrgy; and afr h indusrial conomy has com ino srong sa in nrgy, h procss of conomic growh wih DP accumulaing has bn lasd ou furhr and, h durai im of his conomic procss, is qual o τ, h criical im of supr sa, i.. = τ and =, h indusrial conomy may prsns a supr sa in nrgy, i.. a fracals. Is h supr sa of conomy a final sa? 4 I is ry difficul o kp boh produciiy and DP growing coninuously in a long rm. In gnrally, DP sard rlasing bfor h im of is accumulaing cam o ε h criical im of srong nrgy in conomy. So h indusrial conomy usually is dlopd on h normal sa in nrgy. Of cours, w do no pl som pars of indusry may com ino h srong sa in nrgy. On h srong sa in nrgy, i is mor difficul for boh produciiy and DP sill o kp on growing. Only a ry lil of indusris will com ino h supr sa in nrgy, and his shall b confirmd in h hindr mpirical rsarchs. If w rgard h forc of pric rising or falling as h rsul of nrgy momn for prics in scuriy

11 mark, hr is DP h nrgy of pric flucuaion in scuriy mark also. Thr mus b nrgy flow in h diffusion procss in which h pric flucuaion of on or som scuriis socks, socks inds, undrlying producs, driais, c. migh caus h pric flucuaion of ohr scuriis. So h srong sa or supr sa in scuriis migh occur. If lik his, h supr sa in scuriy mark can b dscribd wih h fracal srucur in som im. If h produciiy is growing and DP is rlasing, i.. µ is incrasing and γ<, w ha Proposiion In h procss of conomic growh wih DP rlasing, boh h supr sa and h srong sa in conomy can no occur. Pro. Owing o γ< DP is rlasing and δ>, hn >, and hr is no h srang poin τ which mak DP in prssion 7 b qual o, namly h supr sa dos no occur. If l =. W ha, i... Owing o < and γ<, h inqualiy Th rsul follows. can no com ino isnc, hus <. 4. Th dloping nrgy analysis in conomic rcssion Hr, w gi som proposiions abou dloping nrgy in conomic rcssion i.. µ is dcrasing, as following. Proposiion Th supr sa in conomy dos no occur in h conomic rcssion wih DP accumulaing. Pro. Whn γ>, h quaion + = is no isn; and whn γ<, + = can b prssd as =, his is conradicing wih < in prssions 8 and 9,h isn condiions δ γ δ γ of produciiy 8 and DP 9. Th rsuls follow. Proposiion 3 Th srong sa in conomy dos no occur in h conomic rcssion wih DP rlasing i.. γ>. Pro. If w suppos = +, hn +, i.., +. As w know, h inqualiy + is no isn whn < and γ>, so i mus b = + < Th rsul follows. Proposiion 4 In h conomic rcssion wih DP accumulaing i.. γ< h supr sa in conomy is no

12 isn, and h srong sa in conomy may b isn whn >. Pro. If w suppos + =, hn τ =, his is conradicing wih < in δ γ δ γ prssions 8 and 9, h isn condiions of produciiy 8 and DP 9. So h supr sa in conomy is no isn. L = + =, hn = ε, and compard wih < in δ γ δ γ prssions 8 and 9, h srong sa in conomy migh b isn only if >. Th rsuls follow. Wha h proposiion 4 mans ha = ε δ γ is h criical im for som indusry in h conomic rcssion wih DP accumulaing. h conomy is a h srong sa whn > and ε, a his im, w could hink ha h indusry can no wihr away, and furhr mor, w δ γ could hink ha h dloping nrgy of ohr rlad indusris has swarmd ino his indusry, and his indusry will ha a largr incrasing spac for growh. = is h limi im for h conomic δ γ rcssion wih DP accumulaing. if h conomy of indusry has no grown y whn h im rachs h limi im = in h conomic rcssion wih DP accumulaing, h indusry migh wihr away δ γ gradually. 4.3 Analysis for h mass of produciiy and conomic nrgy In a crain priod of im, som conomic asss may influnc subsanially h dloping cours of conomic growh or rcssion, hs asss play a mor imporan and magisral rol o incras h producion alu of conomy on his priod of im, so w ha Dfiniion Th all h asss which play a magisral and a ky rol o incras h producion alu of conomy i.., produciiy ar calld h high-qualiy asss of conomy. For ampl, in h pas of sral dcads, h compur indusry plays a magisral and a ky rol in conomic procss, h compur and h chniqu and produc of compur ha h dirc and indirc ky funcion o glob conomic growh. So all of h compur asss ar h high-qualiy asss which play a magisral and a ky rol o incras h producion alu of compur indusry and ohr indusris; and for ampl again, raffic plays h dirc and ky rol o dlop many indusris, So all of h raffic asss ar h high-qualiy asss which play a magisral and a ky rol o incras h producion alu of raffic indusry and ohr indusris. In fac, h high-qualiy asss ar h componn pars of produciiy, and h mos imporan and ky pars of produciiy. Alhough hs high-qualiy asss may b diffrn a diffrn priod of conomic dlopmn, i is no doubabl ha hy ar isn. Th produciiy would los hir hyposaic

13 conns if hr ar no hs high-qualiy asss. In anohr hand, hr ar a lo of high-qualiy asss in conomic sociy mans and using of hm mans ha conomy is growing or will grow. in gnral, h largr h quaniy of high-qualiy asss is, h mor h nrgy of conomic growh is, and h highr h ra of conomic growh is, and ic rsa. Basd on h abo discussions, w gi h dfiniions abou h mass of produciiy and h growing spd of h mass of produciiy as follow Dfiniion 3 Th mass of conomic produciiy is h quaniy of high-qualiy asss in conomy. Th mass of indusrial produciiy is h quaniy of high-qualiy asss in h indusry. Dfiniion 4 Th spd of produciiy growh mans h incrasing spd of high-qualiy asss. Thrfor, if w rgard m= in prssion 6 as h mass of produciiy, and rgard υ = < as h ariy of spd in produciiy, h prssion 7 is jus h basic γδ modl of rlaion bwn mass and nrgy in conomy υ = m 4 whr, m=, υ = < for conomic growh, and m=, γδ υ = + > for conomic rcssion. Th quaion 4 is similar o h modl of conrsion bwn mass and nrgy in physics. basd on prssion 4, if spd υ is inarian, hus, h largr h mass m is, h largr h DPconomic nrgy is; in anohr hand, if mass m is inarian, hus, h spd υ is largr h, h largr h DPconomic nrgy is; and ic rsa. So w can say ha h modl 4 is abl o dscrib h nrgy momn in conomic procss. 4.4 Th analysis for conrsion and consraion of conomic nrgy As w know, a cycl of DP momn includs wo basic sags, h firs sag is of DP accumulaing, and scond sag is of DP rlasing. Suppos ha conomy is growing undr h normal sa in conomy. According o prssion, w ha h modl of rlaion bwn DP conomic nrgy and produciiy a firs sag as following = m γ µ γ µ whr, m = is h mass of produciiy a h sar of firs sag, γ >, µ is h original alu of produciiy a firs sag, ν is h original alu of DP a firs sag. Afr h DP is sufficinly accumulad, DP momn coms ino h scond sag, i.. DP sars rlasing. Also according o prssion, w ha h modl of rlaion bwn DP conomic nrgy and produciiy a scond sag as following 3

14 = m γ µ µ whr, m = γ is h mass of produciiy a h sar of scond sag, γ <, µ is h original alu of produciiy a scond sag, ν is h original alu of DP a scond sag. If DP nds accumulaing and sars rlasing a im, w should ha µ =µ =µ, and h quaion of nrgy consraion as: =, namly m = m. So w obain h formula of nrgy γ µ γ µ conrsion as m γ γ µ = m 5 Th prssion 5 has dscribd h conrsion and h consraion bwn mass and nrgy in conomy. Basd on prssion 5, w s γ >, γ <, and µ>, hus m >m. So w could obain h following conclusions: m >m indicas ha m h produciiy mass a h bginning of DP accumulaing or h nd of DP rlasing is smallr han m a h nd of DP accumulaing or h bginning of DP rlasing. This mans ha accumulaing DP is subsanily o accumula nrgy in h way o incras h mass of produciiy, and rlasing DP is subsanily o rlas nrgy in h way o dcras h mass of produciiy. So h rsul of DP accumulaing is ha h produciiy mass high-qualiy of asss in conomy incrass subsanially, and h rsul of DP rlasing is ha h produciiy mass dcrass subsanially. A h bginning of DP accumulaing, h produciiy mass is smallr. Jus h produciiy mass is smallr, hn DP nds o accumula and has h spac o accumula; and a h bginning of DP rlasing, h produciiy mass is largr. Jus h produciiy mass is largr, hn DP is abl o b conrd and rlasd in nrgy. 3 If l m, γ and µ b inarian in prssion 5, h smallr h mass m is, h largr γ is, namly h quickr h spd of DP accumulaing is. Similarly, If l m, γ and µ b inarian in prssion 5, h largr h mass m is, h smallr γ is, namly h quickr h spd of DP rlasing is. Ths mans ha h mass and spd can b conrd on o anohr. 4 Th amoun of high-qualiy asss, i.. h mass of produciiy, is larg mans ha h nrgis in all of pars and dparmns in conomy or indusrial conomy ar in ordr, and h oal conomic nrgy is highr a his im. Th amoun of high-qualiy asss is small mans ha h nrgis in all of pars and dparmns in conomy or indusrial conomy ar in chaos, and h oal conomic nrgy is lowr a his im. 5 Basd on h discussion abo, w also know ha h foundaion of naional conomy dlopmn is DP. En hough a naion gs a larg amoun of adancd quipmns, h conomic nrgy conaind in hs quipmns will rlas complly if his naion can no accumula coninuously DP as ndd. So w s ha h ral and basic rason of h diffrncs isd in conomic growh for diffrn counry or rgion is h diffrncs in hir abiliy of DP accumulaing and rlasing. Only h DP is h durai moiiy for conomic growh. In gnral, h backward naions or rgions ha a wak abiliy o accumula hir DP for conomic growh, hn hy can no nabl DP, which has bn rlasd, o b accumulad sufficinly again, so ha hir conomy can no grow sadily. Thrfor, how DP is accumulad and rlasd fficinly is a ru difficuly. 6 DP will suppor an conomic growh. If DP is rapidly accumulad and hausd in a shor im, h 4

15 conomic growh loss is DP i.. nrgy, h dcrass of conomic producion or mark sal may occur. In anohr hand, if conomy is in a shor rcssion and DP is rapidly accumulad du o som rasons, h conomic growh may occur. So w could say ha h basic rason of flucuaion in conomy is hr ar many ioln bifurcaions bwn h produciiy and DP is h rason why h flucuaion of conomic producion and mark occur. Th conclusion 5 and 6 ar spcially imporan. 5 Th Analysis for Flucuaions of Economic Enrgy Th accumulaion of DP mans h conomic nrgy is incrasing, and h rlas of DP mans h conomic nrgy is dcrasing. Hr, w call ha conomic nrgy incras and dcras in a fid rang h flucuaions of DP i.. conomic nrgy. Suppos ha h dloping nrgy of conomy or an indusrial conomy is flucuad around a fid non-zro alu. If h fid alu is qual o zro, w hink ha conomy or h indusrial conomy is closd o dah. If h alu is smallr, h flucuaions ar calld a a lowr ll; if h alu is largr, h flucuaions ar calld a a highr ll. A nw accumulaion for DP may sar whn h conomic nrgy is a lowr ll, and a nw rlas for DP may sar whn h conomic nrgy is a highr ll. Thus, a lowr ll, wha im is h accumulaion for DP sars? Or h procss of DP accumulaing is mos asy o sar? And a highr ll, wha im is h rlas for DP sars? Or h procss of DP rlasing is mos asy o sar? W shall sol hs qusions as follow. L Y, DP of an indusrial conomy, is flucuad around a bnchmark nrgy. If h assumpions in [8]-[] com ino isnc, Y follows h DF procss [6], i.. X P, k, <k, k is calld a scal cofficin of nrgy flucuaing. If Y is flucuad in h fild of [-, +] <<, hn dno: + u = y f y dy, whr y k f y = 5 y k dy y y < u is h arag alu funcion of h squar of disanc for nrgy flucuaions, h nrgy flucuaions funcion for shor in h following discussion. From horm, w obain u = + y + k = y k dy + i π k y k dy k πk π k W can s, from h prssion 6, nrgy flucuaions funcion u will dclin oward zro gradually if h im bcoms largr and largr, i... This mak clar ha if a indusry can no sar accumulaing DPi.. dloping nrgy a a ncssary im in ordr o mak conomy growing, i will b closd o dah and disappar finally. hrfor, h conomy or h indusrial conomy mus b accumulad again is nrgy in som way and com ino a nw dloping cycl if is conomic nrgy is smallr o smallr and always no qual o zro. 6

16 Bcaus u u = + y y f y dy u y f y dy] k + y y u = = y k y y k dy dy π k 3 k + 3k π = π k + L 6 qual o 7, w ha u = + y i y k y k dy dy = + y y y πk y k y k + dy dy + 3 k k = u = k, l u =, w obain 7 u 8 Proposiion 5 Th nrgy flucuaions funcion u will rachs is maimum alu a im =τ drmind by quaion 8. Proposiion 5 will b approd in figur 4 o figur 7. Figur4 Th maimum alu of h nrgy flucuaion funcion u. If h bnchmark nrgy =., h scal cofficin of nrgy flucuaing k=., scal of nrgy flucuaing =.8. hus, u rachs is maimum alu a =τ, =τ, h inrscion of u and u u =, is drmind by Figur 5 Comparing h nrgy flucuaion funcion u on diffrn alus of bnchmark nrgy. If h scal cofficin of nrgy flucuaing k ar fid, h im =τ a which u rachs is maimum alu is no rlad o h bnchmark nrgy. h quaion 8. Proposiion 6 Whn h conomic nrgy is a h lowr ll, i.. h is smallr, hn =τ, drmind by prssion 8, is h mos possibl im a which DP is accumulad again, and h opimal im for DP o accumula. Proposiion 7 Whn h conomic nrgy is a h highr ll, i.. h is largr, hn =τ, drmind by prssion 8, is h mos possibl im a which DP is rlasd, and h opimal im for DP o rlas. 6

17 Figur 6 Comparing h nrgy flucuaions funcion u on diffrn alus of scal of nrgy flucuaing. If h scal cofficin of nrgy flucuaing k is fid and h scal of nrgy flucuaing changs, boh h maimum alu of u and h im =τ a which u rachs is maimum ar all diffrn. Wha h qui inrs ar: From h figur 5, w s ha If h scal cofficin of nrgy flucuaing k ar fid, h im =τ a which u rachs is maimum alu is no rlad o h bnchmark nrgy. From h figur 7, w s ha If h scal of nrgy flucuaing is fid and h scal cofficin of nrgy flucuaing k changs, h maimum alu of u dos no chang, bu h im =τ a which u rachs is maimum is diffrn. 3 From figur 4 o figur 7, w s ha whil h conomic nrgy is a h lowr ll, h sochasic flucuaions bcoms srongr, and hn bcoms wakr afr h nrgy flucuaions funcion u rachs is maimum. If h DP dos no sar accumulaing a h maimum of u, h conomic nrgy of indusry will bcom lss and lss, and haus finally. 4 Th flucuaions of conomic nrgy will caus ha h dparmns and componns of conomic sociy ar in ordr a highr ll or in chaos a h lowr ll, and rsul in h flucuaion of conomic mark. 5 If h flucuaions of DP mainains a a lowr ll and DP dos no sar accumulaing all h im, h nrgy flucuaion funcion u will a and flow around zro, and his flucuaions will g mor and mor ioln along wih h procss is coninud, s also in figur 8 and figur 9. 6 Th Empirical Rsarchs for DP Figur 7 Comparing h nrgy flucuaions funcion u on diffrn scal cofficins of nrgy flucuaing. If h scal of nrgy flucuaing is fid and h scal cofficin of nrgy flucuaing k changs, h im =τ a which u rachs is maimum is diffrn, bu h maimum alu of u dos no chang. W could ak h naional conomy as a synhsis indusry. Though US conomy, produciiy µ, has bn growing approimaly from World War II o 3, DP flucuas always. Thr ar many diffrn characrisics of DP in his priod. In h following mpirical rsarchs, w ak US GDP chaind pric ind h GDP ind for shor in h priod of 94-3 as h ll of produciiy, Fiscal Yar =.. Daa rsourc is rfrnc [9]. W ha h following noaion and prssions: µ Th basic ll of conomic produciiy a h yar, =94, 94,, 3, masurd by h GDP ind. Th flucuaing raio of h produciiy ll, could masur h dlopmn powr DP for conomy. = µ- µ- /µ, =94, 94,, 3. X Th acual ll of produciiy, a non- ngai random ariabl. X Pµ,[ ]. 7

18 Figur 8 Th arying characrisic h nrgy flucuaion funcion u undr h larg scal of im. If h conomic nrgy is flucuad a h lowr ll, and DP dos no sar accumulaing in h fild of im [, 9 ], hus u will g smallr and smallr, and clos o zro. Hr, h bnchmark nrgy =., h scal of nrgy flucuaing =.8, h scal cofficin of nrgy flucuaing k=.. Figur 9 Th arying characrisic h nrgy flucuaion funcion uundr h larg scal of im. If h conomic nrgy is flucuad a h lowr ll, and DP dos no sar accumulaing in h fild of im [, ], hus u will g smallr and smallr, flucua round zro, and his flucuaion will g mor and mor ioln. Hr, h =., =.8, k=.. Th alus of µ =94, 94,, 3 and =94, 94,, 3 can b sn in appndi. Th inral of im uni for sampling daa GDP is a yar, h sabiliy of daa is highr, and h diffrnc bwn GDP pric ind of on yar and ha of las yar can nicly dscrib h conomic flucuaion, so w adop h formulas of mniond abo. Th curs of DP and produciiy in US conomy ar shown in figur. In figur 8, h proporion of h ral inds of µ o inds drawn is :. W could s, from figur, ha h local highr poins bwn 94 and 3 go in ascnding, dscnding, ascnding again and dscnding Figur Th curs of US conomic produciiy µ again; and ha h local lowr poins bwn GDP chaind pric ind; Fiscal Yar =.. 94 and 3 go in dscnding, ascnding, and and DPDlopmn Powr in h im fild from 94 o 3. Th proporion of h ral inds of µ dscnding again. So h DP will rlas i.. h o drawn inds is :. Though produciiy µ has local highr poins or h local lowr poins go in bn growing approimaly, DP flucuas always. dscnding if conomic nrgy is largr o a crain dgr, and h DP will accumula i.. h local highr poins or h local lowr poins go in ascnding 8

19 if conomic nrgy is smallr o a crain dgr. Saring from 98, boh h local highr poins and h local lowr poins of DP in US conomy ar dscnding. 6. Th mpirical rsarch for simaing h DP modl W shall gi h simaing analysis for h macrocosmic and microcosmic momn of nrgy in ordr o s h characrisics of DP. 6.. Esimaing analysis for h macrocosmic momn of DP. From figur, w know ha 947 and 975 ar h wo op alus of DP in US conomic dlopmn. Hr, w slc h local op alus of on h yars =947,95, 957,96,97,975 bwn 947 and 975 as our analyic sampls, and gi h simaing rsuls by modl. Bwn 947 and 96, DP =947, 95,957,96 gs smallr and smallr, namly DP in conomy is rlasd. By us of las squar mhod, w ha h following simad rsuls: = µ 9 Th simad rror is s = ] 4 =.3539, =947, 95,957,96. Bcaus µ =µ947=.466,γ = and =947= , hn h arag alu of produciiy mass in his priod of im is m µ = γ = Bwn 96 and 975, DP =96,97,975 gs largr and largr, namly DP in conomy is accumulad. Also by us of las squar mhod, w ha h simad rsuls as following: = µ Th simad rror is s = ] 3 = , = 96, 97,975. Bcaus µ =µ96=.3, γ = and =96= , hn h arag alu of produciiy mass in his priod of im is m µ = γ = Esimaing analysis for h microcosmic momn of DP. Hr, w ak h yars =986~998 as our analyic sampls for DP, and gi h simaing rsuls by modl. From 986 o 989, DP gs largr and largr, namly DP in conomy is bing accumulad. W ha h following simad rsuls: = µ Th simad rror is s = ] 4 = , =986~989. 9

20 Bcaus µ =µ986=.75, γ = and =986=.73684, hn h arag alu of produciiy mass in his priod of im is m µ = γ = From 989 o 998, DP gs smallr and smallr, namly DP in conomy is bing rlasd. W ha h following simad rsuls: = µ Th simad rror is s = ] = , =989~998. Bcaus µ =µ989=.7834, γ = and =989=.37475, hn h arag alu of produciiy mass in his priod of im is m µ = γ = o ~ ~998 Figur Th simaion and finss for DP of US conomy bwn 986 and 989. In his priod of im, DP of US conomy is accumulad coninuously. A h bginning of DP accumulaing, h mass of produciiy is smallr, i.. m =.47848, his indicas ha hr is a largr spac for DP accumulaing; and h sam im, h quaniy of high-qualiy asss in conomy is lss mans ha h arious componns of conomic producion ar in chaos. Th conomic growh wih DP accumulaing from986 o 989 and h conomic growh wih DP rlasing from 989 o 998 ar sparaly shown in figur and figur. In hs wo figurs, w ha gin h simad cur and sampls foldgram of h rlaion bwn DP and produciiy in ordr o mak a Figur Th simaion and finss for DP of US conomy bwn 989 and 998. In his priod of im, DP of US conomy is rlasd coninuously. A h bginning of DP rlasing, h mass of produciiy is largr, i.. m =3.4953, his indicas ha hr is a largr spac for DP rlasing; and h sam im, h quaniy of high-qualiy asss in conomy is largr mans ha h arious componns of conomic producion ar in ordr.

21 comparison. 6. Th mpirical analysis for h conrsion and consraion bwn mass and nrgy in conomy 6.. Th macrocosmic analysis for mass and nrgy in conomy. According o scion 6.., w know ha US conomy prsns mainly a rnd of conomic growh wih DP rlasing a four yars 947,95,957, 96; h mass of conomic produciiy, m = , is lagr comparaily. and US conomy prsns mainly a rnd of conomic growh wih DP accumulaing a hr yars 96,97 and 975; h mass of conomic produciiy in his priod, m = , is lss obiously. Tha mans h arag mass of conomic produciiy in priod of 947~96, m = , is sufficinly rlasd in h way of nrgy, so ha h mass of conomic produciiy a h bginning of priod of 96~975, a procss of DP accumulaing, is only m = , qui lss. US conomy prsns mainly a rnd of DP rlasing in h priod of 947~96, from h prssion 9, DP h conomic nrgy of US is = 96= µ96 = a h nd of his priod; and US conomy prsns mainly a rnd of DP accumulaing in h priod of 96~975, from h prssion, DP of US is = 96= µ96 = a h bginning of his priod. Bcaus h margin of and, - =.93849, is qui small, w hink ha h conomic nrgy is consrai. I is a rsul of simad rror, if say hr is a diffrnc bwn and, no h rror of nrgy consraion. 6.. Th microcosmic analysis for mass and nrgy in conomy. According o scion 6.., w could s ha US conomy princd a whol procss of DP momn from 986 o 998, i.. a sag of DP accumulaing =986~989 and a sag of DP rlasing =989~998. A h sag of DP accumulaing, h arag alu of produciiy mass in h priod of 986~989, m =.47848, is lss; and a h sag of DP rlasing, h arag alu of produciiy mass, m =3.4953, is largr. This plains ha bcaus h arag mass of produciiy is lss in h sag of DP accumulaing from 986 o 989, hr is a largr spac for DP h conomic nrgy o b accumulad; and bcaus h arag mass of produciiy is largr in h sag of DP rlasing from 989 o 998, hr is a largr spac for DP o b rlasd. US conomy prsns a rnd of DP accumulaing in h priod of 986~989, from h prssion, DP h conomic nrgy of US is = 989 = m µ = a h nd of his priod; and US conomy prsns mainly a rnd of DP accumulaing in h priod of 989~998, from h prssion, DP of US is = 989 = m µ989 = a h bginning of his priod. Bcaus h margin of and, - = , is smallr comparaily, w could hink ha DP h nrgy in conomy is consrai A brif summary. To sum up, W s h mass of conomic produciiy is rlasd in h way of nrgy during h priod of DP rlasing, and o push h conomy forward; and in h procss of DP is accumulad, h mass of conomic produciiy, ranslad from h nrgy accumulad coninuously, bcoms largr and largr. This is jus a procss of conrsion bwn mass and nrgy in conomy. In anohr hand, h conomic

22 nrgy is of consraion in h conrsion bwn mass and nrgy. If say hr is a lil diffrnc in conrsion of nrgy, i should b s a rsul of simad rror, no h rror of nrgy consraion islf. 6.3 Th mpirical analysis for conomic formaion and is oluion 6.3. Analysis for srong sa and supr sa in US conomy bwn 986 and 989. According o prssion 9 and h appndi a nd of his papr, w ha = µ Whr, γ= , µ =µ986=.75, µ =µ987=.73 and =986= As w know, US conomy is an conomic growh wih DP accumulaing in h priod of 986~989. By us of formula, w ha calculad δ= And by formula and 3, h criical ims of srong sa and supr sa ar calculad sparaly as following Th criical im of srong sa for US conomy is ε =3.5959, and h criical im of supr sa for US conomy is τ = Basd on h calculaing rsuls abo, if going on dloping for 4 yars in h way of 986~989, US conomy could com ino h srong sa of conomy, and if go on dloping for 7 yars in h way of 986~989, US conomy could com ino h supr sa of conomy. Bu, only US conomy kp on dloping for 4 yars in h way of 986~989, namly DP of US conomy sars rlasing afr 989, h diffrnc is ry largr. Th curs of h produciiy µ and DP drmind sparaly by prssion 6 and 7 ar shown in figur Analysis for srong sa and supr sa in US conomy bwn 998 and. According o prssion 9 and h appndi a nd of his papr, w ha = µ Whr, γ=9.983, µ =µ998=.9675, µ =µ999=.98 and =998= As w know, US conomy is an conomic growh wih DP accumulaing in h priod of 998~. By us of formula, w ha calculad δ= And by formula and 3, h criical ims of srong sa and supr sa ar calculad sparaly as following Th criical im of srong sa for US conomy is ε = , and h criical im of supr sa for US conomy is τ = Basd on h calculaing rsuls abo, if going on dloping for 6 yars in h way of 998~, US conomy could com ino h srong sa of conomy, and if go on dloping for 8 yars in h way of 998~, US conomy could com ino h supr sa of conomy. Bu, only US conomy kp on dloping for 4 yars in h way of 998~, namly DP of US conomy sars rlasing afr, h diffrnc is ry largr. Th curs of h produciiy µ and DP drmind sparaly by prssion 6 and 7 ar shown in figur Th mpirical analysis for flucuaions of conomic nrgy 6.4. Th flucuaions of conomic nrgy and h opimal im for DP saring accumulaing. From 96 o 964, DP of US conomy is flucuad a a lowr ll. If w l = /= and

23 Figur 3 Analysis for US conomic nrgy from 986 o 989. US conomy was growing wih DP accumulaing during 986~989. This procss kp on four yars only. If his procss could kp on fourn yars or mor, US conomy migh com ino h srong sa in conomic nrgy. In his char, ε is h criical im of srong sa. Again if his procss could kp on sin yars or mor, US conomy migh com ino h supr sa in conomic nrgy. Figur 4 Analysis for US conomic nrgy from 998 o. US conomy was growing wih DP accumulaing during 998~. This procss kp on four yars only. If his procss could kp on sin yars or mor, US conomy migh com ino h srong sa in conomic nrgy. In his char, ε is h criical im of srong sa. Again if his procss could kp on ighn yars, US conomy migh com ino h supr sa in conomic nrgy. k= / = in h nrgy flucuaions funcion 6, and l == bcaus h im of which nrgy flucuaions is a a lowr ll is gnrally longr, h flucuaions scal should b largr, so w l i b = % gnrally. Th oluion procss of nrgy flucuaions funcion u is shown in figur 5. According o h formula 8, w find h maimum alu of u which should occur bwn 964 and 965, namly DP of US conomy is mos possibl o sar accumulaing bwn 964 and 965. Acually, US conomy sars a procss of growing wih DP accumulaing from 965 for si yars 965~ Th flucuaions of conomic nrgy and h opimal im for DP saring rlasing. From 989 o 99, DP of US conomy is flucuad a a highr ll. If w l = /= and k= /= in h nrgy flucuaions funcion 6, and l =.75 = bcaus h im of which nrgy flucuaions is a a highr ll is gnrally shorr, hn h flucuaions scal should b smallr, so w l i b = 75% gnrally. Th oluion procss of nrgy flucuaions funcion u is shown in figur 6. According o h formula 8, w find h maimum alu of u which should occur bwn 99 and 99, namly DP of US conomy is mos possibl o sar rlasing bwn 99 and 99. Acually, US conomy sars a procss of growing wih DP rlasing from 99 for nin yars 99~. 7 Conclusions Basd on h hory of Dlopmn Powr and from h lan characrisics of ral conomic procss, 3

24 h works ha bn don as follow in his papr. Figur 5 Th flucuaions analysis of US conomic nrgy and h opimal im for DP saring accumulaing. DP of US conomy is flucuad a a lowr ll from 96 o 964. L = ; k= , = According o h formula 8, w find h maimum alu of u which occurs bwn 964 and 965. Acually, US conomy sars a procss of growing wih DP accumulaing from 965 for si yars. Figur 6 Th flucuaions analysis of US conomic nrgy and h opimal im for DP saring rlasing. DP of US conomy is flucuad a a highr ll from 989 o 99. L = ; k= , = According o h formula 8, w find h maimum alu of u which occurs bwn 99 and 99. Acually, US conomy sars a procss of growing wih DP rlasing from 99 for nin yars. Firs, w ha discussd h main ways o accumula and rlas h Dlopmn Powr DP, sablishd h basic modl of rlaion bwn produciiy or say h ll of conomic dlopmn and DP on h Parial Disribuion []-[3]. Thus, w know ha hr is a symmrical rlaion bwn h conomic produciiy and h conomic DP; and w ha illuminad ha boh of hm ar no discrpibl on from anohr, DP is h lan impus for produciiy growing and h ngin for conomic growh. Scond, his papr adancs hr kind of nrgy sa of conomic dlopmn, i.., h sa of normal nrgy, srong nrgy and supr nrgy in conomic form, and gis h approachs o calcula h criical ims of srong nrgy and supr nrgy. Th DP of conomic sa of supr nrgy is infini, mans h arianc of produciiy ll is infini, and in accordanc wih h basic rqus in fracal conomy. W ha indicad ha h conomic sa of supr nrgy will no occur unil h DP of an indusry.g. compur indusry is diffusd o ohr indusris, so ha DP of hos indusris has bn sirrd up; and ha h srong sa or supr sa in conomic nrgy will no occur if w ak h conomy or indusry as a whol. Th srong sa or supr sa in conomic nrgy may occur only whn wo or mor indusris ar discussd. Third, basd on h modl of rlaion bwn DP and produciiy, his papr has indicad ha hr ar h laws, conrsion and consraion bwn produciiy and DP, in conomic fild. accumulaing DP mans dposi h conomic nrgy and conr i ino mass of produciiy quaniy of high-qualiy conomic asss, and mass of produciiy can b rconrd o conomic nrgy in h way of DP rlasing o acclra conomic dlopmn. This kind of conrsion bwn produciiy and DP follows h law of consraion. 4

25 Fourh, Basd on h laws of conrsion and consraion bwn produciiy and DP, his papr has plaind ha h ral rason of h conomic diffrncs is h diffrncs in hir abiliy of DP accumulaing and rlasing bwn dlopd counris or rgions and undlopd counris or rgions. Only h DP is h durai moiiy for conomic growh. Th diffrncs on h mchanism and nironmn for DP accumulaing and rlasing ar jus h rasons ha conomic dlopmn is unbalanc for diffrn counris or rgions Fifh, DP accumulaing and DP rlasing occur alrnaly. his papr has poind ou h sign ha accumulaion of DP is compld is h mos of conomic facors ar in ordr, and h sign ha rlas of DP is compld is h mos of conomic facors ar in chaos, and gis h ways o calcula h mos possibl im ha h DP sars accumulaing or rlasing; and has indicad h rason ha h flucuaion of conomic producion and mark occurs is hr ar many ioln bifurcaions bwn h produciiy and DP, such as DP is oo small o suppor h conomic growh, or DP is so largr o rrs h original rnd of conomic rcssion quickly. Finally, auhor maks h mpirical analysis for all of conclusions gin in his papr by us of h US GDP daa from 94 o 3, h prfc rsuls ar obaind. Wha w nd o plain ar: A a discussion for DP, if w wan o know h opimal panding of an indusry producion and h acual ffc of a nw chniqu, s [3] and [3] rspcily. Only h conrsion, consraion and flucuaions of singl DP ar discussd in his papr, h problms abou group DP should b discussd afrim; conomic characrisics of som indusris which ha com ino supr sa in conomy should b rsarchd. ACKNOWLEDGMENT Th auhors would lik o hank Prof. William Grn of Economics Srn School of Businss NYU and Prof. Paul W. Wilson of Dparmn of Economics Unirsiy of Tas. REFERENCES [] R.E. Lucas. Undrsanding businss cycls, Sudis in Businss Cycl Thory. MIT Prss, Cambridg, Mass. 98, [] R.E. Lucas. Modls of Businss Cycls. Basil Blackwll, Nw York [3] R.E. Lucas. Economric Policy Ealuaion: A Criiqu. Carngi-Rochsr Confrnc Sris on Public Policy, 976, :9-46. [4] Romr, Paul M, Incrasing Rurns and Long-run Growh. Journal of Poliical Economy, 986, 94 5: -37. [5] P.M. Romr. Cak Eaing, Charing, and Jumps: Eisnc Rsuls for Variaional Problms. Economrica, 986, 54 4: [6] R.E. Lucas. On h mchanics of conomic dlopmn. Journal of Monary Economics, 988, : 3-4. [7] P.M. Romr. Endognous chnological chang. Journal of Poliical Economy, 99, 98 : 7-. [8] F. Kydland and E. Prsco. Tim o Build and Aggrga Flucuaions. Economrica, 98, 5, pp [9] Kydland, Finn E., and Edward C. Prsco. Tim o Build and Aggrga Flucuaions. Economrica, 98, 5: [] J. Long and C. Plossr. Ral Businss Cycls. Journal of Poliical Economy, 983, 9: [] C. Plossr. Undrsanding Ral Businss Cycls. Journal of Economic Prspcis, 989, 3: [] J. Long and C. Plossr. Ral Businss Cycl. Journal of Poliical Economy, 983, 9, pp [3] R. King. C. Plossr and S. Rblo. Growh and Businss Cycls: I &II. Journal of Monary Economics, 988, : 95-3, [4] H.A. Simon. Raional choic and h srucur of h nironmn. Psychological Riw, 954, 63: -38. [5] D. Kahnman, A.Trsky. Prospc Thory: An Analysis of Dcision undr Risk. Economrica, 979, 47 :

26 [6] D. Kahnman, J. L. Knsch, R. H.Thalr. Fairnss and h Assumpions of Economics. Journal of Businss, 986, 59 4: [7] A. Trsky, D. Kahnman. Raional Choic and h Framing of Dcisions. Journal of Businss, 986, 59 4: [8] F. Dai, Dlopmn Powr and Driai Procss: A Modl and Thory for Macroconomy Analysis, hp://conwpa. wusl.du: 8/ps /mac/paprs/45/453.pdf 4. [9] F. Dai, B. H. Sun, J. Sun, Driai Procss Modl of Dlopmn Powr in Indusry: Empirical Rsarch and Forcas for Chins Sofwar Indusry and US Economy, hp://conwpa. wusl.du: 8/ps /mac/paprs/45/455.pdf 4. [] F. Dai, S. T. Wu, Z.F. Qin. Th Lan Moiiy for Indusry Progrss: Dlopmn Powr in Managmn and Is Driai procss Modls. Chins Journal of Managmn Scinc, 4, : [] F.Dai. Th Parial Disribuion: Dfiniion, Propris and Applicaions in Economy. hp:// /Documns/DaiFng [] F. Dai, G. Ji. A Nw Kind of Pricing Modl for Commodiy and Esimaing Inds Sysm for Pric Scuriy. Chins Journal of Managmn Scinc,, 9: [3] F. Dai, L.Lu. Th Insmn Analyic Procss basd on h Parial Disribuion. Chins Journal of Managmn Scinc,. 9supplmn:35-3. [4] F. Dai, L.Liang. Th Mark Valu Analyic Procss for Insmn Basd on h Parial Disribuion. Procdings of SCI,, XVII. [5] F. Dai, W.X. Xu. A Nw Kind of Opimal Pricing for Commodiy. Chins Journal of Managmn Scinc, 3, : [6] F. Dai, H. Liu, Z.F.Qin. Th Modl of Opimal Pricing for Asss Basd on h Parial Disribuion and Is Empirical Rsarch. IEEE-IEMC Procdings, 3:3-35. [7] F.Dai, H. Bai, Z.J. Wang. A Nw Kind Of Mhod For Opions Pricing Basd On Th Parial Disribuion. Procdings of SCI, 3. [8] J. Orlin Grabb. Chaos and Fracals in Financial Marks, hp:// [9] hp:// [3] hp:// [3] F. Dai, J. Sun, P. Chn. Th Opimal Dcision for Epanding h Producion Scal. IEEE-IEMC Procdings, 4, : [3] F.Dai, Y.J.Zhuang, B. H. Sun. Quaniai Ealuaing Modl for h Acual Effc of DSS in Enrpris Managmn. IEEE-IEMC Procdings, 4, : Appndi Yar US GDP chaind pric ind and simad daa of DP Produciiy µ DP Yar Produciiy µ DP 6