Modelyuvannya Economy - Vіtlіnsky VV

17.2. Chastkova model ekonomіchnogo vіdboru

Rozglyanmo vіdbіr s dvoh rіznih vidіv "routines". One s them - "tehnologіya" KOTRA zastosovuє FIRMA. Friend - "rule priy- nyattya rіshen" yak viznachaє koefіtsієnt vikoristannya virobnichih bearing-down (rіven Key infrastructure).

Maєmo deyaku (gіpotetichnu) Galuzo, yak vipuskaє one odnorіdny product. At the Branch vsіh fіrmah nayavna one second that she mnozhina tehnologіchnih alternatives (Persha "routine") virobnitstva їhnogo product. Usі mozhlivі tehnologії harakterizuyutsya postіynimi koefіtsієntami vitrat i postіynim efekta scale. Access in all tehnologіyah odnakovim Je spіvvіdnoshennya Key infrastructure produktsії i vikoristovuvanih virobnichih bearing-down (main kapіtalu). Let him for sproschennya tse vіdnoshennya dorіvnyuvatime odinitsі. Ale tehnologії rіznyatsya mіzh him zmіnnimi vitratami. Pripustimo, scho at the time of skin hour FIRMA zastosovuє deprivation one tehnologіyu.

Other "routine", scho її vikoristovuє FIRMA - usually vikoristannya virobnichih bearing-down. Tacke rule poєdnuє stupіn vikoristannya virobnichih bearing-down s vіdnoshennyam tsіni product to zmіnnih Pete vitrat virobnitstva. Otzhe,

de P i c - vіdpovіdno Rate Product First zmіnnі pitomі vitrati virobnitstva, q, k - i kapіtal vіdpovіdno Key infrastructure (virobnichі potuzhnostі).

Pripustіmo scho funktsіya a (•) - neperervna, monotone spadna, dodatna dostatno for the great values of the argument that zadovolnyaє nerіvnіst 0? a (•)? 1.

Rule vikoristannya bearing-down mozhna іnterpretuvati yak Takeo, scho harakterizuє pokaznik pributku in vіdsotkah to zmіnnih vitrat, yaky Je neobhіdnim for dwellers stimulyuvati fіrmu vіdpovіdnim rank dіyati for rіznih rіvnіv vikoristannya virobnichih bearing-down.

Pripuskaєtsya gіpoteza scho chinniki virobnitstva, kotrі postachayutsya in Galuzo, Yea absolutely elastichnimi, tsіni vsіh chinnikіv dodatnі th postіynі on vsomu promіzhku hour zdіysnennya analіzu. Otzhe, OOO All tehnologії mozhna oharakterizuvati vporyadkuvati zgіdno i Zi zmіnnimi Pete vitratami virobnitstva.

Zvichayno, scho for whether yakoї tehnologії zagalnі pitomі vitrati virobnitstva perebuvayut in Auburn proportsіynіy zalezhnostі od rіvnya vikoristannya virobnichih bearing-down. For zruchnostі inventory pripustimo scho іsnuє in Pevnyi rozumіnnі єdina naykrascha tehnologіya Zi zmіnnimi Pete vitratami virobnitstva with. Je fair gіpoteza scho zhodne Lots Other Mauger perevazhiti rule is not a rule, viokremlene orthodox tehnologієyu:

The Branch vіdpovіdaє strictly spadna neperervna funktsіya popitu, KOTRA virazhaє zalezhnіst tsіni viroblenogo product od zagalnogo obsyagu Key infrastructure. Tsya funktsіya Je viznachenoyu for vsіh nevіd'єmnih obsyagіv Key infrastructure. Pripuskaєtsya, scho if zagalny obsyag Key infrastructure dosit malies the Branch, the deyaka tehnologіya th deyake rule vikoristannya virobnichih bearing-down will bring dodatny Prybutok. Yakscho Well the Branch Key infrastructure Je dosit great, the zhodna superpozitsіya tehnologіy i bearing-down rules vikoristannya not bude pributkovoyu.
It can be formally oharakterizuvati system so. Nekhay usі virobnichі potuzhnostі vikoristovuyut on fіrmah odnakovu tehnologіyu i funktsіonuyut zgіdno s odnakovimi rules schodo vikoristannya bearing-down. Todі camp deyakoї fіrmi i, i = 1, ..., M mozhna oharakterizuvati zmіnnimi: cit, a it, kit, de cit - zmіnnі pitomі vitrati i -ї fіrmi in perіod t; a it - funktsіya scho harakterizuє vpliv vіdnoshennya tsіni product to Pete vitrat virobnitstva i -ї fіrmi in perіod t; kit - virobnichі potuzhnostі i -ї fіrmi in perі- od t. Stan usіh M fіrm in perіodі t (zagalom) viznachaє korotkotermіnovu funktsіyu Offers for tsogo perіodu (t):

Together іz funktsієyu popitu

Won viznachaє Pt i qt for korotkotermіnovogo perіodu. Navedenі vische poached stosovno h (•) that a it (•) garantuyut, scho taka korotkotermіnova rіvnovaga zavzhdi іsnuє. Prybutok fіrmi i t per hour perіod dorіvnyuє:

de r - kapіtalnі Hotel.

Clearly, scho if іsnuє rіvnovaga, over takoї rіvnovagi maksimіzatsіya pributku vimagaє, dwellers usі funktsіonuyuchі fіrmi zastosovuvali tehnologіyu s naynizhchimi Pete vitratami. Otzhe for vsіh fіrm have yakih qi> 0, dwellers Prybutok CCB nevіd'єmnim, rіvnovazhna Rate P * Got Booty bіlshoyu, nіzh deyake tasks . In tsomu vipadku Prybutok bude maksimіzuvatisya zgіdno s such a rule schodo viznachennya obsyagu Key infrastructure, Cauterets potrebuє Povny vikoristannya virobnichih bearing-down for minds scho P = P *. Rіvnovazhna Rate P * Got dorіvnyuvati in protilezhnomu vipadku in fіrmi z'yavitsya incentive zmіniti stupіn vikoristannya bearing-down.

Poached schodo funktsії popitu garantuє іsnuvannya such q *, scho Tse - Key infrastructure rіvnovazhnі i tsіni vіdpovіdno.

Robitsya takozh TAKE poached schodo іnvestitsіy. Yakscho have fіrm s dodatnim mainly kapіtalom Prybutok - nulovy, the second іnvestitsії Je nulovimi. Rozshirennya fіrm scho viluchayut dodatny Prybutok, Got ymovіrnіsny character. Іmovіrnіst zmenshennya for them dorіvnyuє nulevі. W dodatnoyu ymovіrnіstyu stink doluchayut to Svoge slit park one car. In the same hour іsnuє nenulova ymovіrnіst schodo skorochennya nayavnih fіrm, SSMSC toil vіd'єmny Prybutok. Pong, bezumovno not rozshiryuyutsya. Fіrmi - potentsіynі competitors kotrі toil nenulovy postіyny kapіtal i dodatnu ymovіrnіst uvіyti in Galuzo tіlki s odnієyu machine, and a pair of "routines" SSMSC stink planuyut vprovaditi in practice, bring Mauger їm dodatny Prybutok for tsіni Pt.

Potentsіynі competitors scho planuyut couple of "routines" SSMSC bring nulovy chi vіd'єmny Prybutok have Galuzo not vstupayut. Perelіchenі alternative to such taxes can be formally rank:

in іsnuyuchih fіrmah, SSMSC zalishatsya Zi svoїm kapіtalom:

;

in іsnuyuchih fіrmah, SSMSC viluchayut dodatny Prybutok:

s іmovіrnіstyu

in іsnuyuchih fіrmah, SSMSC toil vіd'єmny Prybutok (zbitki):

de characteristics rozpodіlu vipadkovoї quantity d vvazhayutsya vіdomimi (D = kt);

in potentsіynih konkurentіv, SSMSC planuyut "routine", kotrі bring їm dodatny Prybutok: kt +1 = 0 abo 1 de tsі obidva vipadki (0 chi 1) toil nenulovu ymovіrnіst;

in potentsіynih konkurentіv, SSMSC planuyut "routine" for IBAs have maintained upstream stink razі zalishatsya Zi svoїm kapіtalom: kt +1 = 0.

Granite, KOTRA rіzko vіdmezhovuє evolyutsіynі modelі od orthodoxy, Yea those scho fіrmam not nav'yazuєtsya zdatnіst odnochasno th simultaneously rozglyadati Velika Quantity rіshen alternative. Poshuk Provadia navmannya. Obirayutsya takі gіpotezi schodo Poshuk. According au-Perche, search Search results for minds, scho yogo Veda FIRMA actively viznachaєtsya in termіnah іmovіrnіsnogo rozpodіlu "rutin" SSMSC will be found in the protsesі Poshuk chi on pіdstavі, mozhlivo, vzhe іsnuyuchih in fіrmi "routines". Alternatively, vіddayuchi perevagu CIM already іsnuyuchim "routine", viznaєmo nenulovu ymovіrnіst of scho bude in protsesі Poshuk vіdnaydena whether yak іnsha couple "tehnologіya - rіshen rule of acceptance." In tretє, іsnuє nenulova ymovіrnіst of scho novih vіdshukaє FIRMA not "routine" i tim himself for neobhіdnostі zberezhe svoї vzhe іsnuyuchі "routine".

In yakih vipadkah іsnuє Poshuk? Here zdіysnyuyutsya takі mіrkuvannya. Yakscho system Got to come up rіvnovagi, skhozhoї s orthodox pіdhodom then fіrmi povinnі dosit actively zaymatisya Poshuk. W іnshogo side, Poshuk not Got Booty nastіlki activity, dwellers vіn mіg zmusiti system vіdіyti od of the camp, Cauterets from simple (orthodox) vipadku LUVs bi rіvnovazhnim. Pripuskaєtsya scho fіrmi, SSMSC toil dodatnі potuzhnostі, vzagalі not zaymayutsya Poshuk, Yakscho stink viluchayut nevіd'єmny Prybutok. Potentsіynі competitors scho pragnut uvіyti in Galuzo (s fіrmi nulovimi virobnichimi bearing-down), vvazhayutsya such scho perebuvayut zavzhdi in stanі Poshuk, ale if incoming at Galuzo then povinnі mother takі "routine", scho vzhe proyshli test rentabelnіst.

Selektsіyna rіvnovaga

In kontekstі opisanoї vische modelnoї kontseptsії in evolyutsіynіy teorії viznachayut static selektsіynu rіvnovagu yak situatsіyu in yakіy camp usіh nayavnih at the Branch fіrm zalishaєtsya nezmіnnim and perelіk nayavnih fіrm takozh not zmіnyuєtsya.

Poached schodo Poshuk garantuyut, early scho chi pіzno yakas іz fіrm - Yakscho not іsnuyucha then potentsіyny competitor - vіdshukaє descho lіpshu tehnologіyu she usually maintained upstream vikoristannya virobnichih bearing-down, dwellers viluchiti nevіd'єmny Prybutok. Yakscho tsya pair of "routines" bude znaydena and FIRMA tsya vzhe dіyala in the Branch, then won rozshiritsya and Yakscho Tse potentsіyny competitor in the vіn uvіyde rinok. And for tsіni Zi svoїm іnteresom zalishatsya deprivation fіrmi s vіdnosno maintained upstream tehnologіyami th rules of acceptance rіshen scho vimagaє Povny vikoristannya bearing-down for tsієї tsіni; zhodna s fіrm not zmozhe zdіysniti nіchogo lіpshogo.

Pіdkreslimo: Yakscho fіrmi dіyut zgіdno s vische aforesaid rules, scho zabezpechuyut Povny vikoristannya bearing-down for rіvnovazhnoї tsіni P * Then processes Poshuk not porushuє rіvnovagi. Do not Got value reaktsіyu viklikaє yak tse rule for іnshih tsіn.

Zalishaєtsya power: chi given to processes vіdboru rіvnovazhnogo will Galuzo, Yakscho yogo to tsogo not Bulo?

W assumptions evolyutsіynoї teorії viplivaє scho given. To bring tsogo potrіbno dati exact characteristics rіvnovazhnih stanіv. Pid "pitched the Branch" underwrite uvazі perelіk stanіv fіrm M, de camp kozhnoї s them harakterizuєtsya zmіnnimi cit, a it, kit, vіdpovіdno Pete vitratami, bearing-down rules vikoristannya i obsyagami Tsikh bearing-down.

Nazvemo rule vikoristannya bearing-down "priynyatnim" Yakscho vono lead to Povny vikoristannya їh for tsіni , Yakscho tobto . "Rіvnovazhny Stan" - tse Taqiy camp for yakogo sukupnіst bearing-down of the Branch (k *) dorіvnyuє Key infrastructure such q *, scho i have vsіh fіrm scho toil nevіd'єmnі potuzhnostі, Je nayavnimi priynyatnі rules vikoristannya bearing-down i priynyatnі obsyagi vitrat . Easy pobachiti, scho in rіvnovazhnomu stanі Cena dorіvnyuє i єdinim views for Change Je Poshuk profitability "rutin" potentsіynimi competitors and otzhe, panuє selektsіyna rіvnovaga. Movoyu teorії markіvskih protsesіv mnozhina E rіvnovazhnih stanіv Je "closed mnozhinoyu".

Oskіlki mnozhina "rutin" Je skіnchennoyu then postaє power - chi Mauger neskіnchenno zrostati kapіtal the Branch? I do not Mauger. Zaznachimo, scho to whether yakoї bet "routines" (c, a) іsnuє deyaky rіven bearing-down boundary K (in, a), scho Yea naybіlshim the k values, for yakogo mozhut odnochasno vikonuvatis minds:

W spіvvіdnoshennya viplivaє Perche, scho - Dodatne. Іz gіpotezi, scho for dosit temple rіvnya Key infrastructure OAO All "routine" nerentabelnі, maєmo scho Maximum іsnuє the k, yak zadovolnyaє odnochasno obidva spіvvіdnoshennya.

Rozglyanmo teper vipadok, if . Zhodna s fіrm at tsomu not razі spromozhna zbіlshiti svіy kapіtal to rіvnya, yaky perevischuє , Pocha s whether yakogo nizhchogo rіvnya. Oskіlki D obmezhuє mozhlivy prirіst kapіtalu (kt +1 - kt) vprodovzh perіodu one, then for such a move potrіbno, dwellers Pochatkova values kt perevischuvalo b . Prote oskіlki FIRMA guilty mother deyaku tehnologіyu (c, a) i Then tsya FIRMA Got Booty unprofitable otzhe, її rozshirennya nemozhlive.

Zhodna s fіrm not Mauger zbіlshiti svіy kapіtal to obsyagu, yaky perevischuє , I for the fact whether yakogo specific processes funktsіonuvannya kapіtal i -ї fіrmi obmezheny zverhu De ki 1 - kapіtal i -ї fіrmi for Pochatkova become the Branch. Otzhe, s whether yakogo Pochatkova the Branch will mozhna dosyagnuti deprivation skіnchennoї mnozhini stanіv.

Potrіbno utochniti scho oznachaє "dosit great fіrm Quantity": the number of M i factuality potentsіynih fіrm perevischuє . So rank, if not the Branch sukupnі potuzhnostі perevischuyut , Obov'yazkovo povinnі Buti fіrmi s nulovimi bearing-down, tobto potentsіynі competitors. W іnshogo side, Yakscho sukupnі potuzhnostі perevischuyut , The Hoca used one s fіrm obviously Got zbitki th zmushena zaymatisya Poshuk. There whether Money Does vipadku іsnuє nenulova ymovіrnost addition, scho will priynyatі novі "routine" s vitratami that vіdpovіdne vikoristannya bearing-down rule.

Usі fіrmi (nayavnі chi potentsіynі), scho demonstruyut takі bet "routines" - nazvemo takі fіrmi "priynyatnimi" fіrmami - mozhut s nenulovoyu ymovіrnіstyu zberіgati tsі "routine" vprodovzh deyakogo perіodu.

Yakscho set camp for yakogo Je Hoca used one priynyatna FIRMA, the zavzhdi mozhna s bіlshoyu od zero ymovіrnіstyu "zrobiti Krok have bіk" mnozhini E rіvnovazhnih stanіv. Quantity "krokіv", scho vіd- okremlyuyut Danian stan od E can otsіniti yak - Sukupnі potuzhnostі nepriynyatnih fіrm plus absolyutnі values rozhodzhennya mіzh bearing-down kl priynyatnih fіrm i k *. Clearly, scho on skіnchennіy mnozhinі stanіv the Branch tsya Quantity krokіv Je obmezhenoyu. Pripustimo, scho mill Je precisely such scho Cena produktsії fіrmi perevischuє . Todі obviously, kl <k * i zbіlshennya obsyagіv priynyatnoї fіrmi bearing-down on the same machine for nezmіnnogo will іnshih fіrm Je Kroc s vіdmіnnoyu od zero perehіdnoyu ymovіrnіstyu scho zmenshuє vіdstan to E. W іnshogo side, pripustimo, scho mill Je so for yakogo Cena produktsії Je Mensch chi dorіvnyuє . Nepriynyatnі fіrmi obov'yazkovo zaznavatimut zbitkіv, i Yakscho Sered them Je FIRMA s Positive bearing-down, then zmenshennya bearing-down on the same machine - Krok s dodatnoyu ymovіrnіstyu scho skorochuє vіdstan to E. Yakscho kn = 0, then this kind zdіysnennya Kroc not mozhlivim Yea, ale at tsomu vipadku maєmo scho kl? k *. Yakscho vikonuєtsya strict nerіvnіst, then vіdpovіdnomu krotsі s Positive perehіdnoyu ymovіrnіstyu vіdbudetsya skorochennya potuzhnostі priynyatnoї fіrmi for one car, and Got Yakscho Location rіvnіst, the Danian mill already nalezhit to E. Re-hover zastosuvannya vische mіrkuvan pokazuє, scho for vkazanih poached schodo perehіdnih іmovіrnostey mnozhina E dosyagaєtsya for skіnchennu Quantity krokіv.

Rіvnovaga unorthodox. Nagolositi dwellers on vazhlivostі class obranih rules rozglyanemo scho vіdbudetsya, Yakscho mnozhina mozhlivih rules schodo vikoristannya bearing-down is not orthodox mіstitime ni, ni whether yakogo іnshogo priynyatnogo rules. Todі obviously orthodox minds of rіvnovaga Povny vikoristannya bearing-down nemozhlivoyu bude, bo Cena Je dosit great i bude stimulyuvati fіrmi to naroschuvannya bearing-down. Selektsіyna rіvnovaga, however, zalishaєtsya mozhlivoyu.

OAO All Zberezhemo poached poperednogo analіzu, okrіm poached, scho Hoch b odne rule schodo vikoristannya virobnichih bearing-down Je priynyatnim. For whether a rule yakogo іsnuє naynizhcha Cena, sumіsna s tim, dwellers zalishitisya Zi svoїmi іnteresami, if zmіnnі vitrati dorіvnyuyut , Tobto naynizhcha Cena, scho minds zadovolnyaє

Poznachimo by P ** s naynizhchu such tsіn zgіdno s usіma mozhlivimi rules a, and through - Koefіtsієnt vikoristannya bearing-down, for Cauterets dosyagaєtsya tsya mіnіmalna Cena. Dwellers adaptuvati zroblene zadlya zruchnostі poached, scho s pov'yazane nepodіlnіstyu kapіtalu, pripustimo scho іsnuє tsіle number (obsyag kapіtalu k **), scho zadovolnyaє minds:

Nazvemo rule vikoristannya virobnichih bearing-down "psevdopriynyatnim" Yakscho vono porodzhuє koefіtsієnt vikoristannya bearing-down, Cauterets dorіvnyuє , Yakscho - Domіnuyuche vіdnoshennya tsіni to vitrat. Bringing Je mozhlivim, Yakscho just Iti Shlyakhov poperednogo analіzu deprivation іz zamіnoyu "priynyatnogo" rules "psevdopriynyatne»: P *, k *, q 8 on vіdpovіdno

In rezultatі dohodimo visnovku scho selektsіyna rіvnovaga s koefіtsієntom vikoristannya bearing-down in kіntsevomu pіdsumku bude dosyagnuta.