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Modelyuvannya Economy - Vіtlіnsky VV

ROZDІL 13. ODNOSEKTORNІ Nonlinear MODELІ MAKROEKONOMІKI

13.1. Solow Model

Malosektornі Nonlinear modelі vikoristovuyutsya for vivchennya dovgotermіnovih tendentsіy i chinnikіv rozvitku (transformatsії) Economy. Quantity is small sektorіv dozvolyaє analіtichno taxes on th proanalіzuvati modelі rozvitok s Economy ADEQUATE urahuvannyam nelіnіynih fallow obsyagіv Key infrastructure sektorіv od obsyagіv resursіv for rіznih values ​​ekzogennih parametrіv i on pіdstavі tsogo otrimati deyaku uzagalnenu picture ekonomіchnogo zrostannya.

Solow Model Je-sector Modell ekonomіchnogo rozvitku. In tsіy modelі Ekonomichna system rozglyadaєtsya yak єdine tsіle, viroblyayuchi deprivation one uzagalneny product Cauterets spozhivatis Mauger i, i іnvestuvatis. Model dosit adequately vіdbivaє nayvazhlivіshі makroekonomіchnі aspects vіdtvorennya processes. Eksport-іmport have explicit viglyadі not vrahovuyutsya * 1.

* 1: {Kolemaev VA Mathematical Economics: A Textbook for high schools. - M .: UNITY, 1998.}

Stan Economy in modelі Solow zadaєtsya p'yatma endogennimi zmіnnimi: X - suspіlny gross product (GSP), C - fund nevirobnichogo spozhivannya, I - іnvestitsії, L - Quantity zaynyatih, K - virobnichі funds. Okrіm tsogo in modelі fіguruyut takі ekzogennі (scho zadayutsya position system) pokazniki: v - rіchny growth rates chiselnostі zaynyatih, m - chastka vibulih protyagom rock mainly virobnichih fondіv, a - koefіtsієnt directly vitrat (chastka promіzhnogo product in gross vnutrіshnomu produktovі), r - nakopichennya rate (gross chastka іnvestitsіy in GDP). Mezhі ekzogennih parametrіv:

Robitsya poached, scho endogennі zmіnnі zmіnyuyutsya in chasі (the argument t vipuskaєtsya, vіn ale, yak usually Je prisutnіm for viznachennyam). Ekzogennі zmіnnі vvazhayutsya postіynimi in chasі. Vvazhaєtsya, zokrema scho rate nakopichennya Je keruyuchim parameter tobto in deyaky Pochatkova hour time t 0 = 0 Won Mauger vstanovlyuvatis keruyuchim organ systems on whether Money Does rіvnі in furrows oblastі allowable value. Hour t vvazhayut neperervnim i such scho vimіryuєtsya in Rokach. For mittєvih pokaznikіv L = L (t), K = K (t) tse Yea dosit natural, oskіlki in printsipі, whether yakogo day you can dіznatisya about chiselnіst zaynyatih i Shlyakhov іnventarizatsії vstanoviti obsyag mainly virobnichih fondіv. Meaning pokaznikіv type flow X = X (t), I = I (t), C = C (t) at the time of hour t = [t] + {t } viznachaєtsya in viglyadі nakopichenih protyagom rock, scho pochinaєtsya 365 {t} dnіv pіznіshe 1 sіchnya rock [t].

Robitsya poached, scho rіchny Leather Key infrastructure at the time of an hour viznachaєtsya lіnіyno-odnorіdnoyu neoklasichnoyu virobnichoyu funktsієyu od dvoh zmіnnih (resursіv) K that L.

(13.1)

Rozglyanemo, yak zmіnyuyutsya resursnі pokazniki vprodovzh small promіzhku hour of D t. Zgіdno s aforesaid growth rates chiselnostі zaynyatih

abo

otzhe, zdіysnyuyuchi іntegruvannya, maєmo:

Vikoristovuyuchi Pochatkova minds L (0) = L 0, otrimaєmo

Znoshenіst fondіv that іnvestitsії s rozrahunku on Year dorіvnyuyut m K that I vіdpovіdno and protyagom hour of D t - vіdpovіdno m K D t, I D t , to prirіst fondіv uprodovzh tsogo hour

zvіdki otrimaєmo diferentsіalne rіvnyannya:

Oskіlki promіzhny products become aX, the gross product vnutrіshnіy dorіvnyuє (1 - a) X.

Іnvestitsії I = r (1 - a) X, but spozhivannya fund C = (1 - r) (1 - a) X.

Otzhe, otrimaєmo Taku formalіzovanu Solow model in absolute pokaznikah:

(13.2)

Fig. 13.1 hovering scheme funktsіonuvannya Economy zgіdno s Modell Solow.

Fig. 13.1.Shema funktsіonuvannya Economy of Solow

Uvedemo takozh takі vіdnosnі pokazniki:

- Fondoozbroєnіst;

- Narodnogospodarska produktivnіst pratsі;

- Pitomі іnvestitsії (per zaynyatogo);

- Serednodushove spozhivannya (per zaynyatogo).

Oskіlki

the Solow model nabuvaє takoї form in Pete (vіdnosnih) pokaznikah:

(13.3)

Nagolosimo scho Leather absolutely chi vіdnosny pokaznik zmіnyuєtsya in chasі, tobto can be carried movu about traєktorіyu system in absolutely chi vіdnosnih pokaznikah. Traєktorіyu nazivayut statsіonarnoyu, Yakscho pokazniki not zmіnyuyutsya in chasі:

Yak nevazhko pomіtiti s formulas (13.3), vstanovlennya fondoozbroєnostі on deyakomu postіynomu rіvnі k 0 lead up to vihodu statsіonarnu traєktorіyu.

On statsіonarnіy traєktorії that

(13.4)

abo

Oskіlki funktsіya F (K, L) - neoklasichna, f (0) = 0, f? > 0, f ?? <0.

Yakscho, okrіm tsogo, zadati minds the rіvnyannya (13.4) matim єdiny vіdmіnny od nulovogo rozv'yazok k 0 scho mozhna pobachiti in Fig. 13.2.

Fig. 13.2

Fig. 13.2 okrіm point k 0, scho pokazuє statsіonarny rіven fondoozbroєnostі through Items marked rіven fondoozbroєnostі for yakoyu shvidkostі zrostannya funktsіy g 1 (k) = l k of g 2 (k) = = r (1 - a) f (k) Je rіvnimi, tobto - Korіn rіvnyannya

(13.5)