home Economy books Modelyuvannya Economy - Vіtlіnsky VV

Modelyuvannya Economy - Vіtlіnsky VV

9.2. Model Valrasa

Prior warehouse suchasnoї rozvinutoї Economy incoming chislennі gospodarskі odinitsі that spozhivachі. Cutaneous іz Tsikh uchasnikіv Rinku doskonaloї konkurentsії Got svoї tsіlі scho umozhlivlyuє nayavnіst konflіktnih situatsіy. That dwellers Ekonomichna system funktsіonuvala ok іndivіdualnі dії rіznih uchasnikіv povinnі Buti vіdnosno good uzgodzhenimi.

In modelі Walras, scho vklyuchaє skіnchennu Quantity spozhivachіv i virobnikіv, TAKE virіshennya (podolannya) konflіktu dosyagaєtsya not vtruchannyam powers and oposeredkovano through specific rinkovy mehanіzm scho ґruntuєtsya on regulyuyuchіy dії Sistemi tsіn. Yakscho system tsіn viznachena then whether yak rinkova lands Square od of chi Je competitive rinok, chi ni, zdіysnyuєtsya vіdpovіdno to tsієї Sistemi tsіn.

Participants do not Yakscho mozhut vplivati ​​on tsіni then rinok nazivayut competitive. In a competitive market analysis tsіni for dermal s uchasnikіv nekerovanimi Yea, i їm (participant) zalishaєtsya deprivation pristosovuvatisya to іsnuyuchoї Sistemi tsіn.

The basic іdeya Valrasa polyagaє in fact dwellers for pevnoї Sistemi tsіn іndivіdualnі plan (namіri) uchasnikіv steel spіlnimi, tobto such a system tsіn zabezpechuє rozpodіl resursіv i produktsії on osnovі rozv'yazannya konflіktu mіzh uchasnikami. Taku rіvnovazhnu situatsіyu nazivayut competitive rіvnovagoyu.

In modelі Valrasa rozglyadaєtsya ekonomіka spozhivachami s l (i = 1, ..., l), m virobnikami (k = 1, ..., m) i n tovarіv types (j = 1, ..., n). A p = (p 1, ..., pn) poznachatimemo vector-row tsіn, and through x = (x 1, ..., xn)? - Vector stovpchik tovarіv.

In danіy modelі ponyattya "goods" traktuєtsya rozshireno. Pid item underwrite uvazі i object (pratsі product) i zasіb pratsі (kapіtalne obladnannya, sporudi toscho), i pervinnі resources (Prace that prirodnі resources).

Model Valrasa mozhna rozglyadati yak formalіzatsіyu rіchnogo cycle virobnitstva i rozpodіlu tovarіv in rezultatі vzaєmodії sub'єktіv Economy (spozhivachіv virobnikіv i), skin іz yakih Got svoї tsіlі.

Leather spozhivach volodіє income K (p) i Got svoє field perevag schodo tovarіv, yak Mauger Buti job at viglyadі іndikatora perevag (funktsії korisnostі u (x)). Yakscho poznachiti through mnozhinu admissibility naborіv tovarіv scho Yea Available spozhivachevі for tsіn p, X - area viznachennya u (x), then funktsіya popitu spozhivacha Mauger Buti given such rank:

(9.4)

tobto funktsіya popitu - tse taka mnozhina admissibility naborіv tovarіv, skin іz yakih (naborіv) maksimіzuє korisnіst spozhivacha Quest rіvnya tsіn p. Otzhe, skin spozhivach harakterizuєtsya funktsієyu popitu F i (p) i-income K i (p). Pripuskaєtsya scho dohіd skin spozhivacha skladaєtsya s dvoh Chastain: s income pbi od sale Pochatkova stock tovarіv bi income that l i (p) in rezultatі uchastі spozhivacha in virobnitstvі, tobto

Leather virobnik (FIRMA) formalіzuєtsya svoїmi tehnologіchnimi mozhlivostyami. Poznachimo through vector stovpchik vitrat-Key infrastructure k-th virobnika: dodatnі tsogo component vector zadayut Key infrastructure fіrmi, vіd'єmnі components - vitrati. Tom scalar dobutok pyk Je pributkom fіrmi. Tehnologіchnі mozhlivostі fіrmi viznachayutsya yak mnozhina vsіh admissibility vektorіv vitrat-Key infrastructure Yk. Qiu mnozhinu nazivayut mnozhinoyu virobnichih mozhlivostey.

Pid funktsієyu Offers fіrmi rozumіyut one chi kіlka vektorіv vitrat-Key infrastructure, kotrі Quest tsіn p maksimіzuyut Prybutok:

(9.5)

Vvazhaєtsya scho Yk to whether yakogo k Yea i About a closed mnozhinoyu I Yk, tobto FIRMA Mauger not vipuskati produktsіyu she did not ROBIT vitrat.

Vector vitrat-Key infrastructure for vsієї Economy viznachaєtsya yak scrip vektorіv vitrat-Key infrastructure for vsіh virobnikіv:

(9.6)

For takoї іntegratsії promіzhnі produkti vzaєmno skorochuyutsya, in fact do not take away analіzі uchastі.

We have rezultatі vector y s uvіydut dodatnim sign deprivation kіntsevі product (kіntsevy Key infrastructure), and h vіd'єmnim sign - pervinnі resources.

Vector y nabuvaє Pevnyi values іz zagalnoekonomіchnoї mnozhini virobnichih mozhlivostey:

The basic funktsіya Economy Square od addition, Chi Won Je tsentralіzovanoyu and chi detsentralіzovanoyu, polyagaє in rozpodіlі sukupnogo (іntegrovanogo) virobnitstva mіzh virobnikami i in rozpodіlі viroblenih produktіv Sered spozhivachіv.

Rozpodіl virobnitstva zdіysnyuєtsya obrannyam vector vitrat-Key infrastructure yk іz tehnologіchnoї mnozhini virobnichih mozhlivostey Yk for skin virobnika (k = 1, ..., m), suma yavlyaє him sukupny (іntegrovany) virobnichy processes.

Takі sukupnі processes utvoryuyut sukupnu tehnologіchnu mnozhinu Y (zagalnoekonomіchnu mnozhinu virobnichih mozhlivostey).

Suma on vsіh spozhivachah becoming sukupnu Pochatkova vlasnіst.

In ponyattya pochatkovoї vlasnostі mozhut vhoditi not deprivation spozhivchі goods, and second promіzhnі products (Objects pratsі) kapіtalne obladnannya (zasobi pratsі), the land INSHI prirodnі resources Prace. Mnozhina {b} + Y yavlyaє him mnozhinu sukupnoї Offers.

Rozpodіl spozhivannya zdіysnyuєtsya through vibіr cutaneous spozhivachem spozhivannya menu:

Je sukupnogo popitu vector, z component deyakі yakogo shaping can Buti vіd'єmnimi, Yakscho stink Yea propozitsієyu (napriklad Prace).

Pid spіlnim rozpodіlom virobnitstva i spozhivannya underwrite uvazі Taqiy nabіr vektorіv spozhivannya i vektorіv vitrat-Key infrastructure

for yakogo sukupny popit zbіgaєtsya іz sukupnoyu propozitsієyu, tobto

(9.7)

Nabіr zadaє competitive rіvnovagu in modelі Walras Yakscho:

(9.8)

(9.9)

(9.10)

Here p * nazivayut vector tsіn competitive.

Spіvvіdnoshennya (9.9) (9.10) іmenuyut Walras law in a wide rozumіnnі, Yakscho and y (9.9) Location Got rіvnіst - tse Walras law in vuzkomu rozumіnnі.

So rank, competitive rіvnovaga yavlyaє him sumіsny rozpodіl virobnitstva that spozhivannya and sukupny popit at tsomu not razі perevischuє sukupnoї Offers (9.9). Vartіst sukupnogo popitu in competitive tsіnah dorіvnyuє vartostі sukupnoї Offers to quiet themselves tsіnah (9.10), cutaneous de іz spozhivachіv maksimіzuє his korisnіst tsіnah at p *, and cutaneous іz virobnikіv - svіy Prybutok in quiet tsіnah themselves (9.8). Otzhe, іsnuvannya konkurentnoї rіvnovagi oznachaє іsnuvannya takoї Sistemi rіvnovazhnih (competitive) tsіn p *, for yakoї uzgodzhuyutsya konflіktnі Interests spozhivachіv i virobnikіv.

Postaє power for yakih drain іsnuє rіvnovaga is competitive in modelі Walras?

Zgіdno s theorem Errou-Debreu is competitive rіvnovaga іsnuє nayavnostі for such minds:

1. Mnozhina naborіv spozhivchih Xi good for skin іz spozhivachіv Je closed, opukloyu i neobmezhenoyu mnozhinoyu: Xi I Rn.

2. Dermal mnozhina Xi Got bottom border ci: xi? ci, xi I Xi, i = 1, ..., l.

3. Funktsіya Ui neperervna i vvіgnuta on Xi, i = 1, ..., l.

4. Leather spozhivach Got, Saying to vzagalі, neobmezhenі require i volodіє Pevnyi nevіd'єmnoyu Pochatkova vlasnіstyu bi, i = 1, ..., l.

5. Cutaneous tehnologіchna mnozhina Je is closed opukloyu mnozhinoyu: Yk I Rn, O I Yk .

6. Sukupna tehnologіchna mnozhina Y Je opukloyu that zadovolnyaє minds: , Tobto not Mauger іsnuvati dodatnogo pure Key infrastructure Hoca used one s tovarіv without іsnuvannya Hoca used one s tovarіv (resource) vіd'єmnih vitrat.

7. Іsnuyut takі lm Constanti scho , tobto - Chastka (Pete Wagga) uchastі i-th spozhivacha pributkah at k-th virobnika (tse Umov, okrіm іnshogo, oznachaє scho Prybutok skin virobnika without zalishku rozpodіlyaєtsya mіzh spozhivachami, SSMSC Je payovikami).

Zaznachimo scho navіt for іsnuvannya konkurentnoї rіvnovagi Absent garantії that scho Tsei ekonomіka go to the camp. Neobhіdno doslіdzhuvati for yakih stanіv Economy Je mozhlivim perehіd at the camp konkurentnoї rіvnovagi and for yakih vіn nemozhlivy. Yakscho Well perehіd Je mozhlivim requiring vkazati kerіvne rule, yakogo Tsey perehіd mozhna zdіysniti.