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Modelyuvannya Economy - Vіtlіnsky VV

4. ROZDІL PRIKLADNІ MATEMATICHNІ MODELІ FІNANSOVO- EKONOMІCHNIH PROTSESІV

4.1. Organіzatsіya reklamnoї Campaing

Nekhay deyaka FIRMA (pіdpriєmstvo, set) pochinaє reklamuvati Novi goods Chi Hotel. Clearly, scho Prybutok od maybutnogo sale guilty perekrivati ​​vitrati on qiu kampanіyu. Clear takozh, scho spochatku vitrati mozhut perevischuvati Prybutok, more deprivation small chastka potentsіynih pokuptsіv bude іnformovana schodo news. Zgoda, from mіru zbіlshennya obsyagіv sale can vzhe rozrahovuvati on pomіtny Prybutok, i, vreshtі, nastane time, if rinok Nashita, i nadalі reklamuvati goods Buda-sensei.

Model reklamnoї Orthopedic ґruntuєtsya on such basic gіpotezah. Rozglyadaєtsya value of dN / dt - shvidkіst zmіni in chasі kіlkostі spozhivachіv, kotrі dіznalisya about goods Namir toil i i yogo buy Costa (t - h, h scho minuv cob reklamnoї Orthopedic), N (t) - Quantity already poіnformovanih klієntіv. Vvazhaєtsya scho dN / dt proportsіyna kіlkostі pokuptsіv, SSMSC slit do not know about Tsey goods (Hotel) tobto velichinі

a1 (t) (N 0 - N (t)),

de N 0 - zagalna Quantity potentsіynih platospromozhnih pokuptsіv, a1 (t)> 0 harakterizuє іntensivnіst reklamnoї Orthopedic (scho factual viznachaєtsya vitratami on advertising in the Danian time of one hour).

Pripuskaєtsya takozh, scho Ti, hto dіznavsya about the product, so chi іnakshe poshiryuyut otrimanu іnformatsіyu neobіznanih Sered, vistupayuchi in rolі dodatkovih Sponsored "agentіv" fіrmi. Їhnіy vnesok dorіvnyuє velichinі

a2 (t) (N (t ) (N 0 - N (t))).

Vіn bude tim bіlshim, denote bіlsha Quantity agentіv. The value of a2 (t)> 0 harakterizuє stupіn spіlkuvannya pokuptsіv mіzh him (Won Mauger Buti vstanovlena opituvannyam).

In rezultatі otrimaєmo rіvnyannya

(4.1)

Yakscho a1 (t) >> a2 (t ) N (t), then s (4.1) otrimaєmo model type modelі Malthus (div. Rozdil. 2, p. 16), w Yakscho a1 (t) << a2 (t ) n (t), - rіvnyannya logіstichnoї krivoї (divas breather 2, paragraph 18...).

Analogіya Je tsіlkom zrozumіloyu, more in pobudovі danoї modelі that modelі zrostannya chiselnostі populyatsії vikoristovuvalasya she herself іdeya "nasichennya": shvidkіst zrostannya in chasі deyakoї quantities proportsіyna dobutku stream values tsієї magnitude N (t) on rіznitsyu ((N 0 - N (t) ) mіzh її rіvnovazhnim (populyatsіya) chi boundary (Username Lost Password) th Flow values.

Analogіya mіzh oboma processes zakіnchuєtsya, Yakscho in deyaky hour time value of staє nulovoyu chi navіt vіd'єmnoyu (for tsogo neobhіdno, one chi dwellers obidva koefіtsієnti a1 (t), a2 steel vіd'єmnimi). Podіbny negatively efekt dosit zustrіchaєtsya often in advertising kampanіyah i blame natsіlyuvati їh organіzatorіv to those dwellers chi zmіniti nature of advertisements, chi zovsіm vіdmovitisya od neї. Come s metoyu zbіlshennya populyarnostі product mozhut fallow od quantity value spryamovuvatisya on polіpshennya rezultatіv pryamoї yak, so i oposeredkovanoї ADs.

Model (4.1) does not Got rozv'yazkіv scho dorіvnyuyut nulevі in kіntsevy time hour. Yakscho rozglyanuti model (4.1) in okolі point of N (t = 0) = N (0) = 0 (t = 0 - time cob reklamnoї Campaing) vvazhayuchi scho N << N 0, a2 (t) N << a1 (t), then rіvnyannya (4.1) Dial viglyadu:

and Yogo rozv'yazok -

(4.2)

scho zadovolnyaє, natural, Pochatkova minds Yakscho t = 0.

W (4.2) vіdnosno easily Vivest spіvvіdnoshennya mіzh Sponsored vitratami that pributkom s cob reklamnoї Campaing.

Poznachimo by p value pributku od odinichnogo sale yakoyu B Won bula vitrat without advertising. Pripustimo for sproschennya scho Leather pokupets kupuє deprivation odinitsyu one product. Koefіtsієnt a1 (t) for svoїm zmіstom oznachaє Quantity rіvnoznachnih Sponsored Act reasonably in odinitsyu hour (napriklad, rozmіschennya odnakovih afіsh). Through s poznachimo vartіst (tsіnu) elementarnogo act ADs. Todі sumarno Prybutok dorіvnyuvatime:

(4.3)

and vitrati -

Prybutok perevischuє vitrati advertising for minds pN 0> s, i if advertising Je dієvoyu th inexpensive and rinok dosit mіstky then vigrash dosyagaєtsya s Persha same krokіv Orthopedic (in dіysnostі mіzh Payment advertisements Sponsored dієyu th the following kupіvleyu Got Location lag - zatrimka in chasі, KOTRA Mauger bootie deprivation in vrahovana bіlsh detalіzovanih models). Do not vipadku duzhe efektivnoї chi dorogoї ADs FIRMA іz of cob Nese zbitki. Ale tse not privіd, dwellers vіdmovitisya od ADs. Spravdі, viraz (4.3) is the otrimana on yogo pіdstavі Umov pN 0> s spravedlivі deprivation of Malih values of N (t), if P is the S funktsії zrostayut in chasі for odnakovimi laws. Zi zbіlshennyam N (t) vіdkinutі (4.1) skladovі stayut pomіtnimi, zokrema, posilyuєtsya exposure The oposeredkovanoї ADs. Tom funktsіya N (t) Mauger article "shvidshoyu" funktsієyu hour, nіzh in formulі (4.3). Tsey nelіnіyny efekt in zmіnі magnitude N (t) for nezmіnnogo rate zrostannya vitrat daє mozhlivіst vіd- shkoduvati fіnansovu nevdachu pochatkovoї stadії reklamnoї Campaing.

Poyasnimo tse tverdzhennya on chastkovomu vipadku rіvnyannya (4.1) h postіynimi koefіtsієntami a1, a2.

Vikonaєmo zamіnu zmіnnih:

Todі (4.1) zvoditsya to logіstichnogo rіvnyannya

(4.4)

yak Got rozv'yazok

(4.5)

here , Otzhe, N (0) = 0, i Pochatkova Umov vikonuєtsya.

W (4.4) shows scho pohіdna funktsії i, otzhe, funktsіya N (t) of the minds for t> 0 Mauger Buti bіlshoyu, nіzh її Pochatkova value (for minds, scho chi ). Maximum pohіdnoї on dosyagaєtsya, if :

In Tsey perіod stream, tobto otrimuvanogo in odinitsyu hour pributku, maєmo:

Vіdnіmayuchi od Pochatkova precisely Prybutok

.

otrimaєmo:

tobto rіznitsya mіzh Pochatkova i Maximum Flow pributkami Mauger Buti dosit digit. Sumarno (іntegralny) ekonomіchny efekt od Orthopedic (Yogo neobhіdnoyu minds Je obviously vikonannya nerіvnostі ) Viznachaєtsya vsіm її perebіgom, characteristics MDM obchislyuyutsya s (4.4) and (4.5) for the Relief quadrature (іntegruvannya).

Yak viplivaє s (4.4), pochinayuchi s deyakogo time reklamuvannya staє nevigіdnim. Dіysno, if nablizhaєtsya up , Rіvnyannya (4.4) can have zapisati viglyadі:

(4.6)

Yogo rozv'yazok pryamuє to the boundary values for minds t ® 0 (funktsіya and N (t) ® N 0) zgіdno s povіlnim eksponentsіynim law. In odinitsyu hour z'yavlyaєtsya Nadto small Quantity novih pokuptsіv, i oderzhuvany Prybutok for whether yakih minds not Mauger perekriti dodatkovih vitrat.

Analogіchnі characteristics obchislyuyutsya for rіvnyannya (4.1) that yogo rіznih uzagalnen scho takozh vikoristovuyutsya widely for inventory vprovadzhennya tehnologіchnih that іnshih novatsіy. Guidance vische analіz stosuєtsya low urgent tasks mіkroekonomіchnogo rіvnya.