Kushandiswa Kwakabatana muEconomics neBhizinesi
Pendauluan
Kubatanidza masvomhu, kunowanzonzi integral calculus, inzira ine simba guru ine mashandisirwo akawanda muzvikamu zvakasiyana-siyana, kusanganisira economics nebhizinesi. Kubatanidza hakungoshandiswi chete kuverenga nzvimbo yepamusoro kana huwandu hwezvinhu, asiwo kune zvakunoreva zvikuru pakuita sarudzo dzehupfumi uye hurongwa hwebhizinesi. Chinyorwa chino chichatsanangura mamwe mashandisirwo e integrals muhupfumi nebhizinesi uye kuti nzira iyi yemasvomhu inobatsira sei mukuongorora nekugadzirisa matambudziko akaomarara.
Pfungwa Yekutanga Yekubatanidza
Usati wanyatsoongorora mashandisirwo chaiwo, zvakakosha kunzwisisa pfungwa huru yechinhu chinobatanidzwa pachacho. Zvinobatanidza zvinoshandiswa zvakanyanya kuverenga huwandu hwese hwekuchinja kunoramba kuchiitika. Mumashoko emasvomhu, chinhu chinobatanidzwa chebasa f(x) muganho wehuwandu, unowanzozivikanwa seRiemann sum.
MaIntegrals anouya mumhando mbiri huru:
1. Definite Integral inoshandiswa kuverenga nzvimbo iri pasi pekona iri pakati pemapoinzi maviri pa x-axis.
2. Indefinite Integral ibasa rekutanga rinoratidza antiderivative yebasa.
Muhupfumi nebhizinesi, mafomu ese aya akakosha anogona kushandiswa pakuongorora kwakadzama.
Kushandiswa Kwakabatana muEconomics
1. Kuverenga Mari Yose Inowanikwa
Imwe yenzira dzakakosha dzekushandisa zvinhu zvakakosha muhupfumi ndeyekuverenga huwandu hwemari inowanikwa (TR) kubva kumabasa emari inowanikwa (MR). Mari inowanikwa zvishoma nezvishoma kuchinja kwemari inowanikwa kubva pakutengeswa kwechimwe chikamu chemari kana sevhisi. Mari yose inogona kuverengerwa sehuwandu hwemari inowanikwa zvishoma nezvishoma.
\[ TR = \int MR \, dx \]
Ngatitii basa remari shoma rakapihwa muchimiro che \( MR(x) \), saka mari yese inowanikwa kubva kumayuniti x ezvinhu ndeiyi:
\[ TR = \int MR(x) \, dx \]
Nekuita basa rekubatanidza mari iyi, nyanzvi yezvehupfumi inogona kuwana huwandu hwemari inotengeswa.
2. Verenga Mutengo Wose
Kufanana nekuverenga mari yose inowanikwa, zvinhu zvinoshandiswawo kuverenga mari yose inoshandiswa kubva pabasa remari shoma (MC). Mari yose inoshandiswa pakugadzira huwandu hwezvinhu ndiyo mari shoma inoshandiswa pakuverenga huwandu hwezvinhu zvakagadzirwa.
\[ TC = \int MC \, dx \]
Kana basa re "marginal cost" richinzi \( MC(x) \), saka mutengo wese unogona kuverengerwa seizvi:
\[ TC = \int MC(x) \, dx \]
Zvakakosha kunzwisisa mari inoshandiswa mukugadzira, izvo zvinobatsira mumitengo uye sarudzo dzekugadzira.
Kushandiswa Kwakabatana muBhizinesi
1. Kuongorora Kushandiswa uye Kudiwa Kwezvinhu
Mubhizinesi, kunzwisisa maitiro evatengi uye kudiwa kwechigadzirwa kwakakosha. Basa remarginal demand rinogona kupa ruzivo rwekuti shanduko dzemitengo dzinokanganisa sei huwandu hunodiwa. MaIntegrals anogona kushandiswa kuverenga shanduko yese muhuwandu hunodiwa pakuchinja kwemutengo kwakapihwa.
Ngatitii pane basa rekuda \( Q(p) \), apo Q iri huwandu hwechinhu chakanaka uye p iri mutengo wacho. Nekuita basa rekuda remarginal demand, tinogona kuwana huwandu hwese hwechinodiwa.
\[ Q(p) = \int Q'(p) \, dp \]
Izvi zvinobatsira mabhizinesi kusarudza nzira dzinoshanda dzemitengo nekuziva kuti shanduko dzemutengo dzichakanganisa sei huwandu hwezvinhu zvinotengeswa.
2. Kuongorora Njodzi uye Kukosha Kunotarisirwa
Mumari yebhizinesi, zvinhu zvakakosha zvine basa guru pakuongorora njodzi uye kukosha kunotarisirwa. Kutarisira njodzi kunowanzoda kuverenga kukosha kunotarisirwa kwemigumisiro yakasiyana-siyana, iyo inogona kunge yakavakirwa pakugoverwa kwezvingangoitika nguva dzose.
Basa rekuti probability density (PDF) re continuous random variable \( f(x) \) rinogona kushandiswa kuwana tarisiro (expected value) ye random variable kuburikidza ne integral:
\[ E(X) = \int_{-\infty}^{\infty} xf(x) \, dx \]
Inobatsira zvikuru pakuita sarudzo apo kusava nechokwadi kunoita basa guru, semuenzaniso mukudyara mari, inishuwarenzi, uye nzira dzekudzivirira matambudziko.
3. Kufanotaura Kugadzirwa uye Kuronga
MaIntegrals anogonawo kushandiswa mukufanotaura mamodheru ekuronga kugadzirwa uye kudiwa mune ramangwana. Mabasa ekudiwa kwechigadzirwa uye inflation zvinogona kuenzaniswa uchishandisa matekiniki akabatanidzwa kuti unzwisise maitiro ekudiwa uye kufungidzira kudiwa mune ramangwana. Nemamodheru akarurama, makambani anogona kugadzirisa zvinhu zvavo neketani dzezvinhu zvavanotengesa.
Chidzidzo Chenyaya: Kushandiswa Kwekufanotaura Kwakabatana Mukudiwa
Semuenzaniso, ngatitorei chidzidzo chakareruka chekufungidzira kudiwa kwekambani inogadzira zvinhu. Ngatitii kudiwa kwechigadzirwa Q(t) sebasa renguva t kunopiwa nebasa remarginal demand \( Q'(t) \). Kuti tiwane kudiwa kwese kwenguva yakatarwa, tinofanira kubatanidza basa iri.
Semuenzaniso, \( Q'(t) = 100 – 2t \), iyo inoratidza kuti marginal demand inoderera nekufamba kwenguva. Kuti tiwane total demand kubva pakutanga kwenguva (t=0) kusvika kumagumo kwenguva (t=T), tinoita zvinotevera:
\[ Q(T) = \int_0^T (100 – 2t) \, dt \]
Tichishandisa nzira dzekutanga dzekubatanidza, tichawana:
\[ Q(T) = \kuruboshwe[ 100t – t^2 \kurudyi]_0^T \]
\[ Q(T) = 100T – T^2 \]
Kubva pane izvi zvabuda, kambani inogona kufanotaura zvese zvinodiwa zvenguva T uye kuita sarudzo zvichibva pane izvi zvataurwa.
Mhedziso
MaIntegrals ane mashandisirwo akakura uye akakosha muhupfumi nebhizinesi. Kubva pakuverenga mari yese inowanikwa uye mitengo kusvika pakuongorora mashandisirwo, njodzi, uye kufanotaura zvinodiwa, kushandiswa kwemaIntegrals kunobatsira kuwana kunzwisisa kwakadzama uye kwakarurama kwezviitiko zvehupfumi. Munyika iri kuramba ichioma ine data rakawanda, kugona kushandisa maturusi emasvomhu senge maIntegrals pakuongorora bhizinesi mukana wakakosha wekukwikwidza.
Nekuziva matekiniki akabatana, nyanzvi dzezvehupfumi nevanhu vemabhizinesi vanogona kuita sarudzo dziri nani uye dzine musoro, izvo zvinozopedzisira zvawedzera kubudirira kwekushanda uye kushanda zvakanaka.
