Mashandisirwo eCalculus muEconomics
Calculus ibazi remasvomhu rine chekuita nekudzidza kwehuwandu hwekuchinja nekuunganidzwa. Kunyangwe pakutanga yakagadzirwa kugadzirisa matambudziko mufizikisi neinjiniya, calculus yakawana mashandisirwo muzvikamu zvakasiyana-siyana, kusanganisira zvehupfumi. Muhupfumi, calculus inoshandiswa kunzwisisa nekuenzanisa shanduko muzvinhu zvehupfumi, kugadzirisa sarudzo, uye kugadzira dzidziso dzinonyatsoitika. Chinyorwa chino chichakurukura mashandisirwo akasiyana-siyana ecalculus muhupfumi zvakadzama.
Kunzwisisa Kwekutanga kweCalculus muEconomics
Calculus ine zvikamu zviviri zvikuru: differential ne integral. Differential calculus inobata ne rate yekuchinja kwebasa, nepo integral calculus inobata ne cumulative calculus. Mu economics, differential calculus inowanzo shandiswa kuona kuti shanduko diki mune imwe variable dzinogona kukanganisa sei imwe variable. Integral calculus, kune rumwe rutivi, inoshandiswa kuverenga huwandu hwe cumulative ye variable yakapihwa kwenguva yakati.
Kuongorora kweMarginal
Imwe yenzira dzakakosha dzekushandisa differential calculus muhupfumi ndeyekuongorora marginal. Pfungwa ye marginality ine chekuita nekuchinja kudiki muzvinhu zvehupfumi uye inowanzoshandiswa pakuita sarudzo dzakanaka. Mienzaniso yakajairika ndeye Marginal Cost (MC) neMarginal Revenue (MR).
Mutengo wepamucheto
Mari yeMarginal ndiyo mari yekuwedzera inodiwa kugadzira imwe yuniti yechinhu chakanaka. Panyaya yemasvomhu, kana C(q) iri iyo mari yekushanda yekugadzira mayuniti eq echinhu chakanaka, saka Mari yeMarginal, MC, inogona kutsanangurwa sechinobva chekutanga chebasa remari:
\[ MC = \frac{dC(q)}{dq} \]
Mari Inowanikwa Parutivi
Mari yeMarginal imari inowanikwa kubva mukutengesa imwe yuniti yekuwedzera yechinhu. Kana R(q) iri iyo huwandu hwemari inowanikwa pakutengesa mayuniti eQ echinhu, saka Marginal Revenue, MR, ndiyo yekutanga kubva pahuwandu hwemari inowanikwa:
\[ MR = \frac{dR(q)}{dq} \]
Mukuita sarudzo, makambani anowanzo gadzira huwandu hwezvinhu apo MC yakaenzana neMR, nekuti apa ndipo panowanikwa purofiti shoma, zvichiratidza kuti ndiyo nzvimbo yakanakisisa yekugadzira.
Kugadzirisa muEconomics
Kugadzirisa zvinhu (Optimization) inzira yekuwana mamiriro akanakisa kana kushandisa zvirambidzo kuti uwane chinangwa chaunoda. Calculus inobatsira kugadzirisa matambudziko ekugadzirisa zvinhu muzvikamu zvakasiyana-siyana zvehupfumi, zvakaita semitengo, mari inowanikwa, uye magetsi.
Dzidziso yeKugadzira
Mudzidziso yekugadzira, kambani inovavarira kuwedzera huwandu hwezvinhu zvinobuda. Basa rekugadzira, rinowanzo tsanangurwa seQ = f(L, K), apo Q inoburitsa, L inomirira basa, uye K inomirira mari, rinowanzo ongororwa uchishandisa calculus. Kuti uwane nhanho yepamusoro yekugadzira, kambani inofanirwa kuwedzera huwandu hwezvinhu zvinobuda.
Nekushandisa nzira yaLagrange, iyo inosanganisa basa rinofanira kugadziriswa nezvirambidzo zviripo, calculus inobatsira kuona musanganiswa wezvinhu zvinopinda zvichawedzera kubuda.
Dzidziso yeKushandisa
Mudzidziso yekushandiswa kwezvinhu, vatengi vanovavarira kuwedzera kukosha kwavo. Kushandiswa kwezvinhu (Utility) chiyero chekugutsikana kunowanikwa nevatengi kubva muzvinhu nemasevhisi. Basa rekushandisa U(x, y) rinoenderana nehuwandu hwezvinhu zvinoshandiswa x na y. Chinangwa chemutengi ndechekuwedzera kukosha kwavo mukati mebhajeti rakatarwa.
Tichishandisa nzira yaLagrange, calculus inotibvumira kuwana musanganiswa wezvinhu zvinopa rubatsiro rwakanyanya kumutengi.
Kukura kwehupfumi
Kuverengera kwakabatana kunoshandiswa zvakanyanya mukuenzanisa kukura kwehupfumi uye kufanotaura shanduko muhupfumi nekufamba kwenguva. Mamodheru ekukura kwehupfumi anowanzo shandisa maequation akasiyana kutsanangura kuti shanduko dzehupfumi dzinochinja sei.
Muenzaniso weKukura Kwakaderera
Muenzaniso weSolow muenzaniso wekukura kwehupfumi unotsanangura kuti kuunganidzwa kwemari, vashandi, uye tekinoroji kunokanganisa sei kubuda kwezvinhu. Equation yekutanga yemuenzaniso uyu ndeiyi:
\[ \dot{K} = sY - \delta K \]
Apo \( \dot{K} \) iri chiyero chekuchinja kwemari, s iri chiyero chekuchengetedza, Y iri kubuda, uye δ iri chiyero chekuderera kwemari.
Nekugadzirisa ma differential equations aya, tinogona kunzwisisa kuti capital ne output zvinoshanduka sei nekufamba kwenguva uye kufanotaura mamiriro ehupfumi akagadzikana, uko kusina shanduko mu capital kana output.
Zvehupfumi
Econometrics ibazi rezvehupfumi rinoshandisa matekiniki ekuverenga nhamba dze data rezvehupfumi. Calculus inoita basa guru mu econometrics, kunyanya mu linear regression, uko chinangwa chiri chekuwana mutsetse unonyatsokodzera seti ye data.
Kudzoreredzwa Kwemitsara
Kudzoreredza mutsara kunosanganisira kuisa mutsetse wakatwasuka kune seti yemapoinzi edata kuitira kuti huwandu hwezvikanganiso zvesquared huderedzwe. Maitiro aya anoda kushandiswa kwe differential calculus kuderedza basa rekukanganisa, rinozivikanwa senzira ye least squares.
Basa rekukanganisa mumutsara uri nyore rinogona kunyorwa seizvi:
\[ E = \sum_{i=1}^{n} (y_i – (a + bx_i))^2 \]
Apo \( y_i \) dziri mavalues chaiwo, \( a \) uye \( b \) dziri maparamita e regression, uye \( x_i \) dziri mavalues akafanotaurwa. Nekuenzanisa derivative yekutanga yebasa re error maererano na a na b, tinogona kuwana maparamita anoderedza kukanganisa kwese.
Kuongorora Kuenzana Kwakajairwa
Calculus inoshandiswawo mukuongorora kwakajairika, inova hurongwa hunoratidza kuti zvikamu zvakasiyana zvehupfumi zvinodyidzana sei. Mamodheru akajairika anowanzo sanganisira masisitimu ekuenzanisa akasiyana anomiririra kuenzana mumisika yezvinhu zvakasiyana-siyana nemasevhisi.
Muenzaniso weArrow-Debreu
Muenzaniso weArrow-Debreu imuenzaniso wekuenzanisa wakajairika unoratidza mamiriro ezvinhu ayo misika yese muhupfumi iri mukuenzanisa. Tichishandisa calculus, kunyanya linear algebra uye differential analysis, tinogona kutevedzera kuti misika yakasiyana-siyana inosvika sei mukuenzanisa.
Kazhinji, calculus chishandiso chine simba muhupfumi, chinoita kuti munhu akwanise kuongorora shanduko dzinochinja-chinja, kugadzirisa sarudzo, uye kunzwisisa kwakadzama kwemamiriro ehupfumi. Kushandiswa kwecalculus hakungopfumisi dzidziso yehupfumi chete asiwo kunobatsira mukuita sarudzo dzinoshanda pamatanho ese ari maviri ehupfumi hwepamusoro nehwepamusoro.
