Primjena matematičke analize u ekonomiji

master's thesis

• Title (english): Application of mathematical analysis in economics
• Author: Mihaela Božinović
• Mentor: Ana Prlić (mentor)
• Committee member: Ana Prlić (predsjednik povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-07-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Brojne primjene matematičke analize u ekonomiji svjedoče o njihovoj neraskidivoj povezanosti. Granični koncepti poput graničnog troška, prihoda, profita, korisnosti, proizvoda rada i proizvoda kapitala, cjenovna elastičnost, kontrola inventara te komparativnostatička analiza samo su neki od primjera u kojima se primjenjuje diferencijalni račun. Njega direktno koristimo i u maksimizaciji i minimizaciji nekih ekonomskih funkcija. Medutim, uvjeti poput budžetskog ograničenja često proizlaze iz prirode problema što nas vodi do uvjetne optimizacije. Jedna pogodna metoda za pronalaženje uvjetnih ekstrema je metoda Lagrangeovih multiplikatora. Osim diferencijabilnosti, važno svojstvo je i homogenost koja se često pretpostavlja u ekonomskoj teoriji gdje su primjenu pronašli i Eulerov teorem i homogenizacija.

Abstract (english)

There are numerous applications of mathematical analysis in economics evidencing their inextricable bound. Marginal concepts such as marginal cost, revenue, profit, utility, the product of labor and the product of capital, price elasticity, inventory control and comparative statics analysis are only some of the examples where calculus is used. Calculus is also directly used in maximization and minimization of some economic functions. However, constraints like budget constraints naturally arise, which leads us to constraint optimization. One convenient method for finding constrained local extrema is the method of Lagrange multipliers. Other than differentiability, one other important function property is homogenity that is often assumed in economic theory, where also Euler’s theorem and homogenization found their application.

• Keywords: diferencijalni račun; budžetsko ograničenje; metoda Lagrangeovih multiplikatora; Eulerov teorem; homogenizacija
• Keywords (english): calculus; budget constraints; method of Lagrange multipliers; Euler’s theorem; homogenization
• Language: croatian
• URN:NBN: urn:nbn:hr:217:227433
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-09-14 12:22:38