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The maximized utility's role inoptimal saving
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

An economy can roughly be reduced to a few parameters; investment, consumption and production. These parameters depend on the capital, however there is no general case for how they should be weighted against each other in order to obtain a desired outcome. Frank Ramsey's description of said relation is expressed as a dierential equation where the desired outcome is based on maximum utility. In this report, two dierent types of utility functions are studied, one that is designed by ourselves based on given restrictions and one that Greenwood, Hercowitz and Human has developed. The purpose of this study is to formulate and solve the optimal control problem described by Ramsey as well as comparing the eect of dierent utility functions. This is done by using a combination of Lagrange's method and Euler's method for a nite horizon and by analytical calculations when studying an innite time horizon. The results varies when regarding dierent countries, the two dierent utility functions as well as the time span. The common factor is that the capital, consumption and investment increases over time, however the dierence is by how much and how fast. Comparing the two utility functions yields a noticeable dierence for the nite time horizon whereas the parameters are almost indistinguishable for the innite time horizon.

Abstract [en]

En ekonomi kan i grova drag reduceras till ett fatal parametrar; investering, konsumtion samt produktion. Dessa parametrar beror av kapitalet, dock existerar ingen generell regel for hur dessa bor forhalla sig till varandra for att uppna en onskad eekt. Frank Ramseys beskrivning av namnda forhallande uttrycker sig som en dierentialekvation dar den onskade eekten ar en maximal nytta. Denna rapport undersoker tva olika nyttofunktioner, en som designats av oss samt en som Greenwood, Hercowitz och Human utvecklat. Syftet med studien ar att formulera och losa det optimala styrproblem som beskrivs av Ramsey samt att jamfora eekten av olika nyttofunktioner. For att na syftet kan en kombination av Lagranges metod och Eulers metod anvandas da en andlig tidshorisont betraktas medan den oandliga tidshorisonten studeras primart analytiskt. Resultatet for studien varierar beroende pa land, nyttofunktion samt tidsperspektiv. Den gemensamma namnaren ar att kapitalet, konsumtionen samt investeringen okar med tiden dar skillnaden ar hur mycket samt hur snabbt. Da en jamforelse sker mellan de tva nyttofunktionerna ses en noterbar skillnad for det andliga tidsperspektivet, dock en nastan omarkbar skillnad i det oandliga scenariot.

Place, publisher, year, edition, pages
2017. , 28 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-219443OAI: oai:DiVA.org:kth-219443DiVA: diva2:1163145
Supervisors
Examiners
Available from: 2017-12-06 Created: 2017-12-06 Last updated: 2017-12-06Bibliographically approved

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  • apa
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