Isoperimetric Problem in Economics
| Author: | Bc. Mikoláš Volek |
|---|---|
| Year: | 2011 - winter |
| Leaders: | doc. RNDr. Oldřich John CSc. |
| Consultants: | |
| Work type: | Bachelors |
| Language: | English |
| Pages: | 39 |
| Awards and prizes: | |
| Link: | |
| Abstract: | The isoperimetric problem is one of the broad class of optimal control problems, which draw on the generalization of classical calculus developed in the mid-20th century. In the bachelor's thesis I lay down the mathematical framework that permits to rigorously prove both the necessary and sucient conditions for the existence of a maximizer of the objective function. I analyze a simple problem from the eld of project planning, which is a branch of applied economics. On the basis of a 1973 article by Cullingford and Prideaux I present an augmented cost function that involves the concept of the time value of money, which is key to proper economic reasoning. I give an explicit solution along with graphical depictions of the impact of a non-zero discount factor on project planing under the model in question. Finally, I introduce additional constraints and discuss the subproblem of multiple equality and non-equality constraints. |
| Downloadable: | Bachelor Thesis of Volek |
