MAU34804 Fixed point theorems and economic equilibria
| Module Code | MAU34804 |
|---|---|
| Module Title | Fixed point theorems and economic equilibria |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | |
| Module Prerequisites | MAU11204 Analysis on the real line |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Students are assessed based on the exam alone.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Describe and justify with reasoned logical arguments basic properties of convex sets in finite-dimensional spaces.
- Describe and justify with reasoned logical arguments basic properties of simplices and simplicial complexes.
- Describe in reasonable detail how techniques from real analysis and low-dimensional topology can be applied to investigate the existence and properties of equilibria in simple economic models.
Module Content
- Review of results from real analysis.
- Properties of convex subsets of finite-dimensional spaces.
- Simplices and simplicial complexes.
- The Brouwer and Katukani fixed point theorems.
- Mathematical models of simple economies.
- Proof of the existence of equilibria in economic models.