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 | Prof. David Wilkins |
| 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.
- Any failed components are reassessed, if necessary, by an exam in the reassessment 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.