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Module MAU34804: Fixed Point Theorems and Economic Equilibria

Credit weighting (ECTS)

5 credits

Semester/term taught

Hilary term 2019-20

Contact Hours

11 weeks, 3 lectures including tutorials per week

Lecturer

Prof. John Stalker

Learning Outcomes

On successful completion of this module, students will be able to:

using the simplex method;
• describe and justify with reasoned logical argument basic properties of convex sets in finite-dimensional spaces;
• describe and justify with reasoned logical argument 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
• Barycentric subdivision and the Simplicial Approximation Theorem
• The Brouwer and Katukani Fixed Point Theorems
• Mathematical models of simple economies.
• Proof of the existence of equilibria in economic modules

 

Module Prerequisite

MAU11204

Assessment Detail

This module will be examined in a 2-hour examination in Trinity term. Re-assessments if required will consist of 100% exam.