Advanced Mathematical Economics Routledge Advanced Texts in Economics and Finance 1st Edition by Rakesh V Vohra ISBN 0415700086 9780415700085

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ISBN 10: 0415700086 
ISBN 13: 9780415700085
Author: Rakesh V Vohra

This concise textbook presents students with all they need for advancing in mathematical economics. Detailed yet student-friendly, Vohra’s book contains chapters in, amongst others: * Feasibility * Convex Sets * Linear and Non-linear Programming * Lattices and Supermodularity. Higher level undergraduates as well as postgraduate students in mathematical economics will find this book extremely useful in their development as economists.

Advanced Mathematical Economics Routledge Advanced Texts in Economics and Finance 1st Table of contents:

1: Things to know
1.1 Sets
1.2 The space we work in
1.3 Facts from real analysis
1.4 Facts from linear algebra
1.5 Facts from graph theory
Problems
Note
References
2: Feasibility
2.1 Fundamental theorem of linear algebra
2.2 Linear inequalities
2.3 Non-negative solutions
2.4 The general case
2.5 Application: arbitrage
2.6 Application: co-operative games
2.7 Application: auctions
Problems
Notes
References
3: Convex sets
3.1 Separating hyperplane theorem
3.2 Polyhedrons and polytopes
3.3 Dimension of a set
3.4 Properties of convex sets
3.5 Application: linear production model
Problems
Notes
References
4: Linear programming
4.1 Basic solutions
4.2 Duality
4.3 Writing down the dual
4.4 Interpreting the dual
4.5 Marginal value theorem
4.6 Application: zero-sum games
4.7 Application: Afriat’s theorem
4.8 Integer programming
4.9 Application: efficient assignment
4.10 Application: Arrow’s theorem
Problems
Notes
References
5: Non-linear programming
5.1 Necessary conditions for local optimality
5.2 Sufficient conditions for optimality
5.3 Envelope theorem
5.4 An aside on utility functions
5.5 Application: market games
5.6 Application: principal–agent problem
Problems
Notes
References
6: Fixed points
6.1 Banach fixed point theorem
6.2 Brouwer fixed point theorem
6.3 Application: Nash equilibrium
6.4 Application: equilibrium in exchange economies
6.5 Application: Hex
6.6 Kakutani’s fixed point theorem
Problems
Notes
References
7: Lattices and supermodularity
7.1 Abstract lattices
7.2 Application: supermodular games
7.3 Application: transportation problem
7.4 Application: efficient assignment and the core
7.5 Application: stable matchings
Problems
Notes
References
8: Matroids
8.1 Introduction
8.2 Matroid optimization
8.3 Rank functions
8.4 Deletion and contraction
8.5 Matroid intersection and partitioning
8.6 Polymatroids
8.7 Application: efficient allocation with indivisibilities
8.8 Application: Shannon switching game
Problems

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