Mathematical Methods for Economic Theory 1

James C. Moore

ISBN 10: 3540662359 / ISBN 13: 9783540662358

Editore: Springer Berlin Heidelberg, 1999

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Druck auf Anfrage Neuware - Printed after ordering - The two-volume work is intended to function as a textbook for graduate students in economics as well as a reference work for economic scholars. Assuming only the minimal mathematics background required of every second-year graduate student in economics, these two volumes provide a self-contained and careful development of mathematics through locally convex topological vector spaces, and fixed-point, separation, and selection theorems in such spaces. Volume One covers basic set theory, sequences and series, continuous and semi-continuous functions, an introduction to general linear spaces, basic convexity theory, and applications to economics. Volume Two introduces general topology, the theory of correspondences on and into topological spaces, Banach spaces, topological vector spaces, and maximum, fixed-point, and selection theorems for such spaces.

Codice articolo 9783540662358

Dati bibliografici

• Titolo: Mathematical Methods for Economic Theory 1
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 3540662359
• ISBN 13: 9783540662358
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 30 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 30 millimetri di profondità
• Peso: 816 grammi

Descrizione articolo

Riassunto

This two-volume work functions both as a textbook for graduates and as a reference for economic scholars. Assuming only the minimal mathematics background required of every second-year graduate, the two volumes provide a self-contained and careful development of mathematics through locally convex topological vector spaces, and fixed-point, separation, and selection theorems in such spaces. Volume One covers basic set theory, sequences and series, continuous and semi-continuous functions, an introduction to general linear spaces, basic convexity theory, and applications to economics.

Contenuti

Set Theory and Properties of Rn.- Set-Theoretic Notation and Concepts.- Properties of The Real Numbers.- Binary Relations.- Euclidean Norm and Metric.- Open and Closed Sets in Rn.- Relatively Open and Closed Sets.- Some Linear Space Properties of Rn.- Sequences and Infinite Series.- Sequences of Real Numbers.- Subsequences and Cauchy Sequences.- Infinite Series.- Efficient Intertemporal Allocation.- Sequences and Series in Rn.- Continuity.- Continuous Vector-Valued Functions.- Continuity and Compactness.- Semi-Continuous Functions.- Limits Inferior and Superior of a Function.- Transformation Functions.- Production and Cost Functions.- Sequences of Functions and Limits.- Linear Spaces.- Introduction.- Linear Combinations and Subspaces.- Linear Transformations and Functionals.- Normed Linear Spaces.- Inner Product Spaces.- Product Spaces and Direct Sums.- Affine Sets.- Convex Sets and Functions.- Convex Sets.- Relative Interiors of Convex Sets.- Extreme Points of a Convex Set.- Minimum Distance and Projection Theorems.- Basic Separation Theorems in Rn.- Convex and Concave Functions.- Continuity of Convex Functions.- Quasi-Concave Functions.- Applications of Convexity.- Introduction.- Basic Production and Cost Theory.- Distance and Support Functions.- Duality of Cost and Production.- Homotheticity.- Welfare Economics.- Constrained Extrema and Saddle Points.