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9780195133783

Introductory Mathematical Economics

by
  • ISBN13:

    9780195133783

  • ISBN10:

    0195133781

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2003-07-24
  • Publisher: Oxford University Press

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Summary

A strong relationship clearly exists between mathematics and modern economics; mathematics helps extend and formalize economic theory, and quantitative economic data influences the development and refinement of mathematical models. In Introductory Mathematical Economics, 2/e, author D. WadeHands introduces students to a variety of new mathematical tools and explains how to apply those tools to a broad range of economic problems. The book begins with an overview of the necessary mathematical background, then presents a number of more advanced mathematical tools that allow students toexpand their knowledge of economics. It offers a mix of classical and contemporary economic theory, covering the standard mathematical techniques such as optimization and comparative statics, as well as more specialized topics such as uncertainty, dynamics, nonlinear programming, and matrix theory. Thoroughly revised and updated, this second edition offers students a wide range of mathematical techniques and the associated economic theory. The new Chapter 0, a mathematical review covering all prerequisite mathematics, serves as both a precourse mathematics refresher and a handy reference.All end-of-chapter problems are economics problems; many are detailed and require a substantial amount of economic interpretation in addition to the technical analysis. These problems have been revised and expanded in this second edition. Boxes in each chapter provide economic examples of relevantmathematical concepts. Several boxes discuss recent developments in economic theory, while others present results that influenced the evolution of modern economics. Featuring a clear and concise presentation of mathematical and economic concepts, Introductory Mathematical Economics, 2/e, is idealfor undergraduate courses in mathematical economics.

Table of Contents

Starting with Chapter 1, each chapter ends with Problems and Notes
Mathematical Notation
Mathematical Symbols
The Greek Alphabet
Review of Mathematics
Some Basic Mathematical Concepts
Calculus
Matrices and Related Topics
Economic Applications of One-Variable Calculus
Applications of One-Variable Calculus from Introductory Economics
Optimization Examples from Introductory Economics
An Introduction to Concavity and Convexity
Economic Applications of Multivariate Calculus
Partial Derivatives and the Total Difference in Economics
Homogeneous Functions
Homothetic Functions
Concave Functions in n Variables
Comparative Statics I: One and Two Variables with and without Optimization
Equilibrium Comparative Statics in One and Two Dimensions
Comparative Statics with Optimization in One and Two Dimensions
Comparative Statics with Both Equilibrium and Optimization
Integration, Time, and Uncertainty in Economics
Integration
Time
Uncertainty
Introduction to Continuous Time Dynamics in One and Two Dimensions
Single-Market Competitive Equilibrium
Examples of One-Variable Dynamic Economic Models
Multiple-Market Competitive Equilibrium
A Macroeconomic Example
An Alternative Notion of Stability
Matrices and Economic Theory
Submatrices and Minors
Cramer's Rule in Economics
Inverse- and Implicit-Function Theorems
A Special Class of Matrices: M Matrices
The Leontief Input-Output System
Quadratic Forms and Definiteness
Comparative Statics II: n Variables with and without Optimization
Equilibrium Comparative Statics in n Dimensions
Comparative Statics with Optimization in n Dimensions
Comparative Statics III: Optimization under Constraint
The Lagrange Technique: First- and Second-Order Conditions
A Specific Utility Function
Choice between Labor and Leisure
Comparative Statics from Constrained Optimization: Two Approaches
Consumer Choice: The n -Good Case
Additively Separable Utility Functions
Inequality Constraints in Optimization Theory
A Simple Inequality Constraint
The General Kuhn-Tucker Theorem
Economic Examples of Kuhn-Tucker Theory
Linear Programming
References
Appendix: Answers to Selected Problems
Index
Table of Contents provided by Publisher. All Rights Reserved.

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