Mathematics and Methodology for Economics: Applications, Problems and Solutions

✍ Scribed by Wolfgang Eichhorn, Winfried Gleißner (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 644
• Series: Springer Texts in Business and Economics
• Edition: 1
• Category: Library

✦ Synopsis

This book about mathematics and methodology for economics is the result of the lifelong experience of the authors. It is written for university students as well as for students of applied sciences. This self-contained book does not assume any previous knowledge of high school mathematics and helps understanding the basics of economic theory-building. Starting from set theory it thoroughly discusses linear and non-linear functions, differential equations, difference equations, and all necessary theoretical constructs for building sound economic models. The authors also present a solid introduction to linear optimisation and game theory using production systems. A detailed discussion on market equilibrium, in particular on Nash Equilibrium, and on non-linear optimisation is also provided. Throughout the book the student is well supplied with numerous examples, some 2000 problems and their solutions to apply the knowledge to economic theories and models.

✦ Table of Contents

Front Matter....Pages i-xix
Sets, Numbers and Vectors....Pages 1-44
Production Systems Production Processes, Technologies, Efficiency, Optimisation....Pages 45-60
Mappings, Functions....Pages 61-104
Affine and Linear Functions and Transformations (Matrices), Linear Economic Models, Systems of Linear Equations and Inequalities....Pages 105-176
Linear Optimisation, Duality: Zero-Sum Games....Pages 177-207
Functions, Their Limits and Their Derivatives....Pages 209-300
Nonlinear Functions of Interest to Economics. Systems of Nonlinear Equations....Pages 301-371
Nonlinear Optimisation with One or Several Objectives: Kuhn–Tucker Conditions....Pages 373-475
Set Valued Functions: Equilibria—Games....Pages 477-507
Integrals....Pages 509-534
Differential Equations....Pages 535-563
Difference Equations....Pages 565-596
Methodology: Models and Theories in Economics....Pages 597-625
Back Matter....Pages 627-630

✦ Subjects

Economic Theory/Quantitative Economics/Mathematical Methods; Methodology/History of Economic Thought; Game Theory, Economics, Social and Behav. Sciences