Mathematical Tools for Economics

  • ID: 2241227
  • Book
  • 380 Pages
  • John Wiley and Sons Ltd
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With many expensive and lengthy matematics texts for students of economics on the market. Mathematical Tools for Economics provides an affordable, short, and accessible alternative for those requiring an intermediate, semester–length treatment. The focus is on the topic of optimization–both static and dynamic. The essential matrix algebra and differential equations are covered as well.

Designed to demonstrate the essential mathematical concepts – comprehensively and economically – without re–teaching basic material or laboring over superfluous ideas, this text locates the necessary information in a practical economics context. Utilizing clear exposition and dynamic pedagogical features, Mathematical Tools for Economics provides students with the analytical skills they need to better grasp their field of study.

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Preface.

Part I: Matrix Algebra and Linear Economic Models.

1. Matrix Algebra.

1.1 Basic Concepts.

1.2 Determinants.

1.3 The Inverse of a Matrix.

1.4 Linear Dependence of Vectors and the Rank of a Matrix.

1.5 Kronecker Products and Vecs of Matrices.

2. Simultaneous Linear Equations.

2.1 Definitions.

2.2 Homogeneous Case.

2.3 Nonhomogeneous Case.

2.4 Special Case m=n.

3. Linear Economic Models.

3.1 Introduction and Definitions.

3.2 Examples of Linear Economic Models.

3.3 The Use of Matrix Algebra in Statistics and Econometrics.

4. Quadratic Forms and Positive Definite Matrices.

4.1 Introduction.

4.2 Eigen Values of a Symmetric Matrix.

4.3 Eigen Values of Special Matrices.

4.4 Eigen Vectors of a Symmetric Matrix.

4.5 Matrix whose Columns are the Eigen Vectors of a Symmetric Matrix.

4.6 Diagonalization of Quadratic Forms.

4.7 Eigen Values , andAr (A), and trA.

4.8 An Alternative Approach using Determinants.

Part II: Functions of Many Variables and Optimization.

5. Functions of Many Variables.

5.1 Functions in General.

5.2 Partial Differentiation.

5.3 Special Sorts of Functions.

5.4 Comparative Statics and Nonlinear Economic Models.

5.5 Differentials and Taylor’s Approximation.

6. Optimization.

6.1 Unconstrained Optimization.

6.2 Local Optima and Global Optima.

6.3 Constrained Optimization.

6.4 Constrained Local Optima versus Constrained Global Optima.

6.5 An Introduction to Matrix Calculus.

7. Comparative Static Analysis in Optimization Problems.

7.1 Introduction.

7.2 Unconstrained Optimization.

7.3 Constrained Optimization.

7.4 Slutsky’s Equation.

7.5 Applications of the Envelope Theorems in Economics.

Part III: Dynamic Analysis.

8. Integration.

8.1 Introduction.

8.2 Definite Integrals.

8.3 Integration as Anti Differentiation.

8.4 Indefinite Integrals.

8.5 Further Considerations.

8.6 Economic Applications.

9. Continuous Time: Differential Equations.

9.1 Definitions.

9.2 Linear Differential Equations.

9.3 First Order Linear Differential Equations with Constant Coefficients.

9.4 Economic Dynamics Using First Order Differential Equations.

9.5 Second Order Linear Differential Equations with Constant Coefficents.

9.6 Economic Application: A Dynamic Supply and Demand Model.

9.7 Higher Order Linear Differential Equations.

9.8 Descriptive Analysis of Nonlinear Differential Equations.

10. Discrete Time: Difference Equations.

10.1 Introduction and Definitions.

10.2 First Order Linear Difference Equations with Constant Coefficients.

10.3 Second Order Linear Difference Equations with Constant Coefficients.

10.4 Investigating the Nature of the Roots of a Quadratic Equation.

10.5 Economic Applications.

10.6 Higher Order Linear Difference Equations.

11. Dynamic Optimization.

11.1 Introduction.

11.2 Dynamic Optimization versus Static Optimization.

11.3 The Basic Optimal Control Problem and Pontryagin’s Maximum Principle.

11.4 Extensions to the Basic Problem.

11.5 Economic Application: Ramsey/Solow Model.

Answers to exercises.

Further Reading.

Index.

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Darrell A. Turkington is Professor of Economics at the University of Western Australia. He has a Ph.D in theoretical econometrics from the University of California, Berkeley and has held visiting appointments at Berkeley, the University of Warwick, the University of British Columbia, and Nuffield College, Oxford. He is co–author of theEconometric Society monograph,Instrumental Variables (1985), as well as author ofMatrix Calculus and Zero–One Matrices (2002).
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