Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization shows readers how to apply static and dynamic optimization theory in an easy and practical manner, without requiring the mastery of specific programming languages that are often difficult and expensive to learn. Featuring user-friendly numerical discrete calculations developed within the Excel worksheets, the book includes key examples and economic applications solved step-by-step and then replicated in Excel.
After introducing the fundamental tools of mathematical economics, the book explores the classical static optimization theory of linear and nonlinear programming, applying the core concepts of microeconomics and some portfolio theory. This provides a background for the more challenging worksheet applications of the dynamic optimization theory. The book also covers special complementary topics such as inventory modelling, data analysis for business and economics, and the essential elements of Monte Carlo analysis.
Practical and accessible, Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization increases the computing power of economists worldwide. This book is accompanied by a companion website that includes Excel examples presented in the book, exercises, and other supplementary materials that will further assist in understanding this useful framework.
1. Cover image - p. i 2. Title page - p. ii 3. Table of Contents - p. iii 4. Copyright - p. iv 5. About the author - p. ix 6. Preface - p. xi 7. Part I. Excel and fundamental mathematics for economics - p. xii 8. Part I Excel and fundamental mathematics for economics - p. 1 9. Chapter 1. Excel VBA, solver, and other advanced worksheet tools - p. 3 10. Chapter 2. Univariate and multivariate calculus - p. 45 11. Chapter 3. Elements of linear algebra - p. 87 12. 3.1. Built-in Excel matrix functions and basic operations - p. 88 13. 3.2. Linear systems and resolution methods in Excel: Cramer, Solver, Inverse - p. 95 14. 3.3. Eigenvalues and eigenvectors search: analytical and graphical approach - p. 107 15. 3.4. Quadratic forms and definiteness of a symmetric matrix - p. 115 16. 3.5. Leontief open model - p. 121 17. 3.6. Equilibrium in n markets - p. 124 18. 3.7. Economic policy modeling: objectives and instruments - p. 129 19. Exercises - p. 134 20. Chapter 4. Mathematics for dynamic economic models - p. 139 21. 4.1. Ordinary differential equations and numerical methods: Euler and Runge-Kutta - p. 140 22. 4.2. Force of interest, Walrasian stability, utility functions, and capital formation with ordinary differential equation - p. 147 23. 4.3. Difference equations and phase diagrams - p. 159 24. 4.4. Cobweb model of price adjustment and other economic models with difference equations - p. 170 25. 4.5. Systems of linear differential equations - p. 181 26. 4.6. Tourism fight between two competing regions - p. 202 27. 4.7. Walrasian adjustment with entry - p. 206 28. Exercises - p. 209 29. Part II. Static optimization - p. 215 30. Part II Static optimization - p. 217 31. Chapter 5. Classical static nonlinear optimization theory - p. 219 32. 5.1. Classical unconstrained optimization of a univariate function - p. 220 33. 5.2. Classical unconstrained optimization of a multivariate function - p. 232 34. 5.3. Some economic applications of the nonlinear unconstrained optimization - p. 247 35. 5.4. Numerical steepest descent method applied to the unconstrained optimization with VBA - p. 256 36. 5.5. Nonlinear problems in Rn with equality constraints: Lagrange multipliers and Solver - p. 264 37. 5.6. Nonlinear problems in R2 with equality constraints: contour lines - p. 272 38. 5.7. Nonlinear problems with inequality constraints - p. 285 39. Exercises - p. 288 40. Chapter 6. Microeconomic theory in a static environment - p. 295 41. 6.1. The consumer problem: cardinal versus ordinal utility approach - p. 296 42. 6.2. Consumer optimization and derivation of the demand curve in the cardinal approach - p. 297 43. 6.3. Consumer optimization and derivation of the demand curve in the ordinal approach - p. 307 44. 6.4. The firm problem - p. 319 45. 6.5. One-input classical production function - p. 320 46. 6.6. Two-inputs production functions - p. 322 47. 6.7. Isoquants and the constrained production optimization with two inputs - p. 331 48. 6.8. Production Edgeworth box, contract curve, and the possibility frontier construction - p. 335 49. 6.9. Short-run, long-run costs and the envelope average total costs derivation - p. 340 50. 6.10. Perfect competitive markets: short-run, long-run supply curves and market equilibrium - p. 350 51. 6.11. Monopolistic market equilibrium: the Chamberlin model - p. 356 52. 6.12. Markets with high-entry barriers: monopoly and the Cournot duopoly model - p. 360 53. 6.13. Game theory. Zero-sum games and minimax criterion: matrix and graphical resolutions - p. 370 54. Exercises - p. 376 55. Chapter 7. Linear programming - p. 383 56. Chapter 8. Nonlinear optimization applied to the portfolio theory - p. 417 57. Part III. Dynamic optimization - p. 434 58. Part III Dynamic optimization - p. 435 59. Chapter 9. Calculus of variations - p. 437 60. 9.1. The fundamental problem of the Calculus of Variations - p. 438 61. 9.2. Discrete approximate Calculus of Variations: Lagrange multipliers and contour lines solutions - p. 442 62. 9.3. Set up of the Excel worksheet for Calculus of Variations problems: the Solver solution - p. 451 63. 9.4. General cases developed in Excel with fixed and variable terminal points - p. 453 64. 9.5. Dynamic optimization for a monopolist - p. 469 65. 9.6. Unemployment and inflation - p. 471 66. 9.7. The Eisner–Strotz model - p. 475 67. 9.8. The optimal consumption Ramsey model - p. 479 68. 9.9. Inventory dynamic optimization - p. 481 69. 9.10. Optimal capital structure and the firm cost of capital - p. 482 70. 9.11. Contour lines solution for Calculus of Variations using the VBA code - p. 487 71. 9.12. Calculus of Variations with functionals involving two independent functions - p. 494 72. 9.13. Calculus of Variations constrained problems - p. 497 73. 9.14. Checking the Second-Order Conditions in Excel - p. 505 74. Exercises - p. 511 75. Chapter 10. Theory of optimal control - p. 521 76. 10.1. The optimal control problem and the Pontryagin's maximum principle - p. 522 77. 10.2. Nonlinear Hamiltonian and linear Hamiltonian (bang-bang control) - p. 523 78. 10.3. Setup of the Excel worksheet for optimal control problems - p. 525 79. 10.4. Bang-bang control problems - p. 542 80. 10.5. Consumption model - p. 547 81. 10.6. Investment model - p. 554 82. 10.7. Inventory optimization - p. 561 83. 10.8. Two state variables control problems - p. 563 84. 10.9. Current-value Hamiltonian - p. 571 85. 10.10. Constraints on the state variable: a linear case with an inventory application with VBA - p. 576 86. 10.11. Steepest descent numerical approach for optimal control problems using VBA - p. 587 87. 10.12. Checking the sufficient conditions in Excel - p. 593 88. Exercises - p. 600 89. Chapter 11. Discrete dynamic programming - p. 611 90. 11.1. Bellman's principle, discrete shortest path problems, and the Excel MINIFS function - p. 612 91. 11.2. Discrete dynamic systems: tabular method, Excel data table, and Solver - p. 619 92. 11.3. Cargo loading allocation problems: tabular method and the Excel Solver - p. 629 93. 11.4. Multistage allocation problems using the Excel Solver - p. 632 94. 11.5. Equality constrained optimization problems using the recursive Bellman's approach - p. 636 95. 11.6. Dynamic economic problems solved with Discrete Dynamic Programming - p. 639 96. 11.7. Discrete Dynamic Programming, Optimal Control theory, and Calculus of Variations: a synthesis - p. 649 97. Exercises - p. 652 98. Part IV. Special topics - p. 657 99. Part IV Special topics - p. 659 100. Chapter 12. Dynamic production planning and inventory modeling - p. 661 101. Chapter 13. Data analysis for business and economics - p. 695 102. Chapter 14. Essential Monte Carlo analysis - p. 763 103. Index - p. 797
Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization shows readers how to apply static and dynamic optimization theory in an easy and practical manner, without requiring the mastery of specific programming languages that are often difficult and expensive to learn. Featuring user-friendly numerical discrete calculations developed within the Excel worksheets, the book includes key examples and economic applications solved step-by-step and then replicated in Excel.
After introducing the fundamental tools of mathematical economics, the book explores the classical static optimization theory of linear and nonlinear programming, applying the core concepts of microeconomics and some portfolio theory. This provides a background for the more challenging worksheet applications of the dynamic optimization theory. The book also covers special complementary topics such as inventory modelling, data analysis for business and economics, and the essential elements of Monte Carlo analysis.
Practical and accessible, Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization increases the computing power of economists worldwide. This book is accompanied by a companion website that includes Excel examples presented in the book, exercises, and other supplementary materials that will further assist in understanding this useful framework.
1. Cover image - p. i 2. Title page - p. ii 3. Table of Contents - p. iii 4. Copyright - p. iv 5. About the author - p. ix 6. Preface - p. xi 7. Part I. Excel and fundamental mathematics for economics - p. xii 8. Part I Excel and fundamental mathematics for economics - p. 1 9. Chapter 1. Excel VBA, solver, and other advanced worksheet tools - p. 3 10. Chapter 2. Univariate and multivariate calculus - p. 45 11. Chapter 3. Elements of linear algebra - p. 87 12. 3.1. Built-in Excel matrix functions and basic operations - p. 88 13. 3.2. Linear systems and resolution methods in Excel: Cramer, Solver, Inverse - p. 95 14. 3.3. Eigenvalues and eigenvectors search: analytical and graphical approach - p. 107 15. 3.4. Quadratic forms and definiteness of a symmetric matrix - p. 115 16. 3.5. Leontief open model - p. 121 17. 3.6. Equilibrium in n markets - p. 124 18. 3.7. Economic policy modeling: objectives and instruments - p. 129 19. Exercises - p. 134 20. Chapter 4. Mathematics for dynamic economic models - p. 139 21. 4.1. Ordinary differential equations and numerical methods: Euler and Runge-Kutta - p. 140 22. 4.2. Force of interest, Walrasian stability, utility functions, and capital formation with ordinary differential equation - p. 147 23. 4.3. Difference equations and phase diagrams - p. 159 24. 4.4. Cobweb model of price adjustment and other economic models with difference equations - p. 170 25. 4.5. Systems of linear differential equations - p. 181 26. 4.6. Tourism fight between two competing regions - p. 202 27. 4.7. Walrasian adjustment with entry - p. 206 28. Exercises - p. 209 29. Part II. Static optimization - p. 215 30. Part II Static optimization - p. 217 31. Chapter 5. Classical static nonlinear optimization theory - p. 219 32. 5.1. Classical unconstrained optimization of a univariate function - p. 220 33. 5.2. Classical unconstrained optimization of a multivariate function - p. 232 34. 5.3. Some economic applications of the nonlinear unconstrained optimization - p. 247 35. 5.4. Numerical steepest descent method applied to the unconstrained optimization with VBA - p. 256 36. 5.5. Nonlinear problems in Rn with equality constraints: Lagrange multipliers and Solver - p. 264 37. 5.6. Nonlinear problems in R2 with equality constraints: contour lines - p. 272 38. 5.7. Nonlinear problems with inequality constraints - p. 285 39. Exercises - p. 288 40. Chapter 6. Microeconomic theory in a static environment - p. 295 41. 6.1. The consumer problem: cardinal versus ordinal utility approach - p. 296 42. 6.2. Consumer optimization and derivation of the demand curve in the cardinal approach - p. 297 43. 6.3. Consumer optimization and derivation of the demand curve in the ordinal approach - p. 307 44. 6.4. The firm problem - p. 319 45. 6.5. One-input classical production function - p. 320 46. 6.6. Two-inputs production functions - p. 322 47. 6.7. Isoquants and the constrained production optimization with two inputs - p. 331 48. 6.8. Production Edgeworth box, contract curve, and the possibility frontier construction - p. 335 49. 6.9. Short-run, long-run costs and the envelope average total costs derivation - p. 340 50. 6.10. Perfect competitive markets: short-run, long-run supply curves and market equilibrium - p. 350 51. 6.11. Monopolistic market equilibrium: the Chamberlin model - p. 356 52. 6.12. Markets with high-entry barriers: monopoly and the Cournot duopoly model - p. 360 53. 6.13. Game theory. Zero-sum games and minimax criterion: matrix and graphical resolutions - p. 370 54. Exercises - p. 376 55. Chapter 7. Linear programming - p. 383 56. Chapter 8. Nonlinear optimization applied to the portfolio theory - p. 417 57. Part III. Dynamic optimization - p. 434 58. Part III Dynamic optimization - p. 435 59. Chapter 9. Calculus of variations - p. 437 60. 9.1. The fundamental problem of the Calculus of Variations - p. 438 61. 9.2. Discrete approximate Calculus of Variations: Lagrange multipliers and contour lines solutions - p. 442 62. 9.3. Set up of the Excel worksheet for Calculus of Variations problems: the Solver solution - p. 451 63. 9.4. General cases developed in Excel with fixed and variable terminal points - p. 453 64. 9.5. Dynamic optimization for a monopolist - p. 469 65. 9.6. Unemployment and inflation - p. 471 66. 9.7. The Eisner–Strotz model - p. 475 67. 9.8. The optimal consumption Ramsey model - p. 479 68. 9.9. Inventory dynamic optimization - p. 481 69. 9.10. Optimal capital structure and the firm cost of capital - p. 482 70. 9.11. Contour lines solution for Calculus of Variations using the VBA code - p. 487 71. 9.12. Calculus of Variations with functionals involving two independent functions - p. 494 72. 9.13. Calculus of Variations constrained problems - p. 497 73. 9.14. Checking the Second-Order Conditions in Excel - p. 505 74. Exercises - p. 511 75. Chapter 10. Theory of optimal control - p. 521 76. 10.1. The optimal control problem and the Pontryagin's maximum principle - p. 522 77. 10.2. Nonlinear Hamiltonian and linear Hamiltonian (bang-bang control) - p. 523 78. 10.3. Setup of the Excel worksheet for optimal control problems - p. 525 79. 10.4. Bang-bang control problems - p. 542 80. 10.5. Consumption model - p. 547 81. 10.6. Investment model - p. 554 82. 10.7. Inventory optimization - p. 561 83. 10.8. Two state variables control problems - p. 563 84. 10.9. Current-value Hamiltonian - p. 571 85. 10.10. Constraints on the state variable: a linear case with an inventory application with VBA - p. 576 86. 10.11. Steepest descent numerical approach for optimal control problems using VBA - p. 587 87. 10.12. Checking the sufficient conditions in Excel - p. 593 88. Exercises - p. 600 89. Chapter 11. Discrete dynamic programming - p. 611 90. 11.1. Bellman's principle, discrete shortest path problems, and the Excel MINIFS function - p. 612 91. 11.2. Discrete dynamic systems: tabular method, Excel data table, and Solver - p. 619 92. 11.3. Cargo loading allocation problems: tabular method and the Excel Solver - p. 629 93. 11.4. Multistage allocation problems using the Excel Solver - p. 632 94. 11.5. Equality constrained optimization problems using the recursive Bellman's approach - p. 636 95. 11.6. Dynamic economic problems solved with Discrete Dynamic Programming - p. 639 96. 11.7. Discrete Dynamic Programming, Optimal Control theory, and Calculus of Variations: a synthesis - p. 649 97. Exercises - p. 652 98. Part IV. Special topics - p. 657 99. Part IV Special topics - p. 659 100. Chapter 12. Dynamic production planning and inventory modeling - p. 661 101. Chapter 13. Data analysis for business and economics - p. 695 102. Chapter 14. Essential Monte Carlo analysis - p. 763 103. Index - p. 797
