Elements of Numerical Mathematical Economics with Excel

Part I Excel and Fundamental Mathematics for EconomicsChapter 1 Excel VBA, Solver and Other Advanced Worksheet Tools 1.1. VBA Introduction and Main Statements 1.2. The Excel Solver: Simplex LP, Generalized Reduced Gradient and Evolutionary 1.3. What-If Analysis: Scenario Manager, Goal Seek, Data Table and Contour Lines 1.4. Scatter Charts and Trendlines Chapter 2 Univariate and Multivariate Calculus 2.1. Numerical Methods for Univariate Differentiation 2.2. Numerical Methods for Univariate Integration 2.3. Numerical Partial Differentiation 2.4. Applications in Economics Chapter 3 Elements of Linear Algebra3.1. Built-in Excel Matrix Functions and Basic Operations3.2. Linear Systems and Resolution Methods in Excel: Cramer, Solver, Inverse 3.3. Eigenvalues and Eigenvectors Search: Analytical and Graphical Approach 3.4. Quadratic Forms and Definiteness of a Symmetric Matrix 3.5. Leontief Open Model 3.6. Equilibrium In N-Markets 3.7. Economic Policy Modelling: Objectives and Instruments Chapter 4 Mathematics for Dynamic Economic Models 4.1. Ordinary Differential Equations and Numerical Methods: Euler and Runge-kutta 4.2. Force of Interest, Walrasian Stability, Utility Functions and Capital Formation with Ode 4.3. Difference Equations and Phase Diagrams 4.4. Cobweb Model of Price Adjustment and Other Economic Models with Difference Equations 4.5. Systems of Linear Differential Equations 4.6. Tourism Fight Between Two Competing Regions 4.7. Walrasian Adjustment with Entry Part II Static Optimization Chapter 5 Classical Static Nonlinear Optimization Theory 5.1. Classical Unconstrained Optimization of a Univariate Function 5.2. Classical Unconstrained Optimization of a Multivariate Function 5.3. Some Economic Applications of the Nonlinear Unconstrained Optimization 5.4. Numerical Steepest Descent Method Applied to the Unconstrained Optimization with Vba 5.5. Nonlinear Problems in R^N with Equality Constraints: Lagrange Multipliers and Solver 5.6. Nonlinear Problems in R² with Equality Constraints: Contour Lines 5.7. Nonlinear Problems with Inequality Constraints Chapter 6 Microeconomic Theory in a Static Environment 6.1. The Consumer Problem: Cardinal vs. Ordinal Utility Approach 6.2. Consumer Optimization and Derivation opf the Demand Curve in the Cardinal Approach 6.3. Consumer Optimization And Derivation Of The Demand Curve in the Ordinal Approach 6.4. The Firm Problem 6.5. One-Input Classical Production Function 6.6. Two-Inputs Production Functions 6.7. Isoquants and the Constrained Production Optimization with Two Inputs 6.8. Production Edgeworth Box, Contract Curve and the Possibility Frontier Construction 6.9. Short-Run, Long-Run Costs and the Envelope Average Total Costs Derivation 6.10. Perfect Competitive Markets: Short-Run, Long-Run Supply Curve and Market Equilibrium 6.11. Monopolistic Market Equilibrium: The Chamberlin Model 6.12. Markets with High Entry Barriers: Monopoly and the Cournot Duopoly Model 6.13. Game Theory. Zero-Sum Games and Minimax Criterion: Matrix and Graphical Resolutions Chapter 7 Linear Programming 7.1. Standard Formulation of a Linear Program and Resolution Methods 7.2. Applications to the Static Production Planning and Capital Budgeting Chapter 8 Nonlinear Optimization Applied to the Portfolio Theory 8.1. Portfolio Modelling and the Efficient Frontier Construction 8.2. Investor’s Utility and the Optimal Portfolio Choice Part III Dynamic Optimization Chapter 9 Calculus of Variations (COV) 9.1. The Fundamental Problem of the COV 9.2. Discrete Approximate COV: Lagrange Multipliers and Contour Lines Solutions 9.3. Set Up of the Excel Worksheet for COV Problems: The Solver Solution 9.4. General Cases Developed in Excel with Fixed and Variable Terminal Points 9.5. Dynamic Optimization for a Monopolist 9.6. Unemployment and Inflation 9.7. The Eisner-Strotz Model 9.8. The Optimal Consumption Ramsey Model 9.9. Inventory Dynamic Optimization 9.10. Optimal Capital Structure and the Firm Cost Of Capital 9.11. Contour Lines Solution for COV Using the VBA Code 9.12. COV with Functionals Involving Two Independent Functions 9.13. COV Constrained Problems 9.14. Checking the Second Order Conditions in Excel Chapter 10 Theory of Optimal Control (OC) 10.1. The OC Problem and the Pontryagin’s Maximum Principle 10.2. Nonlinear Hamiltonian and Linear Hamiltonian (Bang-Bang Control) 10.3. Set Up of the Excel Worksheet for OC Problems 10.4. Bang-Bang Control Problems 10.5. Consumption Model 10.6. Investment Model 10.7. Inventory Optimization 10.8. Two State Variables Control Problems 10.9. Current-Value Hamiltonian 10.10. Constraints on the State Variable: A Linear Case with an Inventory Application with VBA 10.11. Steepest Descent Numerical Approach for Optimal Control Problems Using VBA 10.12. Checking the Sufficient Conditions in Excel Chapter 11 Discrete Dynamic Programming (DDP) 11.1. Bellman’s Principle, Discrete Shortest Path Problems and the Excel Minifs Function 11.2. Discrete Dynamic Systems: Tabular Method, Excel Data Table and Solver 11.3. Cargo-loading Allocation Problems: Tabular Method and the Excel Solver 11.4. Multistage Allocation Problems Using the Excel Solver 11.5. Equality Constrained Optimization Problems Using the Recursive Bellman’s Approach 11.6. Dynamic Economic Problems Solved with DDP 11.7. DDP, OC Theory and COV: A Synthesis Part IV Special Topics Chapter 12 Dynamic Production Planning and Inventory Modelling 12.1. Multiperiod Production Models with Linear Programming 12.2. Wagner-whitin Algorithm for Inventory Dynamic Modelling 12.3. Eliezer Naddor Stochastic Single-Period Inventory Models Chapter 13 Data Analysis for Business and Economics 13.1. A Simple Way to Organize a Spreadsheet Using the VBA Code and Bookmarks 13.2. Pivot Tables, Pivot Charts and Dynamic Dashboards for Managerial Data Analysis 13.3. Basic Descriptive Statistics 13.4. Some Numerical Calculus Applied to Continuous Densities 13.5. Univariate, Multivariate Regression Analysis and the Anova Tables Chapter 14 Essential Monte Carlo Analysis 14.1. The Monte Carlo Method and the Generation of Random Numbers 14.2. The Monte Carlo Method for Business Decisions 14.3. Numerical Integration