# Elements of Numerical Mathematical Economics with Excel

## 1st Edition

### Static and Dynamic Optimization

Authors:
Paperback ISBN: 9780128176481
Published Date: 6th December 2019
Page Count: 730
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## Description

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.

## Key Features

• Explains how Excel provides a practical numerical approach to optimization theory and analytics
• Increases access to the economic applications of this universally-available, relatively simple software program

Data analysts and research scientists worldwide working in data analytics companies, financial institutions, and other groups that handle economic data

Part I Excel and Fundamental Mathematics for Economics
Chapter 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 Algebra
3.1. Built-in Excel Matrix Functions and Basic Operations
3.2. 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

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 RN 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
11.4. 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

## Details

No. of pages:
730
Language:
English
Published:
6th December 2019
Imprint:
Paperback ISBN:
9780128176481