Distribution of Resources (UMAP)

The people and the nations of the world own many resources: money, land, energy, food, oil, etc. One of the most important questions about these resources has to do with how they are distributed among people or among groups of people. In this module, several ways are investigated in which mathematics can be used to measure the distribution of resources.

Table of Contents:

INTRODUCTION
1. THE LORENZ CURVE
1.1 Distribution Tables and Their Associated Graphs
1.2 Complete Equality
1.3 Complete Inequality
1.4 Exercises
1.5 Model Exam
1.6 Answers to Exercises
1.7 Answers to Model Exam

2. THE EQUAL SHARE COEFFICIENT
2.1 Introduction
2.2 The Slope of a Lorenz Curve
2.3 The Definition
2.4 A Geometric Approach
2.5 A Numerical Approach
2.6 Linear Interpolation
2.7 Exercises
2.8 Model Exam
2.9 Answers to Exercises
2.10 Answers to Model Exam

3. THE GINI INDEX
3.1 Introduction
3.2 Area Under the Lorenz Curve
3.3 The Definition
3.4 Using the Definite Integral
3.5 The Rectangle Method
3.6 A Numerical Method
3.7 Exercises
3.8 Model Exam
3.9 Answers to Exercises
3.10 Answers to Model Exam