An Economic Interpretation of Linear Programming

About the Book

This text covers the basic theory and computation for mathematical modeling in linear programming. It provides a strong background on how to set up mathematical proofs and high-level computation methods, and includes substantial background material and direction. Paris presents an intuitive and novel discussion of what it means to solve a system of equations that is a crucial stepping stone for solving any linear program. The discussion of the simplex method for solving linear programs gives an economic interpretation to every step of the simplex algorithm. The text combines in a unique and novel way the microeconomics of production with the structure of linear programming to give students and scholars of economics a clear notion of what it means, formulating a model of economic equilibrium and the computation of opportunity cost in the presence of many outputs and inputs.

Table of Contents:

1. Introduction to Linear Programming
2. Primal and Dual LP Problems
3. Setting Up LP Problems
4. The Transportation and Transshipment Problems
5. Spaces, Cones, Bases and Extreme Points
6. Solving Systems of Equations
7. Primal Simplex Algorithm: The Price-Taking Firm
8. The Dual Simplex Algorithm
9. Linear Programming and the Lagrangean Function
10. The Artificial Variable Algorithm
11. The Artificial Constraint Algorithm
12. The Diet Problem Revisited
13. Parametric Programming: Input Demand Functions
14. Parametric Programming: Output Supply Functions
15. Dealing with Multiple Optimal Solutions
16. Solid Waste Management
17. The Choice of Techniques in a Farm Production Model
18. Cattle Ranch Management
19. The Measurement of Technical and Economic Efficiency
20. Decentralized Economic Planning
21. Theorems of Linear Programming

About the Author :

Quirino Paris spent his entire academic career at the University of California, USA, earning a PhD from Berkeley in 1966 and serving as Professor of Agricultural Economics at UC Davis from 1969. In 2011 he published a companion book titled Economic Foundations of Symmetric Programming. He is a Fellow of the American Applied Economic Association and of the European Association of Agricultural Economists.

Review :
"An Economic Interpretation of Linear Programming is a serious and meaningful revision of an already excellent book. It provides a refreshing and thoroughly unique perspective on linear programming that is imbued with Paris's characteristic passion for economics in general, and duality and symmetry in particular - beautiful is the word that comes to mind!" - Michael R. Caputo, Professor of Economics, University of Central Florida, USA "Paris's articulation of economic interpretations for mathematical structures is his forte and this book exceeded my expectations. The primary struggle for my students is not mastery of technical aspects but rather the application of those concepts to economic problems. This book's presentation of opportunity cost, relevant examples, and practice exercises will greatly assist students in making these connections. Furthermore, it is accomplished without sacrificing rigor." - Ken Foster, Professor and Head of the Department of Agricultural Economics, Purdue University, USA "This book contains most of what there is to know about linear programming - and, for most readers, about the main lines of economic thought. It is intuitive, clear, and orderly. Paris takes the reader on a walk through the world of linear models: their construction, trouble-shooting, and interpretation. Examples are intuitive and plentiful. The duality theme simplifies everything." - Steven Buccola, Emeritus Professor of Applied Economics, Oregon State University, USA "Paris provides us with a revised edition of his classic linear programming text that demonstrates the value, relevance, and power of this optimization problem to sophisticated applications of economic theory. The defining contribution is Paris's keying in on the two faces of the optimization problem: primal and dual. By orienting the presentation on the dual perspective of this class of optimization problems and the symmetry between the two faces, this book demonstrates that optimization and duality have a natural affinity for microeconomic analysis. The economic interpretation of the dual perspectives is often central to illuminating economic relationships. While there are arguably no new ideas under the sun, this book is in the class of contributions showing that beauty emerges in how you put these ideas together to teach us something new, exciting, and useful." - Spiro E. Stefanou, Professor and Chair of the Food and Resource Economics Department, University of Florida, USA