- Title Pages
- Preface
- Introduction
- I.1 About Choice
- I.2 Processes of Choice
- I.3 Democratic Choice
- I.4 Budget Allocation and Priority
- I.5 Ramsey's Savings Rule
- II.1 Utility Hypothesis
- II.2 Algebra of Revealed Preference
- II.3 Combinatorics of Demand
- II.4 Separable Utility
- II.5 Direct and Indirect Utility
- II.6 Efficiency and Inefficiency
- III.1 Price and Quantity Levels
- III.2 The True Index
- III.3 Fisher and Byushgens
- III.4 The Four‐Point Formula
- III.5 Wald's ‘New Formula’
- IV.1 Opportunity Models
- IV.2 Leontief's Input‐Output
- IV.3 The Market
- IV.4 Sraffa's Prices
- IV.5 General Economic Equilibrium
- IV.6 Von Neumann's Economic Model
- V.1 Optimal Programming
- V.2 Convex Programming
- V.3 Linear Programming
- V.4 Minimum Paths
- V.5 Distribution Matrices
- VI.1 Calculus of Propositions
- VI.2 Algebra of Relations
- VI.3 Intersections and Fixed Points
- Bibliography
- Index

# Linear Programming

# Linear Programming

- Chapter:
- (p.413) V.3 Linear Programming
- Source:
- Logic of Choice and Economic Theory
- Author(s):
### S. N. Afriat

- Publisher:
- Oxford University Press

This is the third of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It discusses linear programming, which might appear to be a special case of convex programming, but is more substantial, and is really an embodiment of the theory of systems of linear inequalities (as reflected here). This chapter initiates the subject with reference to systems of linear inequalities and natural questions about them, and all LP (linear programming) theorems are encountered simply in pursuing those. Theorems about linear inequalities that have uses directly on their own are also derived (and are illustrated in many places in this book). The eight sections of the chapter are: linear inequalities; separation theorems; theorems of alternatives; polyhedra and polytopes; LP Duality Theorem; the pivot operation; the Simplex Algorithm; and BASIC program.

*Keywords:*
choice, duality, economic theory, linear inequalities, linear programming, LP Duality Theorem, mathematical economics, optimal programming, pivot operation, polyhedra, polytopes, separation theorems, Simplex Algorithm, theorems of alternatives

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- Title Pages
- Preface
- Introduction
- I.1 About Choice
- I.2 Processes of Choice
- I.3 Democratic Choice
- I.4 Budget Allocation and Priority
- I.5 Ramsey's Savings Rule
- II.1 Utility Hypothesis
- II.2 Algebra of Revealed Preference
- II.3 Combinatorics of Demand
- II.4 Separable Utility
- II.5 Direct and Indirect Utility
- II.6 Efficiency and Inefficiency
- III.1 Price and Quantity Levels
- III.2 The True Index
- III.3 Fisher and Byushgens
- III.4 The Four‐Point Formula
- III.5 Wald's ‘New Formula’
- IV.1 Opportunity Models
- IV.2 Leontief's Input‐Output
- IV.3 The Market
- IV.4 Sraffa's Prices
- IV.5 General Economic Equilibrium
- IV.6 Von Neumann's Economic Model
- V.1 Optimal Programming
- V.2 Convex Programming
- V.3 Linear Programming
- V.4 Minimum Paths
- V.5 Distribution Matrices
- VI.1 Calculus of Propositions
- VI.2 Algebra of Relations
- VI.3 Intersections and Fixed Points
- Bibliography
- Index