- 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

# Optimal Programming

# Optimal Programming

- Chapter:
- (p.377) V.1 Optimal Programming
- Source:
- Logic of Choice and Economic Theory
- Author(s):
### S. N. Afriat

- Publisher:
- Oxford University Press

This is the first of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It introduces the general ideas of optimal programming in economic terms, with reference to the programming problem of a firm. A theorem is proved that is basic to the entire subject, and requires no special assumptions about the programming functions. The ten sections of the chapter are: bounds, limits and maxima; programming problem of a firm; optimal programming theorem; input–output; output limit function; support gradients and marginal values; complementarity; shadow price decentralization; proof of the theorem; and Lagrange multipliers.

*Keywords:*
choice, complementarity, economic theory, input–output, Lagrange multipliers, mathematical economics, optimal programming, output limit function, shadow price

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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