- 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 R amsey'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 F isher andB yushgens -
III.4 The Four‐Point Formula -
III.5 W ald's ‘New Formula’ -
IV.1 Opportunity Models -
IV.2 L eontief's Input‐Output -
IV.3 The Market -
IV.4 S raffa's Prices -
IV.5 General Economic Equilibrium -
IV.6 V onN eumann'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
Convex Programming
Convex Programming
- Chapter:
- (p.401) V.2 Convex Programming
- Source:
- Logic of Choice and Economic Theory
- Author(s):
S. N. Afriat
- Publisher:
- Oxford University Press
This is the second of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It introduces convexity conditions, and shows where they have effect, together with Slater's condition, in assuring the existence of a support to the limit function, so providing Lagrange multipliers, or shadow prices, of resources that have part in the optimality conditions. Then for the case of differentiable functions the Kuhn–Tucker conditions are obtained. The six sections of the chapter are: convexity; programming convexity theorem; Slater's condition; optimality theorem; non‐negative maxima; the Kuhn–Tucker conditions.
Keywords: choice, convex programming, convexity theorem, economic theory, Kuhn–Tucker conditions, Lagrange multipliers, limit function, mathematical economics, optimal programming, optimality theorem, shadow price, Slater's condition
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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 R amsey'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 F isher andB yushgens -
III.4 The Four‐Point Formula -
III.5 W ald's ‘New Formula’ -
IV.1 Opportunity Models -
IV.2 L eontief's Input‐Output -
IV.3 The Market -
IV.4 S raffa's Prices -
IV.5 General Economic Equilibrium -
IV.6 V onN eumann'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
