Editing Edgeworth box (section)

===The mathematical theory of economic equilibrium===
The conceptual framework of equilibrium in a market economy was developed by [[Léon Walras]]<ref>L. Walras, 'Éléments d'Économie Politique Pure, ou Théorie de la Richesse Sociale' (1874).</ref> and further extended by [[Vilfredo Pareto]].<ref>V. Pareto, ''Manuale''/''Manuel'' (1906/9).</ref> It was examined with close attention to generality and rigour by twentieth century mathematical economists including [[Abraham Wald]],<ref>A. Wald, 'Über einige Gleichungssysteme der mathematischen Ökonomie' (1936), tr. as "On some Systems of Equations of Mathematical Economics" (1951).</ref> [[Paul Samuelson]],<ref>P. Samuelson, "Foundations of Economic Analysis" (1947).</ref> [[Kenneth Arrow]] and [[Gérard Debreu]].<ref>K. Arrow and G. Debreu, "Existence of an Equilibrium for a Competitive Economy" (1954).</ref> This was part of a wider movement in which Wald also sought to bring greater rigour to [[decision theory]] and many mathematicians concentrated on minimising dependence on the [[axiom of choice]].

The theory of Walrasian markets has taken pains to find the most general premises from which a given conclusion can be obtained. Areas in which premises can be strengthened or weakened include:
* Whether functions are differentiable;
* Whether indifference curves are primitive or derivable from [[utility|utility functions]]; and
* Whether indifference curves are convex.
Assumptions are also made of a more technical nature, e.g. non-reversibility, [[Local nonsatiation|saturation]], etc. 
 
The pursuit of rigour is not always conducive to intelligibility. In this article indifference curves will be treated as primitive. At first we will view them as convex and differentiable and concentrate on interior equilibria, but we will subsequently relax these assumptions.