n-1 simultaneous equations, he thus concluded that the general equilibrium exists. Though this argument works when all equations are linear, it does not hold when the equations are nonlinear. It is easy to construct a pairs of equations in two variables with no solutions. A more rigorous version of the argument was developed independently by Lionel McKenzie and the pair Kenneth Arrow and Gérard Debreu in the 1950s. Walrasian auction The Walrasian auction is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. Thus, a Walrasian auction perfectly matches the supply and the demand. Walras suggests that equilibrium will be achieved through a process of tâtonnement (French for "trial and error"), a form of incremental hill climbing. Economic value definition of utility Léon Walras provides a definition of economic utility based on economic value as opposed to an ethical theory of value: I state that things are useful as soon as they may serve whatever usage, as soon as they match whatever need and allow its fulfillment. Thus, there is here no point to deal with 'nuances' by way of which one classes, in the language of everyday conversation, utility beside what is pleasant and between the necessary and the superfluous. Necessary, useful, pleasant and superfluous, all of this is, for us, more or less useful. There is here as well no need to take into account the morality or immorality of the need that the useful things matches and permits to fulfill. Whether a substance is searched for by a doctor to heal an ill person, or by an assassin to poison his family, this is an important question from other points of view, albeit totally indifferent from ours. The substance is useful, for us, in both cases, and may well be more useful in the second case than in the first one. In economic theories of value, the term "value" is unrelated to any notions of value used in ethics, they are homonyms. Legacy In 1941 George Stigler wrote about Walras: What caused the re-appraisal of Walras's consideration in the US, was the influx of German-speaking scientists – the German version of the Éléments was published in 1881. According to Schumpeter: Major works