Theorem of the wellbeing

Both theorems of the economics of welfare are the fundamental results of the theory of the general stability as formulated by Kenneth Arrow and Gerard Debreu.

Under a certain number of constraining assumptions (Pure competition and perfect, homogeneity and continuity of the functions of production and functions of request,…), these authors show by a mathematical demonstration the two following results:

First theorem: For all initial Equipment, there exists a balance of market in pure competition and perfect, and this balance is a Pareto's optimum in the space of the distributions of the goods.

Second theorem: All Pareto's optimum in the space of the distributions of the goods is atteignable in pure and perfect competition with the help of a contractual redistribution of the initial equipments.

The first theorem is often associated with an idea of decentralization. He indeed says that left to themselves, of the markets in pure competition and perfect lead to an optimal allowance, within the meaning of Pareto, of the richnesses. Second on the contrary is rather associated with an idea of intervention, because it stipulates that if the social Planificateur gives itself an effective objective within the meaning of Pareto (what is logically the case), then it can reach it by modifying only the initial equipments of the agents, then by letting them make their own decisions.

Historically, these two theorems were initially proven in the case of a saving in exchanges, then in the case of a saving in production by Maurice Allais.

These two theorems represent a crowning of the neo-classic theory of the general stability. According to some, they are also the judgment. On the one hand, it is difficult to obtain other results of the model, and on the other hand it is practically impossible to preserve these results while slackening the most constraining assumptions.

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