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In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.

In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.

除了分配效率的背景之外，帕累托最优的概念也出现在生产效率对比于x-低效率的背景之下: 如果生产投入没有可行的再分配，即一种产品的产出增加，而所有其他产品的产出增加或保持不变，那么一组产品的产出就是帕累托有效的。

除了分配效率的背景之外，帕累托最优的概念也出现在生产效率对比于x-低效率的背景之下，即如果生产投入没有可行的再分配，或者说一种产品的产出增加，而所有其他产品的产出增加或保持不变，那么一组产品的产出就是帕累托有效的。

Under the idealized conditions of the first welfare theorem, a system of free markets, also called a "competitive equilibrium", leads to a Pareto-efficient outcome. It was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu.

Under the idealized conditions of the first welfare theorem, a system of free markets, also called a "competitive equilibrium", leads to a Pareto-efficient outcome. It was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu.

在第一福利定理的理想条件下，自由市场系统，也称为“竞争均衡” ，导致帕累托有效结果。经济学家肯尼斯•阿罗(Kenneth Arrow)和 g rard Debreu 首先用数学方法证明了这一点。

在福利经济学第一定理的理想条件下，一个自由市场系统，也称为“竞争均衡” ，对应一个帕累托有效的结果。经济学家肯尼斯·阿罗(Kenneth Arrow)和杰拉德·迪布鲁(Gérard Debreu)首先用数学方法证明了这一点。

However, the result only holds under the restrictive assumptions necessary for the proof: markets exist for all possible goods, so there are no externalities; all markets are in full equilibrium; markets are perfectly competitive; transaction costs are negligible; and market participants have perfect information.

However, the result only holds under the restrictive assumptions necessary for the proof: markets exist for all possible goods, so there are no externalities; all markets are in full equilibrium; markets are perfectly competitive; transaction costs are negligible; and market participants have perfect information.

然而，结果只有在证明所需的限制性假设下才成立: 所有可能的商品都存在市场，因此不存在外部性; 所有市场都处于完全均衡状态; 市场是完全竞争的; 交易成本是微不足道的; 市场参与者拥有完全信息。

然而，这个结果只有在证明所需的限制性假设下才成立，即所有可能的商品都存在市场，因此不存在外部效应; 所有市场都处于完全均衡状态; 市场是完全竞争的; 交易成本是可忽略的; 市场参与者拥有完全的信息。