Pareto Optimality | 帕累托最优

📚 Pareto Optimality | 帕累托最优

Pareto optimality is a central idea in welfare economics. It describes an allocation of resources from which no one can be made better off without making someone else worse off.

帕累托最优是福利经济学中的一个核心概念。它描述了一种资源配置状态：在不使他人状况变坏的前提下，无法再使任何人的状况变得更好。

1. Defining Pareto Optimality | 帕累托最优的定义

Pareto optimality, also called Pareto efficiency, is named after the Italian economist Vilfredo Pareto. It is used as a benchmark for judging whether resources are allocated without waste.

帕累托最优，又称帕累托效率，以意大利经济学家维尔弗雷多·帕累托的名字命名。它被用作判断资源配置是否存在浪费的基准。

An allocation is Pareto optimal if there is no alternative allocation that can improve at least one person’s welfare without reducing another person’s welfare.

如果不存在另一种配置能在不降低他人福利的情况下提高至少一个人的福利，那么这种配置就是帕累托最优的。

This does not mean that everyone is equally well off. It only means that all possible mutually beneficial changes have already been exhausted.

这并不意味着每个人的状况都同样好。它只表示所有可能的互利变动都已经用尽。

2. Pareto Improvement | 帕累托改进

A Pareto improvement occurs when a change in resource allocation makes at least one individual better off while making no one worse off.

当资源配置的改变使至少一个人状况变好，同时没有任何人状况变坏时，就出现了帕累托改进。

For example, suppose Asha has an extra apple but would prefer a banana, while Ben has an extra banana but would prefer an apple. If they trade, both can become better off. This exchange is a Pareto improvement.

例如，假设阿莎多一个苹果但更想要香蕉，而本多一根香蕉但更想要苹果。如果他们进行交换，双方的状况都能变好。这种交换就是帕累托改进。

As long as Pareto improvements remain available, the economy is not yet Pareto optimal. Pareto optimality is reached only when no such improvement is possible.

只要仍然存在帕累托改进的机会，经济就尚未达到帕累托最优。只有当不再可能进行这种改进时，经济才达到帕累托最优。

3. Three Conditions for Pareto Optimality | 帕累托最优的三个条件

In a simple economy with two goods, two consumers and two factors of production, Pareto optimality requires three types of efficiency: efficiency in exchange, efficiency in production and efficiency in the product mix.

在一个只有两种商品、两个消费者和两种生产要素的简单经济中，帕累托最优要求三种效率：交换效率、生产效率和产品组合效率。

Exchange efficiency means that goods are distributed among consumers so that no further voluntary exchange can make someone better off without harming another.

交换效率意味着商品在消费者之间的分配已经达到这样的状态：任何进一步的自愿交换都无法在不损害他人的情况下使某人受益。

Production efficiency means that inputs are allocated among producers so that the output of one good cannot be increased without reducing the output of another good.

生产效率意味着投入品在各生产者之间的配置已经使得在不减少另一种商品产量的情况下，无法再增加一种商品的产量。

Product-mix efficiency means that the combination of goods produced matches the combination that consumers most prefer, given the available resources and technology.

产品组合效率意味着在既定资源和技术条件下，所生产的商品组合与消费者最偏好的商品组合相一致。

4. Efficiency in Exchange | 交换效率

Exchange efficiency requires that every consumer has the same marginal rate of substitution between any pair of goods, say X and Y.

交换效率要求每个消费者在任何一对商品（比如 X 和 Y）之间都具有相同的边际替代率。

The marginal rate of substitution, or MRS, measures how many units of good Y a consumer is willing to give up in order to obtain one extra unit of good X while remaining equally satisfied.

边际替代率（MRS）衡量消费者为了多获得一单位商品 X 而愿意放弃多少单位商品 Y，同时保持满足程度不变。

MRS_A = MRS_B = P(x) ÷ P(y)

If consumer A’s MRS is higher than consumer B’s, then A values X relatively more than B does. Both can gain by exchanging Y for X, so the original allocation was not Pareto optimal.

如果消费者 A 的边际替代率高于消费者 B，那么 A 相对于 B 更看重 X。

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