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In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the Greenwald-Stiglitz theorem.

In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the Greenwald-Stiglitz theorem.

根据 Greenwald-Stiglitz 定理，在缺乏完全信息或完全市场的情况下，结果通常是帕累托低效的。

根据 Greenwald-Stiglitz 定理，在缺乏完全信息或完全市场的情况下，这个结果通常是帕累托低效的。

The second welfare theorem is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some competitive equilibrium, or free market system, although it may also require a lump-sum transfer of wealth.

The second welfare theorem is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some competitive equilibrium, or free market system, although it may also require a lump-sum transfer of wealth.

== Weak Pareto efficiency{{anchor|weak}} ==

== Weak Pareto efficiency{{anchor|weak}} ==d

'''Weak Pareto optimality''' is a situation that cannot be strictly improved for ''every'' individual.<ref>{{Cite book | doi=10.1007/978-1-4020-9160-5_341|chapter = Pareto Optimality|title = Encyclopedia of Global Justice| pages=808–809|year = 2011|last1 = Mock|first1 = William B T.| isbn=978-1-4020-9159-9}}</ref>  

'''Weak Pareto optimality''' is a situation that cannot be strictly improved for ''every'' individual.<ref>{{Cite book | doi=10.1007/978-1-4020-9160-5_341|chapter = Pareto Optimality|title = Encyclopedia of Global Justice| pages=808–809|year = 2011|last1 = Mock|first1 = William B T.| isbn=978-1-4020-9159-9}}</ref>  

Weak Pareto optimality is a situation that cannot be strictly improved for every individual.  

Weak Pareto optimality is a situation that cannot be strictly improved for every individual.  

Formally, we define a strong pareto improvement as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good).  A situation is weak Pareto-optimal if it has no strong Pareto-improvements.

Formally, we define a strong pareto improvement as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good).  A situation is weak Pareto-optimal if it has no strong Pareto-improvements.

在形式上，我们将强帕累托改善定义为所有代理人严格处于较好状态的情况(与之相对的只是“帕累托改善” ，它要求一个代理人严格处于较好状态，而其他代理人至少同样优秀)。没有强帕累托改进的情况是弱帕累托最优的。

在形式上，我们将强帕累托改善定义为所有主体严格处于较好状态的情况(与之相对的只是“帕累托改进” ，它要求一个主体严格处于较好状态，而其他主体至少同样良好)。没有强帕累托改进的情况是弱帕累托最优的。

Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0).

Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0).

任何强的帕累托改进也是弱的帕累托改进。反之则不然; 例如，考虑一个有两个资源的资源分配问题，Alice 将其值设置为10,0，George 将其值设置为5,5。考虑将所有资源分配给 Alice 的分配，其中实用程序配置文件为(10,0)。

任何强帕累托改进也是弱帕累托改进。反之则不然; 例如，考虑一个包含两个资源的资源分配问题，Alice 的分配值为10,0，George 的分配值为5,5。考虑将所有资源分配给 Alice 的分配，它的配置方案为(10,0)。

* It is a weak-PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements).  

* It is a weak-PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements).  

* But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5).

* But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5)

A market doesn't require local nonsatiation to get to a weak Pareto-optimum.

A market doesn't require local nonsatiation to get to a weak Pareto-optimum.

Constrained Pareto optimality is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.

Constrained Pareto optimality is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.

受约束的帕累托最优是帕累托最优性的弱化，因为一个潜在的规划者(比如政府)可能无法改善分散的市场结果，即使这个结果是低效的。如果它受到与个体代理人相同的信息或机构约束的限制，就会发生这种情况。

受约束的帕累托最优是帕累托最优的弱化，因为一个潜在的规划者(比如政府)可能无法改善分散市场的结果，即使这个结果是低效的。如果它受到与独立主体相同的信息或机构约束的限制，就会发生这种情况。

An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in [[moral hazard]] or an [[adverse selection]] and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see [[Lindahl prices]]). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".

An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in [[moral hazard]] or an [[adverse selection]] and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see [[Lindahl prices]]). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".

An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in moral hazard or an adverse selection and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see Lindahl prices). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".

An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in moral hazard or an adverse selection and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see Lindahl prices). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".

例如，个人拥有私人信息的情况(例如，劳动力市场中工人自己的生产率为工人所知，而潜在雇主却不知道，或者二手车市场中汽车的质量为卖方所知，而非买方所知)导致道德风险或逆向选择和次优结果。在这种情况下，希望改善局面的规划者不太可能获得市场参与者没有的任何信息。因此，计划者不能执行基于个人特质的分配规则; 例如，”如果一个人属于 a 型，他们支付 p1的价格，但如果属于 b 型，他们支付 p2的价格”(见林达尔价格)。基本上，只有匿名规则(类似于“每个人都支付价格 p”)或基于可观察行为的规则被允许; “如果任何人以价格 px 选择 x，那么他们将得到10美元的补贴，除此之外什么也得不到”。如果不存在能够成功改善市场结果的允许规则，那么该结果被称为“有约束的帕累托最优”。

例如，个人拥有私人信息的情况(例如，劳动力市场中工人自己的生产率为工人所知，而潜在雇主却不知道，或者二手车市场中汽车的质量为卖方所知，而非买方所知)导致道德风险或逆向选择和次优结果。在这种情况下，希望改善局面的规划者不太可能获得市场参与者没有的任何信息。因此，计划者不能执行基于个人特质的分配规则; 例如，”如果一个人属于 a 型，他们支付 p1的价格，但如果属于 b 型，他们支付 p2的价格”(见林达尔价格)。基本上，只有隐性规则(类似于“每个人都支付价格 p”)或基于可观察行为的规则被允许; “如果任何人以价格 px 选择 x，那么他们将得到10美元的补贴，除此之外什么也得不到”。如果不存在能够成功改善市场结果的允许规则，那么该结果被称为是“受约束的帕累托最优的”。

The concept of constrained Pareto optimality assumes benevolence on the part of the planner and hence is distinct from the concept of government failure, which occurs when the policy making politicians fail to achieve an optimal outcome simply because they are not necessarily acting in the public's best interest.

The concept of constrained Pareto optimality assumes benevolence on the part of the planner and hence is distinct from the concept of government failure, which occurs when the policy making politicians fail to achieve an optimal outcome simply because they are not necessarily acting in the public's best interest.