更改

The formal presentation of the concept in an economy is as follows: Consider an economy with <math> n</math> agents and <math> k </math> goods. Then an allocation <math> \{x_1, ..., x_n\} </math>, where <math> x_i \in \mathbb{R}^k </math> for all i, is Pareto optimal if there is no other feasible allocation <math> \{x_1', ..., x_n'\} </math> such that, for utility function <math> u_i </math> for each agent <math> i </math>, <math> u_i(x_i') \geq u_i(x_i) </math> for all <math> i \in \{1, ..., n\} </math> with <math> u_i(x_i') > u_i(x_i) </math> for some <math> i</math>. Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.

The formal presentation of the concept in an economy is as follows: Consider an economy with <math> n</math> agents and <math> k </math> goods. Then an allocation <math> \{x_1, ..., x_n\} </math>, where <math> x_i \in \mathbb{R}^k </math> for all i, is Pareto optimal if there is no other feasible allocation <math> \{x_1', ..., x_n'\} </math> such that, for utility function <math> u_i </math> for each agent <math> i </math>, <math> u_i(x_i') \geq u_i(x_i) </math> for all <math> i \in \{1, ..., n\} </math> with <math> u_i(x_i') > u_i(x_i) </math> for some <math> i</math>. Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.

这个概念在经济体系中的正式表述如下: 考虑一个经济体系有''n''个主体和''k''个商品，如果没有其他可行的分配'''<font color="#32CD32">此处需插入公式</font>'''使得效用函数“ui”对任意主体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，对某些主体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，那么这个分配'''<font color="#32CD32">此处需插入公式</font>'''，是 帕累托最优的，其中对任意''i''，'''<font color="#32CD32">此处需插入公式</font>'''。<ref name="AndreuMas95">{{citation|author-link=Andreu Mas-Colell|last1=Mas-Colell|first1=A.|first2=Michael D.|last2=Whinston|first3=Jerry R.|last3=Green|year=1995|title=Microeconomic Theory|chapter=Chapter 16: Equilibrium and its Basic Welfare Properties|publisher=Oxford University Press|isbn=978-0-19-510268-0|url-access=registration|url=https://archive.org/details/isbn_9780198089537}}</ref>在这个简单的经济体系中，“可行性”是指一种分配，其中每种商品的分配总额不超过该经济体系中所有商品的总额。在一个生产能力更为复杂的经济体中，一种分配将包括消费载体和生产载体，且可行性要求每种消费品的总量不大于初始禀赋加上生产总量。

这个概念在经济体系中的正式表述如下: 考虑一个经济体系有''n''个主体和''k''个商品，如果没有其他可行的分配'''<font color="#32CD32">此处需插入公式</font>'''使得效用函数“ui”对任意主体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，对某些主体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，那么这个分配'''<font color="#32CD32">此处需插入公式</font>'''，是 帕累托最优的，其中对任意''i''，'''<font color="#32CD32">此处需插入公式</font>'''。{{citation|author-link=Andreu Mas-Colell|last1=Mas-Colell|first1=A.|first2=Michael D.|last2=Whinston|first3=Jerry R.|last3=Green|year=1995|title=Microeconomic Theory|chapter=Chapter 16: Equilibrium and its Basic Welfare Properties|publisher=Oxford University Press|isbn=978-0-19-510268-0|url-access=registration|url=https://archive.org/details/isbn_9780198089537}}</ref>在这个简单的经济体系中，“可行性”是指一种分配，其中每种商品的分配总额不超过该经济体系中所有商品的总额。在一个生产能力更为复杂的经济体中，一种分配将包括消费载体和生产载体，且可行性要求每种消费品的总量不大于初始禀赋加上生产总量。