If, for all prices, income distribution is optimal for a planner with a social welfare function, then aggregate demand is the same as that of a single “representative consumer” whose preferences over aggregate consumption are the same as the planner's. This paper shows that the converse is false. Aggregate demand may be the demand function of a representative consumer although the income distribution is not optimal for any social welfare function. The representative consumer may be Pareto inconsistent, preferring situation A to B when all the actual consumers prefer B to A. We give conditions under which existence of a representative consumer implies that the income distribution satisfies first order conditions for optimality. Satisfying the first order optimality conditions for an additively separable social welfare function is essentially equivalent to aggregate demand for every pair of consumers having a symmetric Slutsky matrix.

中文翻译：

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社会福利与非代表性代表性消费者

如果对于所有价格，收入分配对于具有社会福利函数的计划者来说是最优的，那么总需求与单个“代表性消费者”的需求相同，其对总消费的偏好与计划者相同。这篇论文表明反过来是错误的。总需求可能是代表性消费者的需求函数，尽管收入分配对于任何社会福利函数都不是最优的。代表性消费者可能是帕累托不一致的，当所有实际消费者更喜欢 B 而不是 A 时，他们更喜欢情况 A 而不是 B。我们给出了代表性消费者的存在意味着收入分配满足最优性的一阶条件的条件。