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摘要翻译：
在过去五十年中，为进行空间和跨国价格比较，提出了若干多边指数系统。这些多边指数通常表示为线性方程组或非线性方程组的解。本文给出了Geary-Khamis、IDB、Neary和Rao指数存在唯一性的一般定理，以及包括两个广义指数系统的潜在新系统存在唯一性的充要条件。我们的一个主要结果是解存在唯一性的充要条件通常可以用图论概念和基于观察到的商品数量的可验证条件来说明。
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英文标题：
《Multilateral Index Number Systems for International Price Comparisons:
Properties, Existence and Uniqueness》
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作者：
Gholamreza Hajargasht and Prasada Rao
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最新提交年份：
2018
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分类信息：
一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Economics 经济学
二级分类：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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英文摘要：
Over the past five decades a number of multilateral index number systems have been proposed for spatial and cross-country price comparisons. These multilateral indexes are usually expressed as solutions to systems of linear or nonlinear equations. In this paper, we provide general theorems that can be used to establish necessary and sufficient conditions for the existence and uniqueness of the Geary-Khamis, IDB, Neary and Rao indexes as well as potential new systems including two generalized systems of index numbers. One of our main results is that the necessary and sufficient conditions for existence and uniqueness of solutions can often be stated in terms of graph-theoretic concepts and a verifiable condition based on observed quantities of commodities.
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PDF链接：
https://arxiv.org/pdf/1811.04197
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