On the volume-ranking of opportunity sets in economic environments
On the volume-ranking of opportunity sets in economic environments
复制标题
关于经济环境中机会集的数量排名
DOI：
10.1007/s00355-008-0343-7
复制
发表时间：
2009
影响因子：
0.9
通讯作者：
S. Vannucci
中科院分区：
文献类型：
--
作者：
E. Savaglio;S. Vannucci
我们提供了在所有多凸集（即凸集、紧集、欧几里德集的有限并集）上定义的机会集的数量排序的表征。事实上，这样的域足够大，可以涵盖经济环境中通常遇到的大多数机会集，包括非线性甚至非凸预算集，以及由生产集产生的机会集。我们的结果依赖于 Klain 和 Rota 提出的基于估值的数量表征定理（《几何概率导论》，剑桥大学出版社，剑桥，1997 年），并有助于强调一些非常不寻常的条件，在这些条件下，数量排名可以被证明是机会集的自由排名。因此，这也可能有助于理解为什么后者在福利分析中被如此明显地忽视。
We provide a characterization of the volume-ranking of opportunity sets as defined on the set of all polyconvex sets, i.e. finite unions of convex, compact, Euclidean sets. In fact, such a domain is large enough to encompass most of the opportunity sets typically encountered in economic environments, including non-linear or even non-convex budget sets, and opportunity sets arising from production sets. Our result relies on a valuation-based volume-characterization theorem due to Klain and Rota (Introduction to Geometric Probability, Cambridge University Press, Cambridge, 1997) and helps to highlight some quite unusual conditions under which the volume-ranking can be justified as a freedom-ranking of opportunity sets. Therefore, it may also help to understand why the latter has been so conspicuously ignored in welfare analysis.