TY - JOUR
T1 - Limit representations of intergenerational equity
AU - Sakai, Toyotaka
N1 - Funding Information:
I am grateful to two anonymous referees, Marc Fleurbaey, Kohei Kamaga, Michihiro Kandori, Kaname Miyagishima, Akira Okada, Hiroo Sasaki, Koichi Tadenuma, and William Thomson for their insightful comments. Various earlier versions of this paper were presented at Keio University, Okayama University, Tokyo Institute of Technology, University of Tokyo, Waseda University, SWET 2010, the 16th Decentralization Conference at Kwansei Gakuin University, and the Hitotsubashi GCOE Lectures and Workshop on Choice, Games, and Welfare. I thank participants of these seminars for their helpful comments. This research is financially supported by KAKENHI (24220003). Parts of this paper were formerly circulated as “A welfare economics foundation for steady state analysis” and “An impartial representation in infinite time horizon”.
Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - Equal treatment of all generations is a fundamental ethical principle in intertemporal welfare economics. This principle is expressed in anonymity axioms of orderings on the set of infinite utility streams. We first show that an ordering satisfies finite anonymity, uniform Pareto, weak non-substitution, and sup continuity if and only if it is represented by an increasing, continuous function that is a natural extension of the limit function. We then show that whenever such an ordering is infinitely anonymous, it depends only on the liminf and limsup of any utility stream. Our results imply that in ethically ranking utility streams, reflecting only infinitely long-run movements is possible, with liminf and limsup particularly essential, but it is impossible to respect finite generations.
AB - Equal treatment of all generations is a fundamental ethical principle in intertemporal welfare economics. This principle is expressed in anonymity axioms of orderings on the set of infinite utility streams. We first show that an ordering satisfies finite anonymity, uniform Pareto, weak non-substitution, and sup continuity if and only if it is represented by an increasing, continuous function that is a natural extension of the limit function. We then show that whenever such an ordering is infinitely anonymous, it depends only on the liminf and limsup of any utility stream. Our results imply that in ethically ranking utility streams, reflecting only infinitely long-run movements is possible, with liminf and limsup particularly essential, but it is impossible to respect finite generations.
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U2 - 10.1007/s00355-016-0973-0
DO - 10.1007/s00355-016-0973-0
M3 - Article
AN - SCOPUS:84976871028
VL - 47
SP - 481
EP - 500
JO - Social Choice and Welfare
JF - Social Choice and Welfare
SN - 0176-1714
IS - 2
ER -