Equity and Efficiency in Overlapping Generations Economies

Abstract

We introduce several distinct notions of equity as no-envy into the overlapping generations economy formulated by Samuelson (1958). No-Envy in Overlapping Consumptions requires that for each time period, no person should prefer the bundle of any other person who lives in the same period to his/her own. No-Envy in Lifetime Consumptions states that no person should prefer the lifetime consumption plan of any other person to his/her own. Equity in Lifetime Rate of Return requires that the lifetime rate of return (Cass and Yaari,1966) be equal for all persons. For each of the three notions, we characterize allocations satisfying it, and clarify logical relations among these conditions. We also examine existence of a stationary allocation that attains maximal utility under No-Envy in Lifetime Consumptions.

Fair Allocations in an Overlapping Generations Economy

“…Also, unlike other notions of equity, there need be no comparability requirements placed on the utility functions of the various generations, since each generation evaluates its own assignment and the assignment of every other generation, in terms of its own utility function. Shinotsuka et al (2007) have studied alternative notions of envy-free allocations in an overlapping generations economy without production, in which each generation lives for two periods. We retain their framework, but assume in addition that the population is stationary and that there is a social endowment of a unit of a perishable consumption good in each period to be divided between the young and the old living in that period.…”

“…For some recent contributions following this approach, seeMitra (2005),Basu and Mitra (2007), Banerjee and Mitra (2010),Asheim et al (2010b).2 For recent contributions following this approach, seeShinotsuka et al (2007),Asheim et al (2010a).3 Two concepts of equity that have been discussed extensively are Anonymity and the Pigou-Dalton principle.4 Other seminal references on this equity notion areKolm (1972),Varian (1974), andYaari (1981). Some of the recent surveys on envy free allocations areThomson (2010).…”

“…The notion of Pareto efficiency that we use is also somewhat different fromShinotsuka et al (2007). This is explained in Section 2.…”

Fair Allocations in an Overlapping Generations Economy

“…For some recent contributions following this approach, seeMitra (2005),Basu and Mitra (2007), Banerjee and Mitra (2010),Asheim et al (2010b).2 For recent contributions following this approach, seeShinotsuka et al (2007),Asheim et al (2010a).3 Two concepts of equity that have been discussed extensively are Anonymity and the Pigou-Dalton principle.4 Other seminal references on this equity notion areKolm (1972),Varian (1974), andYaari (1981). Some of the recent surveys on envy free allocations areThomson (2010).…”

Repeated implementation with overlapping generations of agents

“…For example,Shinotsuka et al (2007) formulate three different notions of envy-freeness in a model with overlapping generations: No-Envy in Overlapping Consumptions, No-Envy in Lifetime Consumptions, and Equity in Lifetime Rate of Return. The first two notions would coincide in a static setup, while the last notion does not have an analogue in a static setup.…”