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Sustainable Heterogeneity as the Unique Socially Optimal Allocation for Almost All Social Welfare Functions

Taiji Harashima

MPRA Paper from University Library of Munich, Germany

Abstract: The socially optimal allocation has been regarded to be unspecifiable because of utility’s interpersonal incomparability, Arrow’s general possibility theorem, and other factors. This paper examines this problem by focusing not on the social welfare function but instead on the utility possibility frontier in dynamic models with a heterogeneous population. A unique balanced growth path was found on which all of the optimality conditions of all heterogeneous households are equally and indefinitely satisfied (sustainable heterogeneity). With appropriate government interventions, such a path is always achievable and is uniquely socially optimal for almost all generally usable (i.e., preferences are complete, transitive, and continuous) social welfare functions. The only exceptions are some variants in Nietzsche type social welfare functions, but those types of welfare functions will rarely be adopted in democratic societies. This result indicates that it is no longer necessary to specify the shape of the social welfare function to determine the socially optimal growth path in a heterogeneous population.

Keywords: Sustainability; Heterogeneity; Social Optimality; Social welfare; Social welfare function; Inequality; Evolution (search for similar items in EconPapers)
JEL-codes: F40 D63 O41 I31 J38 D64 E20 (search for similar items in EconPapers)
Date: 2012-08-29
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