A never-decisive and anonymous criterion for optimal growth models

We address in this paper the question of the existence of a Social Welfare Function that would be sustainable and would allow us to obtain solutions to optimal growth models. We define sustainability by two new axioms called Never-decisiveness of the present and Never-decisiveness of the future. We first show that a SWF which has Never-decisiveness properties cannot be defined on a ball of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$l_{\infty }^{+}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msubsup> <mrow> <mi>l</mi> </mrow> <mrow> <mi>∞</mi> </mrow> <mrow> <mo stretchy="false">+</mo> </mrow> </msubsup> </mrow> </math> </EquationSource> </InlineEquation>. We must (i) restrict to the set of utility streams for which the value of the SWF is finite and (ii) introduce additional assumptions in order to obtain the Never-decisiveness properties. Our main result in this paper is therefore to show that the undiscounted utilitarian criterion is an anonymous and never-decisive criterion for optimal growth models. We consider the set of utilities of consumptions which are generated by a specific technology, namely a technology with decreasing returns for high levels of capital, and restrict ourselves to good programs, i.e., any program for which intertemporal utility is well defined. Copyright Springer-Verlag Berlin Heidelberg 2014