A Non-dictatorial Criterion for Optimal Growth Models

There are two main approaches for defining social welfare relations for an economy with infinite horizon. The first one is to consider the set of intertemporal utility streams generated by a general set of bounded consumptions, and define a preference relation between them. This relation is ideally required to satisfy two main axioms, the Pareto axiom, which guarantees efficiency, and the Anonymity axiom, which guarantees equity. Basu and Mitra [2003] show that it is impossible to represent by a function a preference relation embodying both the efficiency and equity requirements and Basu and Mitra [2007] propose and characterize a new welfare criterion called utilitarian social welfare relation. In the same framework, Chichilnisky [1996] proposes two axioms that capture the idea of sustainable growth: non-dictatorship of the present and non-dictatorship of the future, and exhibits a mixed criterion, adding a discounted utilitarian part (with possibly non constant discount rates), which gives a dictatorial role to the present, and a long term part, which gives a dictatorial role to the future. The drawback of Chichilnisky's approach is that it often does not allow to explicitly characterize optimal growth paths with optimal control techniques. Moreover, we observe that the optimal solution obtained with Chichilnisky's criterion, cannot in general be approximated by a sequence of optimal solutions with finite horizon. Our aim is less general than Chichilnisky's, and Basu and Mitra's: we want to have a non-dictatorial criterion for optimal growth models. Instead of l + ∞ as set of utilities, we just consider the set of utilities of consumptions which are generated by a specific technology. We show that the undiscounted utilitarian criterion pioneered by Ramsey [1928] is not only convenient if one wants to solve an optimal growth problem but also sustainable, efficient and equitable.