Ram Sewak Dubey

On equitable social welfare functions satisfying the Weak Pareto Axiom: A complete characterization

The paper examines the problem of aggregating infinite utility streams with a social welfare function which respects the Anonymity and Weak Pareto Axioms. It provides a complete characterization of domains (of the one period utilities) on which such an aggregation is possible. A social welfare function satisfying the Anonymity and Weak Pareto Axioms exists on precisely those domains which do not contain any set of the order type of the set of positive and negative integers. The criterion is applied to decide on possibility and impossibility results for a variety of domains. It is also used to provide an alternative formulation of the characterization result in terms of the accumulation points of the domain.

A characterization of Ramsey equilibrium in a model with limited borrowing

This paper considers a one-sector economic growth model with several infinitely-lived heterogeneous households, who differ both in the discount factors as well as preferences over consumption. Unlike the extreme form of borrowing constraint observed in the classical Ramsey model, recently surveyed in Becker (2006), we allow limited borrowing by the households and prove the existence of a perfect foresight equilibrium. We also show that irrespective of production technology employed by the firms, the capital stock sequence converges to the steady state stock and from some time onward all impatient households are in the maximum borrowing state, whereas the most patient household owns entire capital stock and the debts of all other households.

Combining Monotonicity and Strong Equity: Construction and Representation of Orders on Infinite Utility Streams

This paper studies the nature of social welfare orders (SWO) on infinite utility streams, satisfying the efficiency principle known as monotonicity and the consequentialist equity principle known as strong equity. It provides a complete characterization of domain sets for which there exists such a SWO which is in addition representable by a real valued function. It then shows that for those domain sets for which there is no such SWO which is representable, the existence of such a SWO necessarily entails the existence of a non-Ramsey set, a non-constructive object. Copyright Springer-Verlag Berlin Heidelberg 2014

On Social Welfare Functions on Infinite Utility Streams Satisfying Hammond Equity and Weak Pareto Axioms: A Complete Characterization

This paper examines the problem of aggregating infinite utility streams with a social welfare function that respects the Hammond Equity and Weak Pareto axioms. The paper provides a complete characterization of domains (of the one period utilities) on which such an aggregation is possible. A social welfare function satisfying the Hammond Equity and Weak Pareto axioms exists on precisely those domains which are well-ordered sets in which the elements of the set are ordered according to the decreasing magnitude of the numbers belonging to the set. We show through examples how this characterization can be applied to obtain a number of results in the literature, as well as some new ones.

On Construction of Equitable Social Welfare Orders on Infinite Utility Streams

This paper studies the nature of social welfare orders on infinite utility streams, satisfying the consequentialist equity principles known as Hammond Equity and the Pigou–Dalton transfer principle. The first result shows that every social welfare order satisfying Hammond Equity and the Strong Pareto axioms is non-constructive in nature for all non-trivial domains, Y. The second result shows that, when the domain set is Y=[0,1], every social welfare order satisfying the Pigou–Dalton transfer principle is non-constructive in nature. Specifically, in both results, we show that the existence of the appropriate social welfare order entails the existence of a non-Ramsey set, a non-constructive object. The second result also provides an example of a social welfare order which can be represented, but which cannot be constructed.

Impatience implication of weakly Paretian orders: Existence and genericity

We study order theoretic and topological implications for impatience of weakly Paretian, representable orders on infinite utility streams. As a departure from the traditional literature, we do not make any continuity assumptions in proving the existence of impatient points. Impatience is robust in the sense that there are uncountably many impatient points. A general statement about genericity of impatience cannot be made for representable, weakly Paretian orders. This is shown by means of an example. If we assume a stronger sensitivity condition, then genericity obtains.

On Multi-Utility Representation of Equitable Intergenerational Preferences

We investigate the possibility of representing ethical intergenerational preferences using more than one utility function. It is shown that the impossibility of representing intergenerational preferences equitably persists in the multi-utility frame work with some resonable restrictions on the cardinality of the set of utilities.

A Note on Social Welfare Orders Satisfying Pigou-Dalton Transfer Principle

This paper studies the constructive nature of social welfare orders on infinite utility streams defined on X=Yⁿ, satisfying the Pigou-Dalton transfer principle (PD), which are known to be representable (see Alcantud (2010) and Sakamoto (2012)). We describe the restrictions on domain Y for explicit representation or construction of the social welfare orders satisfying (i) PD and monotonicity; or (ii) PD only. We show that the restrictions on Y for either (a) construction; or (b) explicit representation of the social welfare orders are identical in both cases.

Ramsey equilibrium with liberal borrowing

This paper considers a multi-agent one-sector Ramsey equilibrium growth model with borrowing constraints. The extreme borrowing constraint used in the classical version of the model, surveyed in Becker (2006), and the limited form of borrowing constraint examined in Borissov and Dubey (2015) are relaxed to allow more liberal borrowing by the households. A perfect foresight equilibrium is shown to exist in this economy. We describe the steady state equilibria for the liberal borrowing regime and show that as the borrowing regime is progressively liberalized, the steady state wealth inequality increases. Unlike the case of a limited borrowing regime, an equilibrium path need not converge in the case of liberal borrowing regime. We show through an example that a two period cyclic equilibrium exists when agents are allowed to borrow against their two period future wage income. This result is similar to the possibility of non-convergent equilibrium capital stock sequences in the model with no borrowing.

Ordering Infinite Utility Streams: Efficiency, Continuity, and No Impatience

We study two related versions of the no-impatience postulate in the context of transitive and reflexive relations on infinite utility streams which are not necessarily complete. Both are excluded by the traditional (weak) anonymity axiom. We show explicit social welfare relations satisfying Strong Pareto and the weaker version of no-impatience that are compatible with continuity in all the traditional topologies in this field. However the stronger version of no-impatience is violated by all lower semi-continuous (in the sup or Campbell topologies) social welfare relations satisfying the Weak Pareto axiom.