On Commodity Prices and Factor Rewards: A Close Look at Sign Patterns

The effect of changes in commodity prices on factor rewards is studied in the multi-commodity, multi-factor case. It is shown that the inverse of the distributive share matrix must satisfy the following restriction: it cannot be anti-symmetric in its sign pattern. This means that one cannot partition the commodities into two groups (I and II) and factors into two groups (A and B), such that all factors in group A benefit (nominally) from all commodity price increases in group I, and simultaneously all factors in group B suffer from all commodity price increases in group II. It turns out that this is also the only sign-pattern restriction imposed by the general nature of the relationship of commodity prices and factor rewards.

On Competitive Equitable Paths under Exhaustible Resource Constraints: The Case of a Growing Population

The paper examines the nature of competitive paths in an exhaustible resource model, which allows for growing population. For competitive paths which are equitable in the sense that the per capita consumption level is constant over time, the implicit investment rule is derived. This is seen to be a generalization of Hartwick's rule, obtained in the case of a stationary population. It is also shown that the existence of a competitive equitable path implies that population can experience at most quasi-arithmetic growth.

A Characterization of the Turnpike Property of Optimal Paths in the Aggregative Model of Intertemporal Allocation

The paper provides a complete characterization of the turnpike property of optimal paths in the (reduced form) aggregative model of intertemporal allocation. The characterization allows one to identify precisely the bifurcation point between globally stable and cyclical long-run optimal behavior. The complete characterization result is used to evaluate several sufficient conditions for global asymptotic stability of optimal paths that have been proposed in the literature. It is also used to examine sufficient conditions for the emergence of competitive equilibrium cycles in two-sector models.

On Literacy Rankings

This paper is concerned with the issue of characterizing the situations in which all the literacy indices, consistent with a set of reasonable axioms, would provide the same ranking of societies. It is shown that a theory, analogous to that developed for the Lorenz order in the study of income inequality, can be obtained in the study of literacy, by extending the standard mathematical theory relating gauge functions to convex functions, and the theory of majorization.

Intergenerational Equity and the Forest Management Problem

The paper re-examines the foundations of representation of intertemporal preferences that satisfy intergenerational equity, and provides an axiomatic characterization of those social welfare relations, which are representable by the utilitarian ordering, in ranking consumption sequences which are eventually identical. A maximal point of this ordering is characterized in a standard model of forest management. Maximal paths are shown to converge over time to the forest with the maximum sustained yield, thereby providing a theoretical basis for the tradition in forest management, which has emphasized the goal of maximum sustained yield. Further, it is seen that a maximal point coincides with the optimal point according to the well-known overtaking criterion. This result indicates that the more restrictive overtaking criterion is inessential for a study of forest management under intergenerational equity, and provides a more satisfactory basis for the standard forestry model.

On the Continuity of Ethical Social Welfare Orders

In this paper we study the extent to which ethical social welfare orders on infinite utility streams can be continuous. For a class of metrics, we show that ethical preferences can be continuous if and only if the continuity requirement is in terms of a metric which satisfies a simplex condition. This condition requires that the distance from the origin to the unit simplex in the space of utility streams be positive. We use this characterization result to establish that the metric used by Svensson (1980) induces the weakest topology for which there exist continuous ethical preferences.

Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty

We study a one-sector stochastic optimal growth model, where the utility function is iso-elastic and the production function is of the Cobb-Douglas form. Production is affected by a multiplicative shock taking one of two values. We provide sufficient conditions on the parameters of the model under which the invariant distribution of the stochastic process of optimal output levels is of the Cantor type.

Cantor Type Attractors in Stochastic Growth Models.

We study a one-sector stochastic optimal growth model where production is affected by a shock taking one of two values. Such exogenous shock may enter multiplicatively or additively. A result is presented which provides sufficient conditions to ensure that the attractor of the iterated function system (IFS) representing the optimal policy, is a generalized topological Cantor set. To indicate the role of the strict monotonicity condition on the IFS in this result, examples of attractors, which are not of the Cantor type, are constructed with iterated function systems, whose maps are contractions and satisfy a no overlap property.

Efficient Ramsey Equilibria

Ramsey equilibrium models with heterogeneous agents and borrowing constraints are shown to yield efficient equilibrium sequences of aggregate capital and consumption. The proof of this result is based on verifying that equilibrium sequences of prices satisfy the Malinvaud criterion for efficiency.