The Morishima gross elasticity of substitution

We show that the Hotelling–Lau elasticity of substitution, an extension of the Allen–Uzawa elasticity to allow for optimal output-quantity (or utility) responses to changes in factor prices, inherits all of the failings of the Allen–Uzawa elasticity identified by Blackorby and Russell [(1989) Am Econ Rev 79: 882–888]. An analogous extension of the Morishima elasticity of substitution to allow for output quantity changes preserves the salient properties of the original Hicksian notion of elasticity of substitution. We thank Paolo Bertoletti for drawing our attention to the issue addressed in this paper and for his comments on an earlier draft.     

On testing separability restrictions with flexible functional forms

In this paper, we examine the implications of imposing separability on the translog and three other flexible forms. Our results imply that the Berndt-Christensen ‘nonlinear’ test for weak separability tests not only for weak separability, but also imposes a restrictive structure on the macro and micro functions for all currently known ‘flexible’ functional forms. For example, testing for weak separability using the translog as an exact form is in fact equivalent to testing for a hybrid of strong (additive) separability and homothetic weak separability with Cobb-Douglas aggregator functions. Our results show that these ‘flexible’ functional forms are ‘separability-inflexible’. That is, they are not capable of providing a second-order approximation to an arbitrary weakly separable function in any neighbourhood of a given point.     

Rationalizable variable-population choice functions

Summary. We analyze the rationalizability of variable-population social-choice functions in a welfarist framework. It is shown that fixed-population rationalizability and a weakening of congruence together are necessary and sufficient for rational choice, given a plausible dominance property that prevents the choice of alternatives involving low utility levels. In addition, a class of critical-level separable choice functions is characterized. This result, which extends an earlier axiomatization of a related class of bargaining solutions to a variable-population setting, is the first axiomatization of critical-level principles in a general choice-theoretic model. Received: November 30, 1999; revised version: September 11, 2000     

Index numbers and consistency in aggregation

This paper is an analysis of the concept of consistency in aggregation. This is the conjunction of three requirements: (i) for any given partition of the variables, two-stage aggregation is consistent, (ii) that each subaggregate and the overall aggregate have the same functional form, and (iii) that all partitions of the variables are feasible. We show that in the scalar case this results in a quasi-additive functional form. The generalization to many attributes is however shown to lead to few restrictions.     

Aggregation of Efficiency Indices

Measurement of technical efficiency is carried out at many levels of aggregation—at the individual branch, plant, division, or district level; at the company- or organization-wide level; at the industry or sectoral level; or at the economy-wide level. In this paper, we examine the conditions under which these indexes constructed at various levels of aggregation can be consistent with one another—that is, the extent to which efficiency indexes can be consistently aggregated. Unfortunately, our results are discouraging, indicating that very strong restrictions on the technology and/or the efficiency index itself are required to enable consistent aggregation (or disaggregation).     

Critical levels and the (reverse) repugnant conclusion

It is well-known that there is a trade-off among the properties of population principles that are used to make social evaluations when the number of people in the society under consideration may vary. The commonly used principles either lead to the repugnant conclusion (which is the case for classical utilitarianism), or they violate the Pareto-plus principle and related properties (average utilitarianism is an example of such a principle). This paper examines the nature of this trade-off and shows that the incompatibility between avoiding the repugnant conclusion and the Pareto-plus principle is fundamental and not restricted to the commonly used population principles.     

Production Efficiency and the Direct-Indirect Tax Mix

In the design of the optimal direct/indirect tax mix, the canonical view was laid by Atkinson and Stiglitz (1976) who showed that commodity taxes are unnecessary in an economy in which there is an optimal nonlinear income tax provided that commodities are separable from labor in the utility functions of all taxpayers, that the aggregators over these commodities are ordinally equivalent and that wages are fixed. When wages are endogenous, Naito (1999) showed that this result may not hold and in addition that production efficiency may not be Pareto optimal. Given an optimal nonlinear income tax, we show that production inefficiency is Pareto optimal if the aggregate technology set is strictly concave. The Atkinson–Stiglitz condition is neither necessary nor sufficient for zero commodity taxation and commodity taxes are part of almost all Pareto optima.