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.     

A contribution to duality theory,applied to the measurement of risk aversion

This paper determines the precise connection between the curvature properties of an objective function and the ray-curvature properties of its dual. When the objective function is interpreted as a Bernoulli or cardinal utility function, our results characterize the relationship between an agent’s attitude towards income risks and her attitude towards risks in the underlying consumption space. We obtain these results by developing and applying a number of representation theorems for concave functions.The work of Juan E. Martínez-Legaz has been supported by the Spanish Ministry of Science and Technology and the FEDER, project BEC2002-00642, and by the Departament d’Universitats, Recerca i Societat de la Informació, Direcció General de Recerca de la Generalitat de Catalunya, project 2001SGR-00162. He also thanks the Barcelona Economics Program of CREA for its support. John Quah would like to acknowledge with gratitude the financial support of the ESRC (grant number R000271171). He would also like to thank the Department of Economics at UC Berkeley, whose hospitality he enjoyed while completing this project. Both authors would like to thank Simon Cowan for pointing the way to some important references. They are also very grateful to the referee whose insightful suggestions led to a much improved paper     

Homothetic functions revisited

Summary. This paper examines the proposition that homotheticity is equivalent to the property that (e.g., in the context of a production function) the marginal rate of substitution is constant along any ray from the origin. This claim is made in many places, but hitherto the prerequisites have not been stated explicitly. In the present contribution it is demonstrated that an additional condition is required for the claim to hold. We present a theorem that achieves equivalence by also assuming ‘nowhere ray constancy’. It turns out that this condition is implied by assumptions often made, e.g., in production theory. Further, a complete characterization is given of the class of functions that satisfy ray constant marginal rates of substitution or, somewhat more generally, a condition of ray parallel gradients. In addition to homothetic functions this class contains functions homogeneous of degree 0 (i.e., ray constant) and functions which are homothetic in disjoint regions separated by regions of ray constancy. Received: November 5, 1999; revised version: October 31, 2000     

Bias of distance functions estimates and Primont and Primont’s homotheticity test

The question of whether a technology exhibits particular properties such as radial input or output homotheticity is a crucial one for a producer since it should strongly impact on its reactions to market changes. Primont and Primont (Econ Lett 45:191–195, 1994) established that it can be tested using only weak assumptions. They further used their results to test for input homotheticity of an educational production technology (Primont and Primont, Can J Econ 29:587–591, 1996). In this paper, it is shown that if not implemented properly, the test can lead to biased results. Some ways to obtain unbiased results are also suggested.

(Hemi)continuity of additive preference preorders

It is shown that the two common notions of topological continuity for preference preorders, which require closed contour sets and a closed graph respectively, are equivalent even when completeness is not assumed, provided that the domain is a normed linear space or a topological group and the preorder is additive.