Using the compensating and equivalent variations to define the Slutsky Equation under a discrete price change

In our experience, all textbook presentations of the Slutsky Equation under a discrete price change use a compensation scheme based on the compensating variation. Our students have sensed this convention is arbitrary in that they have asked, why consider this compensation scheme, and not one based on the equivalent variation? The present paper outlines how one might address this matter analytically, and then discusses how our findings provide a new insight into the Giffen Paradox.Compensating Variation

Multilinear isometries on function algebras

Let be function algebras (or more generally, dense subspaces of uniformly closed function algebras) on locally compact Hausdorff spaces , respectively, and let Z be a locally compact Hausdorff space. A -linear map is called a multilinear (or k-linear) isometry if (Formula presented.) Based on a new version of the additive Bishop’s Lemma, we provide a weighted composition characterization of such maps. These results generalize the well-known Holsztyński’s theorem and the bilinear version of this theorem provided in Moreno and Rodríguez [Studia Math. 2005;166:83–91] by a different approach.Research of J.J. Font and M. Sanchis was partially supported by the Spanish Ministry of Science and Education [grant number MTM2011-23118], and by Bancaixa [Projecte P11B2011-30]

Holomorphic Hulls and Holomorphic Convexity

Paper by R. O. Wells, Jr