Sur trois contributions d’Allais

Dans ce texte, nous avons choisi de souligner trois contributions de Maurice Allais qui ont le mérite de ne pas le confiner dans un rôle de précurseur. Nous examinons successivement la dynamique microéconomique d’Allais (elle est toujours révolutionnaire), sa caractérisation de la substitution et de la complémentarité (elle est toujours originale) et enfin les liens qu’il y a entre sa généralisation de la théorie du rendement social au cas du risque et la généralisation d’Arrow-Debreu (ces deux théories sont parfaitement complémentaires).This paper contains a discussion on three contributions done by Maurice Allais which are largely unknow. We present his conception on microeconomic dynamics (it is still revolutionary), his characterization of substitution and complementarity (it is still original) and finally, the links between his extension of welfare economics to risk and uncertainty and the Arrow's extension (both theories are complementary)

De la variété de Patinkin-Malinvaud à l’optimum macroéconomique de court terme

En éliminant certaines des conditions nécessaires à l’équilibre walrasien, on obtient une variété différentiable que nous avons appelée ici variété de Patinkin-Malinvaud puisque cette façon de faire revient à prendre la méthodologie de ces auteurs. En plus de fournir un modèle simple qui soit assez souple pour contenir, sans rupture structurelle, autant l’équilibre walrasien temporaire que l’équilibre keynésien, autant la théorie des cycles réels que celle de la stabilité keynésienne (du moins dans leur principe), elle permet d’étudier l’optimalité des équilibres mentionnés plus haut dans le contexte qui leur est propre, c’est-à-dire le contexte temporaire et ce du point de vue du premier comme du second rang.When some necessary Walrasian conditions are eliminated, a differentiable manifold is obtained. Here, it is called the Patinkin-Malinvaud manifold since our device to define it amounts to recover the methodology of these authors. Such a methodology is sufficient to contain in the same logical structure the temporary Walrasian equilibrium, the Keynesian equilibrium, the real business cycle theory and the Keynesian stability theory (at least in their principle). Moreover, the optimality of the above equilibria is studied in their natural context, that is, the temporary one, from the first best viewpoint and the second best viewpoint

Sur l’estimation d’un système complet de demande sous rationnements quantitatifs

The paper is divided into two parts. In the first one, three complete systems of demand equations are derived, namely, the standard neo-classical model, a model under quantity rationing and the general reduced form of walrasian models. The standard neo-classical model has no spillover eflects while the other models allow for them. But the spillover effects of the general reduced form are walrasian while the spillover effects of the model with quantity rationing can be specified as keynesian.In the second part of the paper, the authors try to discriminate among these forms on empirical grounds. As a matter of fact, each model is found consistent with the Canadian data and the authors conclude that to discriminate between the models, one must insert them into more general models

Sharp interface limit of an energy modelling nanoparticle-polymer blends

We identify the $\Gamma$-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase transition thickness of the polymer phases approach zero. The limiting energy consists of two terms: the perimeter of the interface separating the phases and a penalization term related to the density distribution of the infinitely many small nanoparticles. We prove that local minimizers of the limiting energy admit regular phase boundaries and derive necessary conditions of local minimality via the first variation. Finally we discuss possible critical and minimizing patterns in two dimensions and how these patterns vary from global minimizers of the purely local isoperimetric problem.Comment: Minor changes. Rephrased introduction. This version is to appear in Interfaces and Free Boundarie

De la variété de Patinkin-Malinvaud à l’optimum macroéconomique de court terme

When some necessary Walrasian conditions are eliminated, a differentiable manifold is obtained. Here, it is called the Patinkin-Malinvaud manifold since our device to define it amounts to recover the methodology of these authors. Such a methodology is sufficient to contain in the same logical structure the temporary Walrasian equilibrium, the Keynesian equilibrium, the real business cycle theory and the Keynesian stability theory (at least in their principle). Moreover, the optimality of the above equilibria is studied in their natural context, that is, the temporary one, from the first best viewpoint and the second best viewpoint. En éliminant certaines des conditions nécessaires à l’équilibre walrasien, on obtient une variété différentiable que nous avons appelée ici variété de Patinkin-Malinvaud puisque cette façon de faire revient à prendre la méthodologie de ces auteurs. En plus de fournir un modèle simple qui soit assez souple pour contenir, sans rupture structurelle, autant l’équilibre walrasien temporaire que l’équilibre keynésien, autant la théorie des cycles réels que celle de la stabilité keynésienne (du moins dans leur principe), elle permet d’étudier l’optimalité des équilibres mentionnés plus haut dans le contexte qui leur est propre, c’est-à-dire le contexte temporaire et ce du point de vue du premier comme du second rang.

Minimizers of the Landau-de Gennes energy around a spherical colloid particle

We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau-de Gennes model. The nematic is assumed to occupy the exterior of a ball of radius r_0, satisfy homeotropic weak anchoring at the surface of the colloid, and approach a uniform uniaxial state at infinity. We study the minimizers in two different limiting regimes: for balls which are small compared to the characteristic length scale r_0>L. The relationship between the radius and the anchoring strength W is also relevant. For small balls we obtain a limiting quadrupolar configuration, with a "Saturn ring" defect for relatively strong anchoring, corresponding to an exchange of eigenvalues of the Q-tensor. In the limit of very large balls we obtain an axisymmetric minimizer of the Oseen-Frank energy, and a dipole configuration with exactly one point defect is obtained