Existence of Equilibria in Economies with Externalities and Nonconvexities

We consider a general equilibrium model of an economy in which the production possibilities, the consumption sets and the preferences of the consumers are represented by set-valued mappings which depend on the environment to take into account the possibility of external effect. In order to encompass all kinds of nonconvexities, we do not put any convexity assumption either on the graph of the set-valued mapping which describes the technological possibilities or on the production set for a given environment. The firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other producers and on consumption plans.We report an existence result of general equilibria. As in the model without external effects, the key hypotheses are bounded loss and survival assumptions. Nevertheless, we also assume that the set-valued mappings which describe the fundamentals of the economy are lower semi-continuous and have a closed graph.Our framework is sufficiently large to generalize previous works on the existence of competitive equilibria with externalities when the firms have convex production sets and on the existence of equilibria with general pricing rule without externality.     

A Note on the Characterization of Optimal Allocations in OLG Models with Multiple Goods

We consider a pure exchange overlapping generations economy with a varying number of commodities and consumers per period having possibly non-complete non transitive preferences. We provide a geometric and direct proof of the Balasko-Shell characterization of Pareto optimal allocations. As a by-product, we compute an explicit Pareto improving transfer when the criterion is not satisfied, which is minimal for some suitable distance.     

On the equivalence of financial structures with long-term assets

In a stochastic financial exchange economy, two financial structures are equivalent if, for each given state price, the marketable payoffs are identical for the associated asset prices. The key property of two equivalent financial structures is that, when associated with any standard exchange economy, they lead to the same financial equilibrium. We exhibit a sufficient condition for the equivalence of two financial structures without re-trading with possibly long-term assets. We then apply this result to financial structures built upon primitive assets and their re-trading. We also borrow an assumption from Bonnisseau and Chéry (Ann Financ 10:523–552, 2014) to prove the equivalence between a financial structure and its reduced forms.     

The Marginal Pricing Rule in Economies with Infinitely Many Commodities

Clarke's normal cone appears as the right tool to define the marginal pricing rule in finite dimensional commodity space since it allows to consider in the same framework convex, smooth as well as nonsmooth nonconvex production sets. Furthermore it has nice continuity and convexity properties. But it is not well adapted for economies with infinitely many commodities since it does satisfy minimal continuity properties. In this paper, we propose an alternative definition of the marginal pricing rule. It allows us to prove the second welfare theorem and the existence of marginal pricing equilibria for economies with several producers under assumptions similar to the one used for economies with a finite set of commodities. Our approach is sufficiently general to take into account the convex and the smooth cases for which our definition of the marginal pricing rule coincides with the one given by the Clarke's normal cone or the normal cone of convex analysis.     

Une preuve alternative de l'existence d'un équilibre de Nash dans les jeux discontinus

This Note presents a theorem of the existence of the Nash equilibrium for discontinuous games in a topological vector space. We will use an assumption of better reply secure which is stronger then that of Reny. If the payoff function is upper semi-continuous, the two assumptions coincide. Our proof is simple, independent and based on a version of Fan–Browder theorem of existence of maximal element due to Deguire and Lassonde, which is extended to the non-Hausdorf case. To cite this article: J.-M. Bonnisseau et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

237Np Mössbauer spectroscopy on neptunium doped borosilicate glasses

Mössbauer and magnetization measurements have been carried out on borosilicate glasses containing neptunium. Different melting and annealing times, in various crucibles have been investigated. Using the 59.5 keV Mössbauer resonance in²³⁷Np we have characterized valency states of neptunium ions in glasses and studied hyperfine interactions. Roughly, absorption spectra show two sites easily differenciated above 50 K by two lines. Isomer shifts (relative to NpAl₂) are respectively: – 10.0 (1.0) and + 32.5(.5) mm/s. These resonance lines can be assigned, the first at Np⁴⁺, the second at Np³⁺ species. The intensity ratio Np⁴⁺/Np³⁺ varies with elaboration conditions. At 4.2 K, Np⁴⁺ ions exhibit a hyperfine splitting arising from relaxation phenomenon. Magnetization measurements do not show any magnetic ordering.     

Borsuk’s antipodal theorem for approachable correspondences

We present an extension of Borsuk’s antipodal theorem (on the existence of a zero) to antipodally approachable correspondences defined on bounded, symmetric and balanced domains.     

Constrained Consumptions, Lipschitzian Demands, and Regular Economies

We consider an exchange economy where the consumers face linear inequality constraints on consumption. We parametrize the economy with the initial endowments and constraints. We exhibit sufficient conditions on the constraints implying that the demand is locally Lipschitzian and continuously differentiable on an open dense subset of full Lebesgue measure. Using this property, we show that the equilibrium manifold is lipeomorphic to an open, connected subset of an Euclidean space and that the lipeomorphism is almost everywhere continuously differentiable. We prove that regular economies are generic and that they have a finite odd number of equilibrium prices and local differentiable selections of the equilibrium prices.Communicated by J. P. CrouzeixThis work was partially supported by CCE, ECOS, and ICM Sistemas Complejos de Ingeniería.