Jean-Marc Bonnisseau

Valuation equilibrium and pareto optimum in non-convex economies

In this paper, we report an extension of the second welfare theorem when both convexity and differentiability assumptions are violated. Our model allows various formalizations of the marginal rule and considers the general setting of a topological vector space of commodities.

Existence of marginal cost pricing equilibria : the nonsmooth case

In this article, the authors report a general existence theorem of a marginal (cost) pricing equilibrium for an economy that may exhibit increasing returns to scale or more general types of nonconvexities in the production sector. Their model considers an arbitrary number of firms and no smoothness assumption is made on the production sets or on the aggregate production set. Copyright 1990 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Fixed-point theorems and Morse's lemma for Lipschitzian functions

Abstract We prove a fixed-point theorem for set-valued mappings defined on a nonempty compact subset X of R n which can be represented by inequality constraints, i.e., X={x∈ R n| f(x)⩽0}, f locally Lipschitzian and satisfying a nondegeneracy assumption outside of X. This class of sets extends significantly the class of convex, compact sets with a nonempty interior. Topological properties of such sets X are proved (continuous deformation retract of a ball, acyclicity) as a consequence of a generalization of Morses lemma for Lipschitzian real-valued function defined on R n a result also of interest for itself.

On two existence results of equilibria in economies with increasing returns

We consider a general equilibrium model in an economy with increasing returns. This paper provides new proofs of the existence results of Dierker et al. (1985) and of Kamiya (1988) which will be deduced from the main theorem of Bonnisseau and Cornet (1988).

Existence of Marginal Cost Pricing Equilibria in Economies With Several Nonconvex Firms

This paper considers a general equilibrium model of an economy where some firms may exhibit increasing returns to scale or more general types of nonconvexities. The firms are instructed to follow the standard marginal cost pricing rule or to fulfill the first-order necessary conditions for profit maximization. A general existence theorem of equilibria is proved in the case of an arbitrary number of firms. No assumption is made to imply the aggregate productive efficiency of equilibria, a condition that must be excluded in the nonconvex case. Copyright 1990 by The Econometric Society.

Vertical Differentiation: Multiproduct Strategy to Face Entry?

In this paper, we consider an incumbent firm facing potential entry in a vertical differentiation model a la Mussa and Rosen where consumers differ only by their intensity of preference for quality. We ask whether the incumbent firm has the incentive to adopt a multi-product strategy in order to face entry, in a natural duopoly case. It turns out that this strategy is never profitable and that an incumbent always prefers to produce one quality. It appears that either a cost effect or an income dispersion are necessary to urge producers to offer several products.

Continuity and uniqueness of equilibria for linear exchange economies

The purpose of this paper is to study the continuity and uniqueness properties of equilibria for linear exchange economies. We characterize the sets of utility vectors and initial endowments for which the equilibrium price is unique and respectively the set for which the equilibrium allocation is unique. We show that the equilibrium allocation correspondence is continuous with respect to the initial endowments and we characterize the set of full measure where the equilibrium allocation correspondence with respect to the initial endowments and utility vectors is continuous.

Existence of marginal pricing equilibria in economies with externalities and non-convexities

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect. We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.

Regular economies with non-ordered preferences

We consider exchange economies with non-ordered preferences and externalities. Under continuity and boundary conditions, we prove an index formula, which implies the existence of equilibria for all initial endowments, and the upper semi-continuity of the Walras correspondence. We then posit a differentiability assumption on the preferences. It allows us to prove that the equilibrium manifold is a nonempty differentiable sub-manifold of an Euclidean space. We define regular economies as the regular values of the natural projection. We show that the set of regular economies is open, dense and of full Lebesgue measure. From the index formula, one deduces that a regular economy has a finite odd number of equilibria, and, for each of them, the implicit function theorem implies that there exists a local differentiable selection. So, even with only non-ordered preferences and externalities, exchange economies have nice properties for equilibrium analysis.

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.