Maria Bernadette Donato

QUASI-VARIATIONAL APPROACH OF A COMPETITIVE ECONOMIC EQUILIBRIUM PROBLEM WITH UTILITY FUNCTION: EXISTENCE OF EQUILIBRIUM

A Walrasian pure exchange economy with utility functions, a particular case of a general economic equilibrium problem, is considered in this paper. We assume that each agent is endowed with goods and maximizes his utility function, under his budget constraints. We are able to characterize the Walrasian equilibria as solution of an associated quasi-variational inequality. This approach allows us to obtain an existence result of equilibrium solutions. As an application, we provide the explicit equilibrium in the case of two agents and two goods.

A new contribution to a dynamic competitive equilibrium problem

The aim of this paper is to study the Walrasian equilibrium problem when the data are time dependent. For this model an existence result is provided using the variational inequality theory in infinite dimensional spaces. Our results are the generalization of some of the results obtained by several authors in the static case (see e.g. Donato et al. (2008) [5], Donato et al. (2008) [4] and Mordukhovich (2006) [11], Nagurney (1993) [2] and the references therein).

An existence result of a quasi-variational inequality associated to an equilibrium problem

In this paper we consider a Walrasian pure exchange economy with utility function which is a particular case of a general economic equilibrium problem, without production. We assume that each agent is endowed with at least of a commodity, his preferences are expressed by an utility function and it prevails a competitive behaviour: each agent regards the prices payed and received as independent of his own choices. The Walrasian equilibrium can be characterized as a solution to a quasi-variational inequality. By using this variational approach, our goal is to prove an existence result of equilibrium solutions.

Walrasian Equilibrium Problem with Memory Term

The aim of this paper is to study the Walrasian equilibrium problem when the data are time-dependent. In order to have a more realistic model, the excess demand function depends on the current price and on previous events of the market. Hence, a memory term is introduced; it describes the precedent states of the equilibrium. This model is reformulated as an evolutionary variational inequality in the Lebesgue space L2([0,T],ℝ), and, thanks to this characterization, existence and qualitative results on equilibrium solution are given.

A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption

This paper is focused on the investigation of the Walrasian economic equilibrium problem involving utility functions. The equilibrium problem is here reformulated by means of a quasi-variational inequality problem. Our goal is to give an existence result without assuming strong monotonicity conditions. To this end, we make use of a perturbation procedure. In particular, we will consider suitable perturbed utility functions whose gradient satisfies a strong monotonicity condition and whose associated equilibrium problem admits a solution. Then, we will prove that the limit solution solves the unperturbed problem. We stress out that our result allows us to consider a wide class of utility functions in which the Walrasian equilibrium problem may be solved.

Variational Problem, Generalized Convexity, and Application to a Competitive Equilibrium Problem

The main purpose of this article is to present a new formulation of a competitive equilibrium in terms of a suitable quasivariational inequality involving multivalued maps. More precisely, a pure exchange economy is considered where the consumers preferences are represented by utility functions that we assume to be generalized concave and non-differentiable. In the concave context, we have characterized the equilibrium by means of a variational problem involving the subdifferential. Now, by relaxing concavity and differentiability assumptions on utility functions, the subdifferential operator of the utility function is replaced by a suitable multimap involving a new concept, recently introduced in [1]: the normal operator to the adjusted sublevel sets. Thanks to this variational formulation we are able to achieve the existence of equilibrium points by using arguments of the set-valued analysis. Finally, we provide some example of utility functions which verify our assumptions.

Quasivariational Inequalities for a Dynamic Competitive Economic Equilibrium Problem

The aim of this paper is to consider a dynamic competitive economic equilibrium problem in terms of maximization of utility functions and of excess demand functions. This equilibrium problem is studied by means of a time-dependent quasivariational inequality which is set in the Lebesgue space . This approach allows us to obtain an existence result of time-dependent equilibrium solutions.

On the Study of an Economic Equilibrium with Variational Inequality Arguments

The main purpose of this paper is to investigate on the existence of a competitive equilibrium for a market with consumption and exchange. A variational representation is used to study this problem. More precisely, we consider an economy where utility functions are assumed concave and non-differentiable, and we characterize the equilibrium by means of a variational problem involving the subdifferential multimap. Thanks to this approach, by introducing suitable perturbed utility functions, we achieve an existence result when the operator is not coercive and the convex set might be unbounded.

Sensitivity analysis for time dependent spatial price equilibrium problem

We present some sensitivity results for the spatial price equilibrium problem in the case of quantity formulation model and in presence of excess supply and excess demand. The equilibrium conditions that describe the above model are expressed in terms of a time dependent variational inequality. The variational inequality formulation plays a fundamental role in order to achieve the sensitivity results.

On a class of vector optimization problems with a variational approach

A class of vector optimization problems is considered. In particular, we reformulate this problem by means of a suitable vector variational inequality, involving the normal cone operator to the adjusted sublevel sets. Finally, this variational approach allows us to obtain the existence of solutions to our vector optimization problem.