In this paper, we establish an equivalent version of the hairy ball theorem in the form of a fixed point theorem. By using a version of Mas-Colell theorem [6] and by applying homotopy and approximation methods, we obtain our main result.

In the case of a large nuclear set (like the French set), nuclear production needs to be flexible to adjust to the predicted evolutions of the energy demmand. Consequently, the dominant position of nuclear in the national energy mix makes it responsible for the overall equilibrium of the...

We look at the optimal inter-temporal management of the fuel reservoir of nuclear units in a liberalized electricity market. We use the assumption that nuclear fuel works as a "reservoir" of energy due to the periodical shutdown of nuclear units to reload their fuel. In the medium-term, how a...

In many countries, the electricity systems are quitting the vertically integrated monopoly organization for an operation framed by competitive markets. It therefore questions how flexible nuclear plants capable of load-following should be operated in an open market framework. A number of...

We consider a stochastic financial exchange economy with a finite date-event tree representing time and uncertainty and a nominal financial structure with possibly long-term assets. We exhibit a sufficient condition under which the payoff matrix and the full payoff matrix have the same rank....

We consider a standard overlapping generation economy with a simple demographic structure with a new cohort of agents at each period with an economic activity extended over two successive periods and finitely many firms active forever. The production possibilities are described by a sequence of...

The purpose of the paper is to introduce a tighter definition for the marginal pricing rule. By means of an example, we illustrate the improvements that one gets with the new definition with respect to the former one with the Clarke's normal come.

Dans un modèle de différenciation verticale où les consommateurs sont uniformément distribués par rapport à leurs intensités de préférence pour la qualité et par rapport à leurs revenus, nous cherchons la stratégie optimale d'un monopole naturel : le nombre de qualités offertes, les...

This paper deals with the existence of marginal pricing equilibria or equilibria with general pricing rules in an economy with increasing returns to scale or more general types of non convexities in production. Its main contribution is to posit the bounded loss and survival assumptions on a...

This paper discusses necessary optimality conditions for multi-objective optimization problems with application to the Second Theorem of Welfare Economics. We use the extremal principle, since we consider non-convex sets non-smooth functions. Particularly, we develop a slight generalization of...