[This article considers an economy in which there is one public good financed by means of commodity taxes (lump sum transfers being not available). The first part of the paper is devoted to the study of tax equilibria. Sufficient conditions for the existence of an equilibrium with respect to a given tax system are given. When the tax system is modified, the structure of the corresponding set of tax equilibria is analyzed, and continuity properties of equilibria (with respect to the tax system) are stated. In the second part, attention is focused on the Pareto ranking of tax equilibria. In a given equilibrium, the directions of policy tools changes for a Pareto improvement (if any) are characterized. The "size" of the set of second best Pareto optima in the set of tax equilibria is evaluated.]

[This article uses the concept of "cone of interior displacements," which extends the notion of differentiability, to set up a characterization of Pareto optima in non-convex economies. A general theorem asserting that a Pareto optimum is a PA equilibrium is given and specifications are discussed. It is finally argued that the usual formulation of the doctrine of "marginal cost pricing"--as a doctrine Pareto optimal states in a non-convex decentralized economy--has unsatisfactory logical basis, and a way of defining a minimum degree of centralization inherent to non-convex economies is suggested.]

This article uses the concept of cone of interior displacements, which extends the notion of differentiability, to set up a characterization of Pareto optima in non-convex economies. A general theorem asserting that a Pareto optimum is a PA equilibrium is given and specifications are discussed. It is finally argued that the usual formulation of the doctrine of marginal cost pricingas a doctrine for achieving Pareto optimal states in a non-convex decentralized economy has unsatisfactory logical basis, and a way of defining a minimum degree of centralization inherent to non-convex economies is suggested. THE MAIN RESULTS of the economic theory of allocation of resources rest upon assumptions of convexity: convexity of production sets, and convexity of preferences. The relevance of these assumptions is often doubtful; even if in a many consumer economy the classical statements can be extended to the case of nonconvex preferences (this idea, pointed out first by Farrell [13] and Rothenberg [24], was developed in the general framework of economics with a continuum of agents as introduced by Aumann [4]; see W. Hildenbrand [18 and 19]), the indivisibilities arising in production are often large and create non-convexities that cannot be overlooked. Furthermore, non-convexities may arise with externalities (see Baumol [5], Kolm [20], and Starrett [25]), exchange of information (see Radner [23]), or stock markets (see Dreze [10]). Even if one must take the risk of producing less elegant results, a relevant economic theory cannot ignore non-convexities.

[This article focuses on the desirability of quantity controls in an economy when the first best optimum is not attainable. Based on the analysis of constrained consumer demand, a formula for the desirability of small personalized compensated quotas is first established. Conclusions for the desirability of anonymous quotas: redistribution in kind, rationing, are derived. Actions on prices through taxes and quantity controls are compared. The analysis is also shown to have implications for the theory of optimum income taxation.]

[The paper considers a world in which one public good is financed by commodity taxes. It concentrates on the global study of the set of tax equilibria (corresponding to any possible taxation scheme). In particular conditions for "regularity" and connectedness of this set are exhibited. Consequences obtain both for the positive theory of tax incidence in general equilibrium (existence, continuity, uniqueness) and for normative theory ("regularity" of optimal solutions, algorithms of tax reform...).]

2advantageous. We are particularly concerned in this note by this latter type of cheating which involves initial resources. We point out that besides the intuitive explanation of

, Pierre-Yves Geoffard, Roger Guesnerie, Sunspot Fluctuations Around a Steady State: The Case of Multidimensional One-Step Forward Looking Economic Models, Econometrica, Vol. 60, No. 5 (Sep., 1992), pp. 1097-1126

IN THIS PAPER, we study the existence of a general equilibrium in an economy in which some of the firms behave competitively, whereas others follow special pricing rules. An even casual observation of economic reality confirms the need for the inclusion of price setting firms in the study of general equilibrium models. And, in fact, this has been emphasized in the economic literature for some time. We consider this a sufficient justification to present a general equilibrium model which allows for both types of behavior-price setting as well as price taking behavior. The model to be presented will account for a wide range of price setting rules. We, however, find it appropriate to point out at the start that not all economically relevant price setting rules are covered. Although our model permits the drawing of useful conclusions for the general equilibrium theory of oligopolistic competition through prices, it is not especially designed for that purpose. In particular, our results are not applicable to the general equilibrium analysis with price making monopolistic firms, a subject on which there exists some literature.2 Our motivation as well as our modelling options and assumptions are directed to two fields where an increased interest in the theoretical foundations recently could be noticed.