This paper examines justifications of the rational-expectations hypothesis that rely on the analysis of the agents' mental forecasting ("educing") activity (which involves "forecasting the forecasts" of others, etc.). The corresponding concept of eductive learning stability, based on the game-theoretical concept of rationalizability, is primarily used within the classical Muth model. Conditions for coordination of beliefs are interpreted and discussed; they are robust to the introduction of noise. More generally, eductive stability fits economic intuition on coordination: stability increases when the industry product differentiation increases and when decisions are sequential and observable.

[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 paper examines justifications of the rational-expectations hypothesis that rely on the analysis of the agents' mental forecasting ("educing") activity (which involves "forecasting the forecasts" of others, etc.). The corresponding concept of eductive learning stability, based on the game-theoretical concept of rationalizability, is primarily used within the classical Muth model. Conditions for coordination of beliefs are interpreted and discussed; they are robust to the introduction of noise. More generally, eductive stability fits economic intuition on coordination: stability increases when the industry product differentiation increases and when decisions are sequential and observable.

[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

Because sunspot equilibria seem to be of central importance for an understanding of rational expectations, we seek here to characterize completely a limited class of sunspot equilibria (stationary ones with two possible natural events) in the simplest overlapping generations model of production. We present a sufficient condition for the existence of stationary sunspot equilibria, examine how these are related to strictly periodic equilibria of the same order, and investigate how deterministic stationary equilibria bifurcate to stationary sunspot equilibria. A concluding section examines how our results survive in more general settings.