Monique Florenzano

General Equilibrium Analysis

Warning!! These lecture notes are to help students during the lectures. Reading these notes without attending lectures can be misleading. INTRODUCTION In previous lecture: effects of various trade policies within a partial equilibrium framework Today: changes in relative prices caused by the introduction of tariffs in one market are likely to have general equilibrium effects in other markets This lecture: * Focuses on the neo-classical model of trade (differences in tastes, technologies and factor endowments) * Considers the general equilibrium effects of the introduction of a tariff * Considers the arguments for protection 3

Finite Dimensional Convexity and Optimization

Convexity in Rn.- Separation and Polarity.- Extremal Structure of Convex Sets.- Linear Programming.- Convex Functions.- Differential Theory of Convex Functions.- Convex Optimization With Convex Constraints.- Non Convex Optimization.- Appendix.

Linear and non-linear price decentralization

Compendious and thorough solutions to the existence of a linear price equilibrium problem, the second welfare theorem, and the limit theorem on the core are provided for exchange economies whose consomption sets are the positive cone of arbitrary ordered Frechet-dispensing entirely with the assumption that the vector ordering of the commodity space is a lattice. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory vector orderings that are not lattices, which arise in the typical model of portfolio trading with missing options. The assumptions are on the primitives of the model. They are bounds on the marginals of non-linear prives and for omega-proper economies they are both sufficient and necessary.

Production equilibria in vector lattices

Abstract. The general purpose of this paper is to prove quasiequilibrium existence theorems for production economies with general consumption sets in an infinite dimensional commodity space, without assuming any monotonicity of preferences or free-disposal in production. The commodity space is a vector lattice commodity space whose topological dual is a sublattice of its order dual. We formulate two kinds of properness concepts for agents preferences and production sets, which reduce to more classical ones when the commodity space is locally convex and the consumption sets coincide with the positive cone. Assuming properness allows for extension theorems of quasiequilibrium prices obtained for the economy restricted to some order ideal of the commodity space. As an application, the existence of quasiequilibrium in the whole economy is proved without any assumption of monotonicity of preferences or free-disposal in production.

Edgeworth and Lindahl–Foley equilibria of a General Equilibrium Model with Private Provision of Pure Public Goods

In this paper, we propose a definition of Edgeworth equilibrium for a private ownership production economy with possibly infinitely many private goods and a finite number of pure public goods. We show that Edgeworth equilibria exist and can be decentralized as Lindahl-Foley equilibria, whatever be the dimension of the private goods space. Existence theorems for Lindahl-Foley equilibria are a by-product of our results.

On The Existence Of Berge'S Strong Equilibrium

In this paper, we establish the existence of Berges strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berges strong equilibrium correspondence and prove that most of Berges strong games are essential.

Government and the provision of public goods: from equilibrium models to mechanism design

Abstract This paper investigates to what extent the seminal contribution of Samuelson has been or not incorporated by the theories of general equilibrium and mechanism design in their analysis of optimal public good provision, and more generally of optimal public policy. Our conclusion is that, far from taking up the challenges raised by Samuelsons contribution, both paradigms lead to the negative conclusion of the impossibility of a fully decentralized optimal public goods provision through market or market-like institutions, without giving a key for (re)defining the role of state in market economies.

Linear exchange economies with a continuum of agents

Abstract. The purpose of this paper is to study how the equilibrium prices vary with respect to the initial endowments in a linear exchange economy with a continuum of agents. We first state the model and give conditions of an increasing strength for existence, uniqueness and continuity of equilibrium prices. Then, if we restrict ourselves to economies with essentially bounded initial endowments and if we assume that there is, from the point of view of preferences, only a finite number of types of agents, we show that, on an open dense subset of the space of initial endowments, the equilibrium price vector is an infinitely differentiable function of the initial endowments. The proof of this claim is based on a formula allowing to compute the equilibrium price vector around a so-called “regular” endowment where it is known.

Existence of equilibria in the overlapping generations model. the nontransitive case

SummaryThis paper investigates the existence of competitive equilibria in dynamic exchange models with countably many periods and countably many agents. At each period the commodity space can be finite or infinite dimensional. The preferences of agents are not assumed to be transitive or complete. A first equilibrium existence theorem is established under the classical assumption that there exists a finite set of non-negligible agents. In the particular case of an overlapping generations model, a second existence theorem allows simultaneously for finite-lived assets and infinite-lived assets and limits the previous assumption to infinite-lived assets. This theorem covers obviously the standard case of an overlapping generations model where the agents have no endowment outside their lifetime.

Two lemmas that changed general equilibrium theory

This short paper published in Games and Economic Behavior (July 2009) In Memoriam of David Gale, emphasizes the seminal role played by two lemmas of David Gale in the development of the foundations of General Equilibrium Theory.