On the number of critical equilibria separating two equilibria

It is shown that two arbitrary equilibria in the general equilibrium model without sign restrictions on endowments can be joined by a continuous equilibrium path that contains at most two critical equilibria. This property is strengthened by showing that regular equilibria having an index equal to one, a necessary condition for stability, can be joined by a path containing no critical equilibrium. These properties follow from the real-algebraic nature of the set of critical equilibria in any fiber of the equilibrium manifold.Equilibrium prices, equilibrium manifold, equilibrium path, critical equilibrium, catastrophe

General Equilibrium without Utility Functions: How far to go?

How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers’ preferences. We show in this paper that if consumers’ non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: 1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; 2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; 3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; 4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; 5) the pathconnectedness of the sets of stable equilibria.general equilibrium; equilibrium manifold; natural projection; demand functions

Equilibrium Data Sets and Compatible Utility Rankings

Sets consisting of finite collections of prices and endowments such that total resources are constant, or collinear, or approximately collinear, can always be viewed as subsets of some equilibrium manifold. The additional requirement that such collections of price-endowment data are compatible with some individual preference rankings is reduced to the existence of solutions to some set of linear inequalities and equalities. This characterization enables us to give simple proofs of the contractibility of the set whose elements are finite equilibrium data collections compatible with given individual preference rankings and the path-connectedness of the set made of finite equilibrium data set.

The Probability of Condorcet Cycles and Super-Majority Rules

Majority voting aggregates individual preference profiles into a binary relation on the set of alternatives. Condorcet cycles are cycles of the aggregated binary relation. We show that the relative volume of the subset of the (n!−1)-simplex that represents profile distributions such that the aggregated preferences display Condorcet cycles is a decreasing function of the super majority levelτbounded by the expressionThis expression shows that Condorcet cycles become rare events for super majority rules larger than 53%

Market Participation and Sunspot Equilibria

We investigate the structure of competitive equilibria in an exchange economy parametrized by (i) endowments and (ii) restrictions on market participation. For arbitrary regular endowments, if few consumers are restricted, there are no sunspot equilibria. If endowments are allowed to vary, while restrictions on market participation are fixed, there is a generic set of preferences such that sunspot equilibria exist for a non-empty subset of endowments. Our analysis extends to the general case of an arbitrary number of restricted consumers the results of Cass and Shell for the polar cases in which either (i) no consumers are restricted or (ii) all consumers are restricte

Pareto : improving default

Fil: Balasko, Yves. Universidad de San Andrés. Departamento de Economía; Argentina.Fil: Kawamura, Enrique. Universidad de San Andrés. Departamento de Economía; Argentina.This paper answers the question of whether non-strategic default improves welfare, not only for borrowers with uncertain future income but also for lenders with certain future endowments, relative to no default. We show that the answer is a¢ rmative for a positive- Lebesgue-measure set of individual endowments. Numerical computations show that the size of such endowment set is larger the larger are both the risk aversion and the probability of default. Other numerical examples show that with defaultable securities lenders may nance the purchase of the latter by selling short default-free assets. This portfolio reminds those of hedge-funds such as LTCM