1,720,973 research outputs found
A note on local uniqueness of equilibria: How isolated is a local equilibrium?
Get PDFThe motivation of this note is to show how singular values affect local uniqueness. More precisely, Theorem 3.1 shows how to construct a neighborhood (a ball) of a regular equilibrium whose diameter represents an estimate of local uniqueness, hence providing a measure of how isolated a (local) unique equilibrium can be. The result, whose relevance in terms of comparative statics is evident, is based on reasonable and natural assumptions and hence is applicable in many different settings, ranging from pure exchange economies to non-cooperative games
Manipulation of endowments and sunspot equilibria
No full textWe study the connection between occurrence of manipulation via
reallocating endowments by coalitions and sunspot equilibria. The uncertainty about which coalition will form introduces extrinsic uncertainty into the economy. Under certain conditions, manipulation of endowments by coalitions can occur if and only if sunspots matter
A riemannian metric on the equilibrium manifold
No full textUnder the assumption that the utility function is real analytic, we construct a complete metric on the equilibrium manifold with fixed total resources such that a minimal geodesic joining any two regular equilibria intersects the set of critical equilibria in a finite number of points
Minimality and uniqueness of equilibrium
Get PDFIn this paper we propose the following conjecture: the equilibrium manifold E(r) is a minimal submanifold if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and for an arbitrary number of consumers and two goods under the assumption that the normal vector field of E(r) is constant outside a compact subset
Measures of economies with an arbitrarily large number of equilibria
No full textBalasko (1978) shows that in a compact subset of the space of economies, not too many economies can have too many equilibria. We extend Balasko’s result to the whole set of economies for a suitable measure. We show that the measure of economies with a large number of equilibria approaches zero as this number tends to infinity. An analogous result in the infinite-dimensional setting is also established
Evolution paths on the equilibrium manifold
No full textIn a pure exchange smooth economy with fixed total resources, we define the length between two regular equilibria belonging to the equilibrium manifold as the number of intersection points of the evolution path connecting them with the set of critical equilibria. We show that there exists a minimal path according to this definition of length
A note on the structural stability of the equilibrium manifold
Get PDFIn a smooth pure exchange economy with fixed total resources we
investigate whether the smooth selection property holds when endowments are
redistributed across consumers through a continuous (non local) redistribution
policy. We show that if the policy is regular then there exists a unique continuous
path of equilibrium prices which support it. If singular economies are involved in
the redistribution, then an analogous result can be obtained if the singular policy
is the projection of a path transversal to the set of critical equilibria
Geodesics on the equilibrium manifold
No full textWe show the existence of a Riemannian metric on the equilibrium manifold Such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, Outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning
Structural stability and catastrophes
No full textWe show that, in a pure exchange smooth economy, a redistribution of endowments involving singular economies can be supported by a unique and continuous path of supporting equilibrium price vectors if this redistribution is the projection of a path on the equilibrium manifold transversal to the set of critical equilibria
Endowments, patience types, and uniqueness in two-good HARA utility economies
Get PDFThis paper establishes a link between endowments, patience types, and the parameters of the HARA Bernoulli utility function that ensure equilibrium uniqueness in an economy with two goods and two impatience types with additive separable preferences. We provide sufficient conditions that guarantee uniqueness of equilibrium for any possible value of γ in the HARA utility function γ 1−γ b+ a
γx 1−γ. The analysis contributes to the literature on uniqueness in pure exchange economies with two-goods and two agent types and extends the result in Loi and Matta (2022)
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