A New Approach for General Equilibrium with Discontinuous Excess Demand Function

2005 ◽  
Author(s):  
Zhiping Xie
Keyword(s):  
General Equilibrium ◽  
Demand Function ◽  
Excess Demand ◽  
New Approach

scholarly journals Regular Infinite Economies

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Enrique Covarrubias
Keyword(s):  
Demand Function ◽  
Excess Demand ◽  
Natural Projection ◽  
Banach Manifold ◽  
Equilibrium Manifold ◽  
Equilibrium Set ◽  
Regular Economies

The main contribution of this paper is to place smooth infinite economies in the setting of the equilibrium manifold and the natural projection map à la Balasko. We show that smooth infinite economies have an equilibrium set that has the structure of a Banach manifold and that the natural projection map is smooth. We define regular and critical economies, and regular and critical prices, and we show that the set of regular economies coincides with the set of economies whose excess demand function has only regular prices. Generic determinacy of equilibria follows as a by-product.

Imperfect Competition and General Equilibrium: Elements for a New Approach

1999 ◽  
pp. 125-151
Author(s):  
Claude d'Aspremont ◽  
Dos Santos Ferreira Rodolphe ◽  
Louis‐André Gérard‐Varet
Keyword(s):  
General Equilibrium ◽  
Imperfect Competition ◽  
New Approach

WHAT A DIFFERENCE A SUM (∑) MAKES: SUCCESS AND FAILURE IN THE RATIONALIZATION OF DEMAND

2012 ◽  
Vol 34 (3) ◽  
pp. 379-396 ◽  
Author(s):  
D. WADE HANDS
Keyword(s):  
General Equilibrium ◽  
Excess Demand ◽  
Previous Literature ◽  
Equilibrium Theory ◽  
General Equilibrium Theory ◽  
Success Story ◽  
Demand Functions ◽  
Individual Demand

This paper discusses the Sonnenschein–Mantel–Debreu (SMD) theorems in general equilibrium theory. It argues that the SMD results were related to the previous literature on the integrability of demand. The integrability question involved rationalizing individual demand functions, and the SMD theorems asked the same question about aggregate (market) excess demand functions. The paper’s two goals are to demonstrate how the SMD results followed naturally from the earlier work on integrability, and to point out that the profession’s reception was quite different; the integrability results were considered a success story, while the SMD results were quite negative.

General Equilibrium Theory of Land

2020 ◽  
Author(s):  
Masahisa Fujita
Keyword(s):  
General Equilibrium ◽  
Urban Economics ◽  
Location Theory ◽  
Equilibrium Theory ◽  
General Equilibrium Theory ◽  
New Approach ◽  
Early 21St Century ◽  
Rich Variety ◽  
National Economies ◽  
The Relationship

Land is everywhere: the substratum of our existence. In addition, land is intimately linked to the dual concept of location in human activity. Together, land and location are essential ingredients for the lives of individuals as well as for national economies. In the early 21st century, there exist two different approaches to incorporating land and location into a general equilibrium theory. Dating from the classic work of von Thünen (1826), a rich variety of land-location density models have been developed. In a density model, a continuum of agents is distributed over a continuous location space. Given that simple calculus can be used in the analysis, these density models continue to be the “workhorse” of urban economics and location theory. However, the behavioral meaning of each agent occupying an infinitesimal “density of land” has long been in question. Given this situation, a radically new approach, called the σ-field approach, was developed in the mid-1980s for modeling land in a general equilibrium framework. In this approach: (1) the totality of land, L, is specified as a subset of ℝ2, (2) all possible land parcels in L are given by the σ-field of Lebesgue measurable subsets of L, and (3) each of a finite number of agents is postulated to choose one such parcel. Starting with Berliant (1985), increasingly more sophisticated σ-field models of land have been developed. Given these two different approaches to modeling land within a general equilibrium framework, several attempts have thus far been proposed for bridging the gap between them. But while a systematic study of the relationship between density models and σ-field models remains to be completed, the clarification of this relationship could open a new horizon toward a general equilibrium theory of land.

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