The Equilibrium Manifold and the Natural Projection

2009 ◽  
Keyword(s):  
Natural Projection ◽  
Equilibrium Manifold

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.

The Exchange Model

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
General Equilibrium ◽  
Smooth Manifold ◽  
Comparative Statics ◽  
Exchange Model ◽  
Natural Projection ◽  
Equilibrium Models ◽  
Manifold Structure ◽  
Equilibrium Manifold ◽  
Complex Models ◽  
Smooth Map

The exchange model is the simplest of all general equilibrium models. Studying it will show us the directions to follow when studying more complex models like those that include production or take explicitly into account time and uncertainty. This chapter introduces the exchange model defined by the equilibrium manifold and the natural projection. It presents proof that the equilibrium manifold is indeed a smooth manifold. The smooth manifold structure implies that the natural projection is a smooth map. In terms of comparative statics, this tells us that equilibrium prices can be considered as depending linearly on the fundamentals defining an economy in sufficiently small neighborhoods of regular equilibria.

scholarly journals NMPC WITH STATE-SPACE MODELS OBTAINED THROUGH LINEARIZATION ON EQUILIBRIUM MANIFOLD

2006 ◽  
Vol 39 (2) ◽  
pp. 1015-1020
Author(s):  
Stephan Koch ◽  
Ricardo G. Duraiski ◽  
Pedro Bolognese Fernandes ◽  
Jorge O. Trierweiler
Keyword(s):  
State Space ◽  
State Space Models ◽  
Equilibrium Manifold

UNKNOTTING OF PSEUDO-RIBBON n-KNOTS

2004 ◽  
Vol 13 (02) ◽  
pp. 259-275 ◽  
Author(s):  
KYOUHEI YOSHIDA
Keyword(s):  
Disjoint Union ◽  
The Self ◽  
Natural Projection ◽  
Double Points

Let K be a classical knot in ℝ3. We can deform the diagram of K to that of a trivial knot by changing the overcrossings and undercrossings at some double points of the diagram of K. We consider the same problem for higher dimensinal knots. Let n≥2 and π:ℝn+2=ℝn+1×ℝ→ℝn+1 denote the natural projection map. A pseudo-ribbon n-knot is an n-knot f:Sn→ℝn+2 such that the self-intersection set of π◦f:Sn→ℝn+1 consists of only double points and is homeomorphic to a disjoint union of (n-1)-spheres. We prove that for n≠3,4, the projection (π◦f)(Sn)⊂ℝn+1 of any pseudo-ribbon n-knot f is the projection of a trivial n-knot.

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