Ebook: Differential Topology and General Equilibrium with Complete and Incomplete Markets

General equilibrium In this book we try to cope with the challenging task of reviewing the so called general equilibrium model and of discussing one specific aspect of the approach underlying it, namely, market completeness. With the denomination "general equilibrium" (from now on in short GE) we shall mainly refer to two different things. On one hand, in particular when using the expression "GE approach", we shall refer to a long established methodolog­ ical tradition in building and developing economic models, which includes, as of today, an enormous amount of contributions, ranging in number by several 1 thousands • On the other hand, in particular when using the expression "stan­ dard differentiable GE model", we refer to a very specific version of economic model of exchange and production, to be presented in Chapters 8 and 9, and to be modified in Chapters 10 to 15. Such a version is certainly formulated within the GE approach, but it is generated by making several quite restrictive 2 assumptions • Even to list and review very shortly all the collective work which can be ascribed to the GE approach would be a formidable task for several coauthors in a lifetime perspective. The book instead intends to address just a single issue. Before providing an illustration of its main topic, we feel the obligation to say a word on the controversial character of GE. First of all, we should say that we identify the GE approach as being based 3 on three principles .

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The goal of this publication is to provide basic tools of differential topology to study systems of nonlinear equations, and to apply them to the analysis of general equilibrium models with complete and incomplete markets. The main content of general equilibrium analysis is to study existence, (local) uniqueness and efficiency of equilibria. To study existence Differential Topology and General Equilibrium with Complete and Incomplete Markets combines two features. As a first step, first order conditions (of agents' maximization problems) and market clearing conditions, instead of aggregate excess demand functions, are used. As a second step, a homotopy argument, stated and proved in relatively elementary manner, is applied to that "extended systemof equations. Local uniqueness and smooth dependence of the endogenous variables from the exogenous ones are studied using a version of a so called parametric transversality theorem.

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The goal of this publication is to provide basic tools of differential topology to study systems of nonlinear equations, and to apply them to the analysis of general equilibrium models with complete and incomplete markets. The main content of general equilibrium analysis is to study existence, (local) uniqueness and efficiency of equilibria. To study existence Differential Topology and General Equilibrium with Complete and Incomplete Markets combines two features. As a first step, first order conditions (of agents' maximization problems) and market clearing conditions, instead of aggregate excess demand functions, are used. As a second step, a homotopy argument, stated and proved in relatively elementary manner, is applied to that "extended systemof equations. Local uniqueness and smooth dependence of the endogenous variables from the exogenous ones are studied using a version of a so called parametric transversality theorem.
Content:
Front Matter....Pages i-xxxi
Front Matter....Pages 1-1
Prerequisites....Pages 3-27
Manifolds in Euclidean Spaces....Pages 29-48
Differentials....Pages 49-78
Regular Values....Pages 79-106
Manifolds with Boundary....Pages 107-132
Sard’s Theorem and Transversality....Pages 133-158
Homotopy and Degree Theory....Pages 159-204
Front Matter....Pages 205-205
Exchange Economies....Pages 207-256
Production Economies....Pages 257-287
Time, Uncertainty and Incomplete Markets....Pages 289-305
Numeraire Assets....Pages 307-326
Nominal Assets....Pages 327-354
Real Assets....Pages 355-393
Restricted Participation....Pages 395-415
Planner Intervention on the Market Outcome....Pages 417-460
Back Matter....Pages 461-473

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The goal of this publication is to provide basic tools of differential topology to study systems of nonlinear equations, and to apply them to the analysis of general equilibrium models with complete and incomplete markets. The main content of general equilibrium analysis is to study existence, (local) uniqueness and efficiency of equilibria. To study existence Differential Topology and General Equilibrium with Complete and Incomplete Markets combines two features. As a first step, first order conditions (of agents' maximization problems) and market clearing conditions, instead of aggregate excess demand functions, are used. As a second step, a homotopy argument, stated and proved in relatively elementary manner, is applied to that "extended systemof equations. Local uniqueness and smooth dependence of the endogenous variables from the exogenous ones are studied using a version of a so called parametric transversality theorem.
Content:
Front Matter....Pages i-xxxi
Front Matter....Pages 1-1
Prerequisites....Pages 3-27
Manifolds in Euclidean Spaces....Pages 29-48
Differentials....Pages 49-78
Regular Values....Pages 79-106
Manifolds with Boundary....Pages 107-132
Sard’s Theorem and Transversality....Pages 133-158
Homotopy and Degree Theory....Pages 159-204
Front Matter....Pages 205-205
Exchange Economies....Pages 207-256
Production Economies....Pages 257-287
Time, Uncertainty and Incomplete Markets....Pages 289-305
Numeraire Assets....Pages 307-326
Nominal Assets....Pages 327-354
Real Assets....Pages 355-393
Restricted Participation....Pages 395-415
Planner Intervention on the Market Outcome....Pages 417-460
Back Matter....Pages 461-473
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