Singularity Theory and General Equilibrium

Norman Schofield
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Norman Schofield: Washington University in Saint Louis

Chapter 5 in Mathematical Methods in Economics and Social Choice, 2014, pp 189-229 from Springer

Abstract: Abstract In Chap. 5 we introduce the fundamental result in singularity theory, that the set of singularity points of a smooth preference profile almost always has a particular geometric structure. We then go on to use this result to discuss the Debreu-Smale Theorem on the generic existence of regular economies. Section 5.4 uses an example of Scarf (Int. Econ. Rev. 1:157–172, 1960) to illustrate the idea of an excess demand function for an exchange economy. The example provides a general way to analyse a smooth adjustment process leading to a Walrasian equilibrium. Sections 5.5 and 5.6 introduce the more abstract topological ideas of structural stability and chaos in dynamical systems.

Keywords: Vector Field; Phase Portrait; Price Equilibrium; Smooth Manifold; Closed Orbit (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-642-39818-6_5

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