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Singularity Theory and General Equilibrium

In: Mathematical Methods in Economics and Social Choice

Author

Listed:
  • Norman Schofield

    (Washington University in Saint Louis)

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.

Suggested Citation

  • Norman Schofield, 2014. "Singularity Theory and General Equilibrium," Springer Texts in Business and Economics, in: Mathematical Methods in Economics and Social Choice, edition 2, chapter 5, pages 189-229, Springer.
    • Handle: RePEc:spr:sptchp:978-3-642-39818-6_5
    DOI: 10.1007/978-3-642-39818-6_5
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