8 - Genericity analysis
Published online by Cambridge University Press: 05 January 2013
Summary
This chapter has two purposes. The first is to make good on the repeated promise to justify our attention to regular objects by establishing their typicality or, in the terminology of this chapter, their genericity. Hence, we shall argue that whenever a property has been called regular, the term is deserved. The second purpose is to illustrate by reiterated application the uses of transversality theory, an important mathematical technique that can be informally described to economists as a sophisticated version of the old counting of equations and unknowns.
A general introduction to the generic point of view is presented in Section 8.2. Section 8.3 describes the formal setting underlying the mathematical transversality theorems. Those are then applied to an investigation of the generic structure of demand (Section 8.4), production (Section 8.5), optima (Section 8.6), equilibria (Section 8.7), and some aspects of the equilibrium correspondence (Section 8.8). The aim is not to be exhaustive but to discuss a repertoire of typical situations and useful tricks. It is part of the objective of the chapter to make clear that, although they may differ in degree of complexity, most genericity arguments are, at bottom, very similar.
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- Information
- The Theory of General Economic EquilibriumA Differentiable Approach, pp. 316 - 352Publisher: Cambridge University PressPrint publication year: 1985