Buch, Englisch, 131 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 256 g
Buch, Englisch, 131 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 256 g
Reihe: Lecture Notes in Economics and Mathematical Systems
ISBN: 978-3-540-06622-4
Verlag: Springer
In winter 71/72 I held a seminar on general equilibrium theory for a jOint group of students in mathematics and in econo mics at the university of Bonn, w.Germany1~ The economists, how ever, had a mathematical background well above the average • Most of the material treated in that seminar is described in these notes. The connection between smooth preferences and smooth demand func tions [ see Debreu (1972) ] and regular economies based on agents with smooth preferences are not presented here • Some pedagogical difficulties arose from the fact that elementary knowledge of algebraic topology is not assumed although it is helpful and indeed necessary to make some arguments precise • It is only a minor restriction, at present, that functional ana lysis is not used • But with the development of the theory more economic questions will be considered in their natural infinite dimensional setting • Economic knowledge is not required, but especially a reader without economic background will gain much by reading Debreu's classic "Theory of Value" (1959) • Although the formulation of our economic problem uses a map between Euclidean spaces only, we shall also consider ma- folds • Manifolds appear in our situation because inverse images under differentiable mappings between Euclidean spaces are very often differentiable manifolds • ( Under differentiability assump tions, for instance, the graph of the equilibrium set correspon
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Weitere Infos & Material
1. The Economic Framework.- 2. Introduction to the Mathematics.- 3. Differentiable Manifolds and Mappings, Tangents, Vectorfields.- 4. Regular Equilibria. A First Approach.- 5. Scarf’s Example.- 6. Excess Demand Functions.- 7. Debreu’s Theorem on the Finiteness of the Number of Equilibria of an Economy.- 8. Continuity of the Walras Correspondence for C° Demand Functions.- 9. Density of Transversal Intersection.- 10. Regular Economies.- 11. Stability Questions and the Number of Equilibria.- 12. Large Economies.- Some Standard Notation.- References.
