Abstract
The goal here is to illustrate ‘global analysis in economics’ by putting the main results of classical equilibrium theory into a global calculus context. The advantages of this approach are fourfold:
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(1)
The proofs of existence of equilibrium are simpler. Kakutani’s fixed point theorem is not used, the main tool being the calculus of several variables.
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(2)
Comparative statics is integrated into the model in a natural way, the first derivatives playing a fundamental role.
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(3)
The calculus approach is closer to the older traditions of the subject.
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In so far as possible the proofs of equilibrium are constructive. These proofs may be implemented by a speedy algorithm, which is Newton’s method modified to give global convergence. On the other hand, the existence proofs are sufficiently powerful to yield the generality of the Arrow—Debreu theory.
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Bibliography
Mas-Colell, A. 1985. The Theory of General Economic Equilibrium, a Differentiable Approach. Cambridge: Cambridge University Press.
Smale, S. 1981. Global analysis and economics. In Handbook of Mathematical Economics, Volume 1, ed. K. J. Arrow and M. D. Intriligator. Amsterdam: North-Holland.
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© 1989 Palgrave Macmillan, a division of Macmillan Publishers Limited
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Smale, S. (1989). Global Analysis in Economic Theory. In: Eatwell, J., Milgate, M., Newman, P. (eds) General Equilibrium. The New Palgrave. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-19802-3_18
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DOI: https://doi.org/10.1007/978-1-349-19802-3_18
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-0-333-49525-4
Online ISBN: 978-1-349-19802-3
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