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Computable Demand

Author

Listed:
  • Marcel K. Richter

    (University of Minnesota)

  • Kam-Chau Wong

    (Chinese University of Hong Kong)

Abstract

A natural bound on rationality arises from computability:-I can't use a number if I can't compute it, and \hfill\break -I can't use a preference relation or utility function that I can't compute.We assume that all magnitudes (quantities, prices) are computable real numbers, and all relations and functions (preference, utility, and demand) are computable. Although several other approaches to computability have led to negative results, we show that a theory of computably bounded consumer demand is possible: a) computable quasiconcave utility functions (equivalently, computable convex preferences) have computable demand bundles, and b) their demand functions are also computable; c) we provide a behavioral characterization of computable rationality for finite data; and d) we give algorithmic procedures for computing demand functions and for approximating demand correspondences of c-quasiconcave computable utility functions.Beyond bounded rationality, these results have implications for the foundations for computational economics: they establish that certain algorithms exist, and certain others do not. Our proof shows that quasiconcavity is a useful assumption in computing maximizers.The positive results hold in spite of the fact that commodity spaces, though dense, are not topologically complete.

Suggested Citation

  • Marcel K. Richter & Kam-Chau Wong, 2000. "Computable Demand," Computing in Economics and Finance 2000 260, Society for Computational Economics.
    • Handle: RePEc:sce:scecf0:260
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