Abstract
We consider the problem of a rational consumer who does nota priori know what his optimal feasible consumption bundle is, but attempts to find it by continuously moving in a direction of increasing preferences, starting with an arbitrary bundle. We show that this process is only then guaranteed to lead to the consumption optimum whena the consumer preferences are transitive; and/orb the consumer follows in each point the exact direction of fastest preference increase (that is in the integrable case: the utility gradient). If this is not the case, there may exist limit cycles to which the consumer may get attracted, thus never reaching his optimum.
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This note is dedicated to Yves Richelle, the ever-cycling economist.
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Deissenberg, C. Limit cycles in local preference optimization. Ann Oper Res 37, 125–140 (1992). https://doi.org/10.1007/BF02071052
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DOI: https://doi.org/10.1007/BF02071052