We consider the problem of a rational consumer who does not a 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 when a the consumer preferences are transitive; and/or b 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.
