Walrasian solutions without utility functions

This note reviews consumers’ preference orderings in economics and shows that irrationality is a poor explanation for apparent violations of some axioms of order. Apparent violations seem to be better explained by the fact that consum-ers’ utility functions, if they exist at all, might not even belong to the class of quasi-concave functions. However, the main task of markets is the determination of equilibrium price vectors. The note shows in addition that, in Walrasian structures, quasi-concave utility functions are unnecessary for the determination of equilibrium price vectors.