Incompatibility of Usual Conditions for Equilibrium Existence in Continuum Economies without Ordered Preferences

In recent years attempts were made to extend the equilibrium existence results of Gale and Mas-Colell (1975, J. Math. Econ. 2, 9 15) and Shafer and Sonnenschein (1975, J. Math. Econ. 2, 345 348) to continuum economies. Here it is shown that the usual conditions used for these attempts force the ``preferred to'' correspondence to be empty-valued almost everywhere on the nonatomic part of the measure space of agents. Several published continuum extensions of the existence results of Shafer and Sonnenschein are thus rendered pointless. Journal of Economic Literature Classification Number: C72. 2000 Academic Press