A note on the "size" of determinacy and indeterminacy

Davila Muro, Julio [UCL]

It is shown in this note that in an incomplete markets economy with uncountably many states of the world there may be uncountably many isolated equilibria as well as uncountably many non-isolated equilibria. Moreover, both subsets can be simultaneously of second category. Therefore, none of the subsets can be considered negligible with respect to the other, neither from a cardinality point of view nor from a topological one. Unfortunately, this fact prevents from claiming that these economies may have ``typically'' determinate equilibria ± even though uncountably many of them ± as would have been desirable for comparative statics exercises.