We investigate the structure of competitive equilibria in an exchange
economy parametrized by (i) endowments and (ii) restrictions on market
participation. For arbitrary regular endowments, if few consumers are
restricted, there are no sunspot equilibria. If endowments are allowe
d to vary, while restrictions on market participation are fixed, there
is a generic set of preferences such that sunspot equilibria exist fo
r a non-empty subset of endowments. Our analysis extends to the genera
l case of an arbitrary number of restricted consumers the results of C
ass and Shell for the polar cases in which either (i) no consumers are
restricted or (ii) all consumers are restricted.