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This paper studies competitive equilibria in economies characterized by the presence of asymmetric information, where non-exclusive contracts are traded on competitive markets and agents may be privately informed over their payoff. For such economies competitive equilibria may not exist when contracts trade at linear prices. We show that (non-trivial) competitive equlibria exist, under general conditions, with a minimal requirement on the observability of agents' trades: two-part tariffs suffice, where the cost of trading each contract consists of an entry fee and a linear component in the quantity traded. The entry fee is determined at equilibrium and represents a measure of adverse selection in the economy. (Copyright: Elsevier)