This paper examines how, in the presence of individual risk, economic efficiency can be achieved without an unrealistically large number of contingent markets. The authors show that consistency of beliefs and optimality of allocation can be guaranteed with an appropriate array of Arrow...

This paper examines the effects of extrinsic uncertainty or sunspots on competitive equilibrium when financial markets are incomplete. For the canonical two-period, pure-exchange model with bonds (or so-called "nominal assets," yielding overall returns specified in units of account, and...

The authors investigate the structure of competitive equilibria in an exchange economy parametrized by endowments and restrictions on market participation. For arbitrary regular endowments, if few consumers are restricted, there are no sunspot equilibria. If endowments are allowed to vary, while...