Contingent Commodities and Implementation

In this note we consider the problem whether contingent commodity allocations can be used when the states are not directly contractible. In such a setting a contingent commodity allocation takes the form of a social choice function, and the question is whether this function is implementable (in the sense of full implementation). Using only very mild assumptions on the rule for selecting contingent commodity allocations, we derive a strong negative result which also proves to be robust with respect to different solution concepts employed for implementation. These findings have interesting implications for the interpretation of Arrow-Debreu economies.