Contingent commodities and implementation

In this note we study the relevance of using contingent commodity allocations when 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. Using only very mild assumptions on the rule for selecting contingent commodity allocations, we derive a strong negative result which 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.