A feasible social state is irreducible if and only if, for any non-trivial partition of individuals into two groups, there exists another feasible social state at which every individual in the first group is equally well-off and someone strictly better-off. Competitive equilibria decentralize...

Incomplete asset markets cause competitive equilibria to be constrained suboptimal and provides scope for Pareto improving interventions. In this paper, we examine how intervention in prices in asset or spot commodity markets serve this purpose. We show that, if ?x-price equilibria behave...

At arbitrary prices of commodities and assets, fix-price equilibria exist under weak assumptions: endowments need not satisfy an interiority condition, utility functions need only satisfy are very weak monotonicity requirement, and the asset return matrix allows for redundant assets. Prices of...