This paper investigates the economics of uncertainty using a state-contingent approach with a focus on the role of non-convexity. Under efficiency, the slopes of a separating hypersurface measures state-contingent prices. As argued by Yaari, normalized state-contingent prices provide a measure of subjective probabilities. But efficiency under non-convexity can require non-linear pricing. The analysis identifies non-convexity conditions under which probability assessments are not appropriate. Implications for economic and welfare analysis under uncertainty are discussed.