The single crossing property plays a crucial role in economic theory, yet there are important instances where the property cannot be directly assumed or easily derived. Difficulties often arise because the property cannot be aggregated: the sum or convex combination of two functions with the single crossing property need not have that property. We introduce a new condition characterizing when the single crossing property is stable under aggregation, and also identify sufficient conditions for the preservation of the single crossing property under multidimensional aggregation. We use our results to establish properties of objective functions (convexity, logsupermodularity), the monotonicity of optimal decisions under uncertainty, and the existence of monotone equilibria in Bayesian games.

We present a model for the equilibrium movement of capital between asset markets that are distinguished only by the levels of capital invested in each. Investment in that market with the greatest amount of capital earns the lowest risk premium. Intermediaries optimally trade off the costs of intermediation against fees that depend on the gain they can offer to investors for moving their capital to the market with the higher mean return. The bargaining power of an investor depends on potential access to alternative intermediaries. In equilibrium, the speeds of adjustment of mean returns and of capital between the two markets are increasing in the degree to which capital is imbalanced between the two markets, and can be reduced by competition among intermediaries.