Cross-listed Securities and Multiple Exchange Memberships: Demand Differentiability and Equilibrium Existence

The previous literature on general equilibrium has assumed that all traders belong to a single market. However, traders often participate in more than one exchange to diversify their portfolios. Moreover, there is evidence that the security listings of exchanges overlap. Our model captures these facts: there are multiple exchanges, the same security is listed in different exchanges, and traders can belong to more than one exchange. We show that, in the presence of convex transaction costs, there exists an equilibrium, and that individual demand is a continuously differentiable function in prices.