Optimal risk adjustment in a model with adverse selection and spatial competition

We develop a model that incorporates both spatial heterogeneity and adverse selection to examine the features of optimal prices paid by an agency purchasing a bundle of services on behalf of consumers with different underlying characteristics. Service bundles are two dimensional, and to be implementable a proposed allocation must respect incentive compatibility constraints. Equilibrium provision by a duopoly is characterized, and delivery of the constrained optimal bundles is possible, as long as providers are paid risk-adjusted fees for each individual they serve. When the payment can be made on the basis of an individual's type, it should be sufficient to cover the cost of delivering the socially optimal bundle for that person, plus a mark-up over cost. If payments can be made only on the basis of a partially informative signal, the optimal type-based payments should be adjusted according to a simple linear transformation, identified by Glazer and McGuire (2000). Finally, if payments differentiated by consumer type or signal are infeasible, subsidising the cost of one of the services relative to the other can improve welfare, but in general the constrained social optimum cannot be attained.