Notes on "Competition among differentiated health plans under adverse selection" (P. Olivella and M. Vera-Hernandez)

Competition among differentiated health plans under adverse selection 
P. Olivella and M. Vera-Hernandez
In part of Discussion Papers in Economics 03-04. Department of Economics, University College London: London, UK. (2003) 

• the effect of horizontal differentiation in a model of competition among pre-paid health care plans in the presence of adverse selection
• interpret horizontal differentiation as geographical differentiation which it taken as exogenous
• profits derived from a low risk are higher than from a high risk as one of the important empirical implications of our paper. We have proven by example that there exist equilibria with cross-subsidisation, i.e., where the profits derived from high risks are negative.
• the planner has a role to play for sure precisely when the equilibrium presents cross-subsidisation.
• the planner can improve both types' welfare without hurting profits by forcing both firms to correct the distortion imposed on the low risks
• allow us to give more precise predictions on the equilibrium mix of agents that each health plan attracts and on the minimal firm complexity even if transportation costs are arbitrarily small but positive
• allow firms to locate in other points in the line other than the extremes would introduce tow possible extensions
• a simple one where locations are exogenous but not the extremes: firms would gain market power with respect to the agents located around their closest extreme, bit loose market power with respect to the agents located around the centre of the line
• firms choose their location simultaneously in a stage previous to competition: by changing the traveling costs from a linear to a quadratic function of distance, we believe we would obtain the maximum-differentiation result and our results would not be altered.