Utilitarian Social Welfare and Insurance Loss Coverage Under Restricted Risk Classification

This thesis considers the effect of restrictions on insurance risk classification on utilitarian social welfare and insurance loss coverage. First, we consider two regimes: full risk classification, where insurers charge the actuarially fair premium for each risk, and pooling, where risk classification is banned and for institutional or regulatory reasons, insurers do not attempt to separate risk classes, but charge a common premium for all risks. For iso-elastic insurance demand, we derive sufficient conditions on higher and lower risks' demand elasticities which ensure that utilitarian social welfare is higher under pooling than under full risk classification. Using the concept of arc elasticity of demand, we extend the results to a form applicable to more general demand functions. Empirical evidence suggests that the required elasticity conditions for social welfare to be increased by a ban may be realistic for some insurance markets. Next, we consider scenarios where the regulator does not ban risk classification, but instead imposes a price collar, i.e. a limit on the ratio of premiums for high risks relative to those for low risks. Pooling and full risk classification could be considered as limiting cases of a price collar. A regulator imposed price collar would force insurers to use partial risk classification - where some risk-groups might be merged to pay the same premium. We find that for iso-elastic demand, a price collar can give higher loss coverage than either pooling or full risk classification, but only if high and low risks have certain combinations of demand elasticities (both greater than one).