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)

Can Price Collars Increase Insurance Loss Coverage?

Loss coverage, defined as expected population losses compensated by insurance, is a public policy criterion for comparing different risk classification regimes. Using a model with two risk-groups (high and low) and iso-elastic demand, we compare loss coverage under three alternative regulatory regimes: (i) full risk-classification (ii) pooling (iii) a price collar, whereby each insurer is permitted to set any premiums, subject to a maximum ratio of its highest and lowest prices for different risks. Outcomes depend on the comparative demand elasticities of low and high risks. If low-risk elasticity is sufficiently low compared with high-risk elasticity, pooling is optimal; and if it is sufficiently high, full risk classification is optimal. For an intermediate region where the elasticities are not too far apart, a price collar is optimal, but only if both elasticities are greater than one. We give extensions of these results for more than two risk-groups. We also outline how they can be applied to other demand functions using the construct of arc elasticity

When is utilitarian welfare higher under insurance risk pooling?

This paper focuses on the effects of bans on insurance risk classification on utilitarian social welfare. 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 the case of 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. Empirical evidence suggests that these conditions may be realistic for some insurance markets

When is utilitarian welfare higher under insurance risk pooling?

This paper considers the effect of bans on insurance risk classification on utilitarian social welfare. 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