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.