Fig. 5.

The inefficiency of categorical pricing bans. This figure illustrates the efficiency and re-distribution metrics described in Eqs. (14) and (15). When categorization is banned, the market provides the contract A^H (A^L) to high-risk (low-risk) types of both categories. Since this allocation involves positive cross subsidies from low-risk to high-risk types, it also involves redistribution across categories with different risk type fractions. Eq. (15) quantifies this redistribution. Insofar as category is observable, the allocation (A^L, A^H) is also inefficient. In this example, the inefficiency stems from the fact that one category has fewer high-risk types. This means that each risk type within that category can be made at least as well off with the contract pair (A′^L, A′^H) at a lower expected cost to annuity providers. Eq. (14) quantifies this inefficiency.