According to the Rothschild-Stiglitz model (referenced in the Adverse Selection – a definition, some examples, and some solutions blog posting, and on page 22 of the Asymmetric Information: Moral Hazard and Adverse Selection lecture note), insurers will limit contract choices such that there is no adverse selection. To see this, assume there are equal numbers of high-risk and low-risk insureds, all of whom have an initial wealth of $125 and square root utility. There are two states of the world – loss and no loss, and the probabilities of loss are 75% for high-risk types and 25% for low-risk types. By offering high-risk types full coverage at their actually fair price of $75 and offering low-risk types partial (10%) coverage at their actuarially fair price of $2.50, both types of risks buy insurance and there is no adverse selection.
This is illustrated in the figure below and in the spreadsheet located at http://fin4335.garven.com/spring2023/rothschild-stiglitz-model.xls. Clearly, neither the B (full coverage for low-risk insureds) nor C (based on the average cost of the actuarially fair prices for the low-risk and high-risk) contracts would ever be offered because both of these contracts incentivize high-risk types to adversely select against the insurer.
Rothschild-Stiglitz model (numerical and graphical illustration)