For the second question, the insurer would not make a positive economic profit if they offer a premium of $2,000. The expected healthcare costs for the low-risk subgroup are $1,000 (10% x $10,000), so they would not be willing to pay a premium of $2,000 which is higher than their expected costs plus the additional $1,500 they are willing to pay due to their risk aversion. The expected healthcare costs for the high-risk subgroup are $5,000 (50% x $10,000), and they would be willing to pay a premium of $6,500 ($5,000 expected costs plus $1,500 additional premium due to their risk aversion). However, if the insurer charges a premium of $2,000, they would not make a positive economic profit since the premium collected is lower than the expected healthcare costs for the high-risk subgroup.