Final answer:
If an individual is not risk-averse and has no family history of cancer, their expected loss is $1,000, which is much less than the $2,560 insurance premium. Therefore, it is financially rational not to buy the insurance as the expected loss is smaller than the premium. This decision-making is based on expected loss calculations and considers adverse selection in insurance markets. Therefore, correct option is: You don't buy coverage because your expected loss is smaller than the premium.
Step-by-step explanation:
Understanding Insurance and Expected Loss
When considering whether to purchase insurance, an individual should assess the expected loss versus the cost of the insurance premium. If an individual is not risk-averse and does not have a family history of cancer, the expected spending is $1,000 since 96% of the population spend that amount on average. Calculating the expected loss without insurance in this scenario involves multiplying the probability of an event with its potential cost.
For example, if the probability is 4% (0.04) to spend $40,000 and 96% (0.96) to spend $1,000, the expected loss would be (0.04*$40,000) + (0.96*$1,000), which equals $2,560. Considering the individual has no family history of cancer, their expected loss from healthcare spending due to cancer is likely to be the lower amount of $1,000 - much less than the $2,560 insurance premium.
Therefore, a rational decision for an individual who is not risk-averse and has no family history of cancer would be not to purchase the insurance, as their expected loss is smaller than the premium. This decision aligns with the concept that low-risk individuals often opt out of insurance when premiums reflect average risks that include high-risk individuals - a phenomenon that can lead to adverse selection in insurance markets. In conclusion, based on the expected loss being smaller than the insurance premium, the correct option is: You don't buy coverage because your expected loss is smaller than the premium.