Final answer:
The life insurance scenario demonstrates how actuarially fair premiums are calculated and the adverse selection problem that arises when premiums do not reflect individual risk levels. Healthier individuals are more likely to opt out of insurance if the premium is higher than their expected payout, while higher-risk individuals will purchase insurance, potentially causing financial losses for the insurer.
Step-by-step explanation:
The subject of this question is related to the field of insurance and actuarial science, which is a part of the broader business discipline. The scenario described involves calculating premiums for life insurance policies and addresses the concept of adverse selection within insurance markets.
Let's consider a group of 1,000 50-year-old men divided into two categories based on family history of cancer. For those with a family history (20% of the group), the probability of dying in the next year is 1 in 50. For those without (80% of the group), the probability is 1 in 200. An insurance policy is being sold that offers a $100,000 payout upon death within the next year. To find the actuarially fair premium, we calculate the expected payout and divide it by the number of policyholders.
a. Actuarially fair premium for each group:
- With family history: (1/50) * $100,000 = $2,000
- Without family history: (1/200) * $100,000 = $500
b. Actuarially fair premium for the whole group:
Combining both groups, the overall fair premium can be calculated by weighting the premiums according to the proportion of each group in the population: (0.2 * $2,000) + (0.8 * $500) = $900.
c. Consequences of charging the fair premium to the whole group:
If the insurance company charges the actuarially fair premium to the entire group without distinguishing between the two groups, there will be an adverse selection problem. Individuals with a family history of cancer will find the premium more attractive than those without, as it is cheaper than their fair premium of $2,000. However, healthier individuals will opt out because $900 is more expensive than their fair premium of $500. This imbalance can lead to the pool of insured individuals being riskier than average, potentially causing financial losses to the company.
The example of auto insurance demonstrates the problem of adverse selection, where asymmetric information leads to only high-risk individuals purchasing insurance at a set price, ultimately resulting in significant losses for the insurance company due to payouts far exceeding premiums collected.