Final answer:
Insurance companies use actuarial analysis to predict losses, determining actuarially fair premiums for each risk group. However, charging an average premium to a mixed-risk group could lead to a situation of adverse selection, impacting the company's risk pool and profitability.
Step-by-step explanation:
Insurance companies use actuarial analysis to predict how many losses will occur in a given group or class of individuals. An actuarially fair premium is a premium that, on average, covers the expected claims costs, and administrative expenses, and includes a provision for profit.
To illustrate, consider a group of 50-year-old men, where 20% have a family history of cancer with a 1 in 50 chance of dying in the next year, and the remaining 80% have a 1 in 200 chance. Separately insuring each group would yield different actuarially fair premiums: Group A with family cancer history would have a higher premium, while Group B without the history would have a lower premium.
If the insurance company cannot differentiate between the two groups due to a lack of information about family cancer histories, they would need to charge one actuarially fair premium to the entire group. This combined premium would be higher than Group B's but lower than Group A's separate premiums. Charging only the average premium for the entire group can be problematic as healthier individuals might find the premium too high and look for insurance elsewhere (adverse selection), leaving the company mostly with higher-risk individuals.