Question

macmillan learning decisions involving uncertainty - end of chapter problem according the u.s. fire administration (check out the source for some very informative and sobering statistics about fires in the u.s.), there were around 383,974 residential fires in the u.s. in 2017. according the u.s. census bureau there were about 126,220,000 households in the u.s. in 2017. therefore, any household faces a 0.304% chance of a fire in a year. suppose you are looking at purchasing renters insurance that costs $10 a month and provides you with $20,000 a year in coverage in the event of a fire. a. what is the expected monthly payout of this policy? expected monthly payout: $

Answer 1

The actuarially fair premium for 50-year-old men with a family history of cancer would be $2,000, whereas it would be $500 for those without such a history. When considering the entire group without differentiating risk, the fair premium would be $800. However, this could cause adverse selection, where low-risk individuals opt out, leaving the insurer with insufficient premiums to cover the riskier pool.

Step-by-step explanation:

To calculate the actuarially fair premium for life insurance, we consider the probability of the event (death) occurring and the payout upon the event. Given that 20% of the 50-year-old men have a family history of cancer, with a 1 in 50 chance of dying, and the remaining 80% with a 1 in 200 chance, we would calculate the premiums as follows:

Group 1 (Family history of cancer):

• 200 men x (1/50 chance of death) x $100,000 payout = $400,000 total expected payout
• Actuarially fair premium for Group 1 = $400,000 / 200 = $2,000 per person per year

Group 2 (No family history of cancer):

• 800 men x (1/200 chance of death) x $100,000 payout = $400,000 total expected payout
• Actuarially fair premium for Group 2 = $400,000 / 800 = $500 per person per year

For the entire group:

• Total expected payout = Group 1 payout + Group 2 payout = $400,000 + $400,000 = $800,000
• Actuarially fair premium for the entire group = $800,000 / 1,000 = $800 per person per year

However, if the insurance company charges the entire group the same premium, individuals with lower risk might opt out, leaving the insurer with mostly higher risk individuals, leading to adverse selection. This could render the company's premiums insufficient to cover payouts, potentially causing financial losses.