Imagine that 50-year-old men can be divided into two groups: those who have a family history of cancer and those who do not. For the purposes of this example, say that 20% of a group of 1,000 men have a family history of cancer, and these men have one chance in 50 of dying in the next year, while the other 80% of men have one chance in 200 of dying in the next year. The insurance company is selling a policy that will pay $50,000 to the estate of anyone who dies in the next year. a. If the insurance company were selling life insurance separately to each group, what would be the actuarially fair premium for each group?
b. If an insurance company were offering life insurance to the entire group, but could not find out about family cancer histories, what would be the actuarially fair premium for the group as a whole?
c. What will happen to the insurance company if it tries to charge the actuarially fair premium to the group as a whole rather than to each group separately?

2. taxes paid for a given income level rosa is getting ready to do her taxes. she is single and lives in denver. rosa earned $60,000 in taxable income in 2015. she reviews the following table, which shows the irs tax rates for a single taxpayer in 2015. on annual taxable the tax rate (percent) up to $9,225 10.0 from $9,225 to $37,450 15.0 from $37,450 to $90,750 25.0 from $90,750 to $189,300 28.0 from $189,300 to $411,500 33.0 from $411,500 to $413,200 35.0 over $413,200 39.6 based on the irs table, rosa calculates that her marginal tax rate is when her annual taxable income is $60,000. rosa calculates that she owes in income taxes for 2015. rosa then calculates that her average tax rate is , based on the annual income level and the amount of taxes she owes for 2015. after figuring out what she owes in taxes in 2015, rosa decides to ask an accountant for tax advice. the accountant claims that he has found a legal way to shelter $4,000 of taxable income from the federal government. the maximum amount that rosa is willing to pay to learn this strategy and reduce her taxable income by $4,000 is . (hint: sheltering some income means finding a legal way to avoid being charged income tax on that income. for example, someone who has $50,000 in taxable income and shelters $10,000 pays income tax on only $40,000.)