Suppose all individuals have a utility function of u = √c, where c is the amount of consumption a person has in any given period. there are two types of people: those at high risk, with a 4% chance of accident, and those at low risk, with a 2% chance of accident. half of individuals are high risk, and half are low risk. the income of all individuals is $40,000 per year, and a catastrophic accident costs $30,000. calculate the actuarially fair full insurance premium for each type of person, assuming the insurance company can identify who is high risk and who is low risk.

Suppose you win a small lottery and have the choice of two ways to be paid: you can accept the money in a lump sum or in a series of payments over time. if you pick the lump sum, you get $2,950 today. if you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. 1) at an interest rate of 6% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 2) at an interest rate of 9% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 3) years after you win the lottery, a friend in another country calls to ask your advice. by wild coincidence, she has just won another lottery with the same payout schemes. she must make a quick decision about whether to collect her money under the lump sum or the payments over time. what is the best advice to give your friend? a) the lump sum is always better. b) the payments over time are always better. c) it will depend on the interest rate; advise her to get a calculator. d) none of these answers is good advice.