1) On any given day, a salesman can earn $0 with a 20% probability, $100 with a 40% probability, or $300 with a 20% probability.

1a. Calculate the expected value.

1b. Calculate the variance.

2) Peter has a current wealth of $90,000, including his brand new Cadillac which is worth $50,000. His son just got a driver's license and Peter is contemplating whether to (i) let his son borrow the Cadillac, or (ii) buy him a used car as a gift. Peter estimates that the likelihood that his son will total the Cadillac is around 10% and the used car will cost somewhere between $5,000 and $6,000.

2a. If Peter's utility function is given by () = x^0.5, then what is his expected utility from letting his son borrow the Cadillac?

2b. What is the maximum amount that Peter would be willing to pay to buy his son a used car as a gift?

3. Simone is planning an around-the-world trip on which she plans to spend $10,000. The utility from the trip is a function of how much she actually spends on it (x), given by: u(x) = ln(x)

3a. If there is a 25% probability that Simone will lose $1,000 of her cash on the trip, what is the trip's expected utility? Use your calculator, and round to the third decimal point.

3b. Now, suppose that Simone can buy insurance against losing the $1,000 (say, by purchasing traveler's checks) at the actuarially fair price of $250. What is her expected utility if she purchases this insurance? Again, use your calculator and round to the third decimal point.

3c. What is the maximum amount that Simone would be willing to pay to insure her $1,000?