You would like to buy a used car. suppose there are three types of quality (a): low (a = 0), medium (a = 1) and high (a = 3), each equally likely (i. e. each with probability 1 3 ). only the seller knows the exact quality of his/her car. also suppose that for any quality of the car, your utility is 1.6 times the seller’s utility, that is, for a car of quality a, the seller’s utility from it is a, but your utility from it is 1.6ai) the market price for a used car is p. for what values of p, all three types of sellers want to sell? for what values of p, exactly two types want to sell? for what values of p, only one type wants to sell?

Risk is the risk of a decline in a bond's value due to an increase in interest rates. this risk is higher on bonds that have long maturities than on bonds that will mature in the near future. risk is the risk that a decline in interest rates will lead to a decline in income from a bond portfolio. this risk is obviously high on callable bonds. it is also high on short-term bonds because the shorter the bond's maturity, the fewer the years before the relatively high old-coupon bonds will be replaced with new low-coupon issues. which type of risk is more relevant to an investor depends on the investor's , which is the period of time an investor plans to hold a particular investment. longer maturity bonds have high risk but low risk, while higher coupon bonds have a higher level of risk and a lower level of risk. to account for the effects related to both a bond's maturity and coupon, many analysts focus on a measure called , which is the weighted average of the time it takes to receive each of the bond's cash flows. conceptual question: which of the following bonds would have the largest duration? a)10year-zero coupon bonds b)10year-7% annual coupon bonds c)10year-3% annual coupon bonds d)5year-3% annual coupon bonds e)3year-7% annual coupon bonds