Question

Sam's utility of wealth function is U(w) =15w. Sam owns and operates a farm. He is concerned that a flood may wipe out his crops. If there is no flood, Sam's wealth is $360,000. The probability of a flood is 1/15. If a flood does occur, Sam's wealth will fall to $160,000.

a. Calculate Sam's expected utility. (please just enter the number, round to integer)

b. Calculate the Sam's risk premium. (please just enter the number, round to integer)

Answer 1

solution : » when there is no floods, income=$ 3, 60,000 , s when there are floode, income = $ 1,60,000. Expected utility of sam is =f(probability of motoccurence of t floods) ((probability of happening of floods floods occus X Income during mo flood) X Income when hon Z + XU 15 (1-5) * 0 (3160,000) (1160,000 x 15 (3160,000) + 5 x 15 (1) 60,000) x 15 (3160,000+ 14% 3169000 t, 1,60,000 5,04 0000. + 1, 60,000 Ev[Uw $ 5,200000. u(wc = 15w= 15W-52000 55,200,000 for WC- 15 we 5,200,000 W = 51200,000 15 be [W=$346, 66 D Sam's risk premium is the difference between current wealth and wc. 360,000 – 346,667 = $ 13,333 Therefore sam is willing to pay $13,333 for insurance against a flood. n