3. I[ Option Value) Suppose that you are assessing the value of a storm barrier to reduce the ilnpact of ooding in downtown Manhattan. The barrier is especially useful during those years when the city experiences ooding {which occurs about 15% of the time}. The payoffs (measured in billions of 3 of annual GDP] with and without the barrier are given below: Barrier No Barrier No Flooding $105 $100 Flooding $90 $T5 (a) {4 points) What is the expected value of annual GDP if no barrier is built? (b) {4 points} What is the expected value of annual GDP if the barrier is built? (c) (6 points} W'hat is the variance of annual GDP if no barrier is built? (d) (6 points} What is the variance of annual GDP if the barrier is built? (e) (5 points) What is the expected surplus from building the barrier? (f) {3 points} Assuming that the decisionmaker is riskaverse. is the option price of the bar rier greater than, equal to or less than the expected surplus you calculated in part (c)? (g) Suppose the decisionmaker's utility function is given by U[g) = ln 9 where g is GDP. i. (3 points) Is the decisionmaker risk averse? ii. [ti points} Compute the option price of the barrier, to the nearest $10 million. iii. [3 points} Compute the option value of the barrier, to the nearest $10 million