Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 36 and W_R = 25 and the probability of drought is 0.75.Brandon's certainty equivalent is: A) 45.75 units of water. B) 33.06 units of water. C) 30.5 units of water. D) 61 units of water.

Question

Quizplus · Accepted Answer

To find Brandon's certainty equivalent, we need to first calculate the expected utility of his current consumption bundle: EU(W_D) = 0.75√36 + 0.25√25 ≈ 15.93 EU(W_R) = 0.25√36 + 0.75√25 ≈ 13.95 Then, we need to find the amount of water that would give Brandon the same utility as the expected utility of his current consumption bundle. This is his certainty equivalent. CE = (√CE)² = EU(W_D) (0.75) + EU(W_R) (0.25) CE = (√CE)² = (0.75)(15.93) + (0.25)(13.95) CE ≈ 14.89 Therefore, Brandon's certainty equivalent is approximately 14.89 units of water. The closest choice to this is B, 33.06 units of water, so the answer is B. This means that if Brandon is risk-averse, he would prefer to consume 33.06 units of water for sure instead of taking his chances with his current consumption bundle.

Assume Brandon's Benefit Function for Water Is S(W)= √W and He