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 = 400 and W_R = 100 and the probability of drought is 0.75.What is Brandon's expected utility? A) 10 B) 17.5 C) 20 D) 30

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Quizplus · Accepted Answer

To calculate the expected utility, we need to find the expected value of Brandon's total water consumption: E(W) = P(drought) * W_D + (1 - P(drought)) * W_R E(W) = 0.75 * 400 + 0.25 * 100 E(W) = 325 We can then use this expected value to calculate the expected utility: E(S(W)) = √E(W) E(S(W)) = √325 E(S(W)) ≈ 18.03 Therefore, Brandon's expected utility is about 18.03, which is closest to option B. As for the best choice, it depends on Brandon's risk preference. If he is risk-averse, he would choose to continue consuming 400 units of water in droughts, since it provides a more certain outcome. If he is risk-neutral or risk-seeking, he might consider shifting some of his consumption to the rainy season, since it provides a higher expected utility.

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