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.Brandon's risk premium is: A) 250 units of water. B) 325 units of water. C) 17.5 units of water. D) 18.75 units of water.

Question

Quizplus · Accepted Answer

Brandon's expected utility from his current consumption bundle is calculated as follows:$$EU = 0.75 \times \sqrt{400} + 0.25 \times \sqrt{100} = 0.75 \times 20 + 0.25 \times 10 = 15 + 2.5 = 17.5$$To find the certain equivalent (CE), we set the utility of the certain equivalent equal to the expected utility:$$\sqrt{CE} = 17.5$$Solving for CE gives:$$CE = 17.5^2 = 306.25$$The risk premium (RP) is the difference between the expected value of the risky prospects and the certain equivalent:$$RP = EV - CE$$The expected value (EV) of the consumption bundle is:$$EV = 0.75 \times 400 + 0.25 \times 100 = 300 + 25 = 325$$Thus,$$RP = 325 - 306.25 = 18.75$$Therefore, Brandon's risk premium is 18.75 units of water.

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