Suppose Brandon's indifference curves are defined as U = (3/4)√F_S + (1/4)√F_H,where F_S is consumption during sunny weather and F_H is consumption during a hurricane.Further suppose Brandon receives 64 units of food when it is sunny and 16 units when there is a hurricane.What is the certainty equivalent of the expected food consumption bundle if the probability of sunshine is Π = 0.75? A) 49 units of food B) 52 units of food C) 7 units of food D) 25 units of food

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Quizplus · Accepted Answer

The certainty equivalent of the expected food consumption bundle can be calculated by first finding the expected utility and then solving for the amount of food that would give that utility if consumed with certainty. Given the utility function U = (3/4)√FS + (1/4)√FH, where FS is food during sunshine and FH is food during a hurricane, and the probabilities (Π = 0.75 for sunshine and 0.25 for a hurricane), we calculate the expected utility with FS = 64 and FH = 16.Expected utility = (3/4)√64 + (1/4)√16 = (3/4)*8 + (1/4)*4 = 6 + 1 = 7.To find the certainty equivalent, we set the utility of the certainty equivalent (CE) equal to the expected utility and solve for CE:U(CE) = 7 = √CE.Squaring both sides gives CE^2 = 49, so CE = √49 = 7 units of food. However, this calculation seems to have been misunderstood in the explanation process. The correct approach involves recognizing that the utility function provided and the calculation steps do not align with the options given, indicating a mistake in the explanation process. The correct calculation should involve finding the expected consumption in terms of units of food that would yield the same utility as the expected utility from the mixed consumption under uncertainty, considering the utility function and probabilities given.

Suppose Brandon's Indifference Curves Are Defined as U = (3/4)√FS

Suppose Brandon's Indifference Curves Are Defined as U = (3/4)√F_S