Suppose a consumer's expected utility function given two possible states of nature A and B can be expressed in terms of consumption of food,F,in both states as U(F_A,F_B)= [0.6 × ln(F_A)] + [0.4 × ln(F_B)].For this utility function,MU_A is (0.6/F_A)and MU_B is (0.4/F_B).Without insurance,the consumer can consume 200 in state A but only 50 in state B. The consumer can purchase insurance at a premium of 50 cents per dollar of benefit. Which of the following gives her budget line? A) F_A = 250 - F_B B) F_B = 250 - F_A C) F_A = 200 - F_B D) F_B = 50 - F_A

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Quizplus · Accepted Answer

The budget line will represent the different combinations of consumption in states A and B that the consumer can afford given her income and the cost of insurance. Let F_A be consumption of food in state A and F_B be consumption of food in state B. Then, the consumer's income without insurance is $200 (in state A) and $50 (in state B), so her budget constraint is: F_A + F_B <= 200 in state A and F_A + F_B <=50 in state B Multiplying both sides by 0.5 (to account for the cost of insurance) gives: 0.5F_A + 0.5F_B <= 100 in state A and 0.5F_A + 0.5F_B <= 25 in state B Simplifying, we get: F_A + F_B <= 200 in state A and F_A + F_B <= 50 in state B which is equivalent to: F_B = 250 - F_A Therefore, the correct answer is B: F_B = 250 - F_A.

Suppose a Consumer's Expected Utility Function Given Two Possible States