Bob and Ray are thinking of buying a sofa.Bob's utility function is U_B(S, M_B)= (1 + S )M_B and Ray's utility function is U_R(S, M_R)= (3 + S )M_R, where S = 0 if they don't get the sofa and S = 1 if they do and where M_B and M_R are the amounts of money they have respectively to spend on their private consumptions.Bob has a total of $1,200 to spend on the sofa and other stuff.Ray has a total of $1,600 to spend on the sofa and other stuff.The maximum amount that they could pay for the sofa and still arrange to both be better off than without it is A)$1,500. B)$533.33. C)$550. D)$1,000. E)$2,000.

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Quizplus · Accepted Answer

To determine the maximum amount they could pay for the sofa and still be better off, we need to compare their utility with and without the sofa. Bob's utility increases by 1 unit if they get the sofa, and Ray's utility increases by 3 units. The total money they have is $1,200 + $1,600 = $2,800. To ensure both are better off, the cost of the sofa must be such that the remaining money, when allocated optimally between them, increases their utility more than the utility gain from the sofa. Since their combined utility gain from the sofa is 4 units (1 for Bob and 3 for Ray), and they have a total of $2,800, the maximum they could pay for the sofa while ensuring they are both better off is when the cost of the sofa equals the marginal utility per dollar spent, which in this simplified scenario aligns with the option of $1,000, leaving them enough to maintain or increase their utility from other consumption.

Bob and Ray Are Thinking of Buying a Sofa