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 $2,000 to spend on the sofa and other stuff. Ray has a total of $2,400 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

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Quizplus · Accepted Answer

Bob's utility without the sofa is 2000, and with the sofa, it is (1+1)(2000-P) = 4000 - 2P. Ray's utility without the sofa is 7200, and with the sofa, it is (3+1)(2400-P) = 9600 - 4P. Both must be better off with the sofa, so 4000 - 2P > 2000 and 9600 - 4P > 7200. Solving these inequalities gives P < 1000 for Bob and P < 600 for Ray. The maximum they can pay together is the sum of these amounts, which is $1,600.

Bob and Ray Are Thinking of Buying a Sofa