Bob and Ray are two hungry economics majors who are sharing an apartment for the year. In a flea market they spot a 25-year-old sofa that would look great in their living room. Bob’s utility function is uB(S,MB) = (1 + S)MB, and Ray’s utility function is uR(S,MR) = (2 + S)MR. In these expressions MB and MR are the amounts of money that Bob and Ray have to spend on other goods, S = 1 if they get the sofa, and S = 0 if they don’t get the sofa. Bob has
WB dollars to spend, and Ray has WR dollars.
(a) What is Bob’s reservation price for the sofa?
(b) What is Ray’s reservation price for the sofa?
(c) If Bob has a total of WB = $100 and Ray has a total of WR = $75 to spend on sofas and other stuff, they could buy the sofa and have a Pareto improvement over not buying it so long as the cost of the sofa is no greater than