4. Smith and Jones are trying to decide whether to share an apartment. To live separately, each would have to pay $300/mo in rent. An apartment large enough to share can be rented for $450/mo. Costs aside, they are indifferent between living together and living separately except for these two problems: Smith likes to play his stereo late at night, which disturbs Jones’s sleep; and Jones likes to sing in the shower at 6 A.M., which awakens Smith. Jones would sacrifice up to $80/mo rather than stop singing in the shower, and Smith would sacrifice up to $155/mo rather than stop playing his stereo late at night. Smith would tolerate Jones’s singing and Jones would tolerate Smith’s stereo in return for compensation payments not less than $75/mo and $80/mo, respectively.

a. Should they live together? If so, indicate how they can split the rent so that each does better than by living alone. If not, explain why no such arrangement is feasible.

b. Now suppose Smith wins a free pair of stereo headphones. If he wears them late at night, Jones’s sleep is not disturbed. Smith likes the headphones well enough, but would be willing to pay $40/mo to keep on listening to late-night music through his speakers. How, if at all, does the existence of this new option affect your answer to part (a)? Explain carefully.