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 playhis stereo late at night, which disturbs Jones's sleep; and Jones likes to sing in theshower at 6 AM, 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 ratherthan stop playing his stereo late at night. Smith would tolerate Jones's singing andJones wouldtolerate Smith's stereo in return for compensation payments not less than 75/mo and 80/mo, respectively.

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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 themlate at night, Jones's sleep is not disturbed. Smith likes the headphones wellenough, 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.

1. With the headphone option, the least costly solution to the stereo noise problem falls to 40/mo, making the total cost of accommodation only 115/mo. Now it pays them to live together, so that they can share the 150- 115= 35/mo surplus. Since all of the costs of adjustment fall on Smith, his share of the rent must be at least 115/mo less than he would have paid living alone. That is, Smith will pay at most 185/mo if they live together. If they split the 35/mo surplus equally, Smith's share will be 185-17.50= 167.50/mo. Jones will pay the remaining 282.50.

Answer part b only, the one highlighted in bold, why was the smith and jones pay at that amount only?? I dont understand how that was coming from.