Smith can operate his sawmill with or without soundproofing. Operation without$$soundproofing results in noise damage to his neighbor Jones. The relevant$$gains and losses for Smith and Jones are listed in the table: $($LO$3,$ LO$4)$Without With$$soundprooi ng soundprooi ng$$Gains to Smith $$150/$wk $$34/$wk$$Damage to Jones $$125/$wk $$6/$wk$$a$.$ If Smith is not liable for noise damage and there are no negotiation costs,$$will he install soundproofing? Explain.$$b$.$ How, if at all, would your answer differ if the negotiation costs of maintaining$$an agreement were $$4/$wk$?$ Explain.$$c$.$ Now suppose Jones can escape the noise damage by moving to a new location,$$which will cost him $$120/$wk$.$ With negotiation costs again assumed to$$be zero, how, if at all, will your answer to part $($a$)$ differ? Explain.