Please help. Urgent!

Question 3 [30 points] Two individuals, A and B, share an apartment. A is a smoker and B is not. A's payoff or utility function is given by UA (294,5) = xAS where 95,, = yA PS is A's consumption of a composite good, yA is A's income, S is the amount of cigarettes A smokes, and P is the price of cigarettes. Thus, xA measures the money A spends on everything else after buying S cigarettes. B's utility function is given by 03013, S) = 313 b5 where yB is B's income, and b measures the damage B suffers whenA smokes. Suppose yA = 160, 373 = 2000,P = 5,17 = 60. a)[10 points] Suppose the property right is such that A can freely decide how many cigarettes he can smoke. Find A's optimal choice, and the sum of A's and B's utilities. b)[10 points] Find the socially optimal level of smoking that maximizes the sum of A's and B's utilities. What is the sum of A's and B's utilities? c)[10 points] Given the property right structure in a), suppose A and B can engage in costless bargaining. Further, suppose the bargain power lies with B. Find the outcome of the bargaining process, re, the amount of smoking after bargaining, and who should pay whom how much in order to obtain this amount of smoking