Ian likes to make a barbeque. His utility is ui(b,wi) =root (bwi) where b is the amount of barbeque food and wi is the amount of money Ian spends on other things. He has an income of $120.Janet lives next to Ian and her utility function is uj(s,wj) = wj - s^2 where s is the amount of smoke created by the barbeque and wj is the amount of money Janet spends on consumption goods. Janet has an income of $100.The price of b is $4. Let one unit of b creates 0.5 units of s.

Question 2 (5 marks) lan likes to make a barbeque. His utility function is wi (b, wi) = bw, where b is the amount of barbeque food and wi is the amount of money lan spends on other things. He has an income of $120. Janet lives next to lan and her utility function is uj (s, w ) = wj - s? where's is the amount of smoke created by the barbeque and w, is the amount of money Janet spends on consumption goods. Janet has an income of $100. The price of b is $4. Let one unit of b creates 0.5 units of s. Find the amounts of consumptions lan and Janet would choose if both individuals can do what they want. (1.5 marks) ii) Find the set of all Pareto optimal amounts of b when the target utility for Janet is u,. (2 marks) ifi) Compare and discuss the results in i) and ii). (1.5 marks)