need step by step explanations thank you

Question 1 (17 marks) Consider a model of a negative consumption externality. Both households have Cobb-Douglas preferences over composite (x4, xrespectively) and a hours of activity per day chosen by household A measured by 0 S t S 24. The households' utility functions are UA(x4, t) = x1/2+1/2 and UB(xB, t) = x1/2(24 - t)1/2 Suppose the initial endowment of composite is ed = 5 and e = 5. Laws limit Household A's daily activity to be at most 12 hours, ie. the legal maximum is t = 12. i) (3 marks) In an Edgeworth Box, identify the set of allocations that would make both households better off than they are at the initial endowment (it is called the set of mutually beneficial trades relative to the initial allocation). ii) (2 marks) Explain why the set of Pareto Efficient allocations (contract curve) is represented by the 45 degree line connecting the bottom left to the top right of the Edgeworth box, ie x4 = t. iii) (3 marks) Introduce a market for units of t traded relative to the initial value, E = 12 . Find household demands, market equilibrium allocation and price. iv) (3 marks) Add the market equilibrium you found in iii) to your sketch of the set of mutually beneficial trades in your Edgeworth box in i) (or draw a new one). V) (4 marks) Describe using a graph how some endowment distributions (ed, eB) with ed + e = 10 will lead household B to use all of their initial endowment of composite to pay household A for reducing the level of nuisance. (Continue to assume that t = 12.) vi) (2 marks) What is the largest value of e" that will lead household B to use all of their initial endowment of composite to pay household A for reducing the level of nuisance (with ed + e = 10 ie. in the case in v))