Two individuals, Charlie and Harry live in the same village. Harry usually litters everywhere. Let L be the amount of litter Harry creates. xc and X be Charlie's and Harry's consumption amounts respectively, Assume that Harry has an income of $80 and his utility function is up (XH, L) = x* Charlie has an income of $60 and his utility function is uc(Xc, L) = Inxc 20 Let the price of consumption good x be $2 and litter is free to create with the maximum amount equal to 10 units. **L1/4 i) If there is no rule or law to forbid littering in the village, how many units of litter will there be in the village? Is this Pareto optimal and why? (3 marks) Suppose that in order to litter, Harry must buy the permits for littering. If the permits belong to Charlie, find the equilibrium amounts of L, xc, and XH. (6 marks) Find the set of Pareto optimal allocations. Is the equilibrium in ii) Pareto optimal? Discuss briefly. Draw the set together with the equilibrium on a diagram (7 marks) If there is an authority who can impose a per unit tax on littering. How much should be the tax if the amount of littering must not exceed 2 units? Suppose that all the tax revenue is given to Charlie. Will this achieve a Pareto optimal allocation? Explain.
