2) Say there are H people in the society and one good with a total endowment...
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2) Say there are H people in the society and one good with a total endowment of X and that the utility functions are such that the UPF is bowed out from the origin. a) Assume that the utility function for each is identical Ui = u(¹) for i = 1,2 where Ju(r¹)/or* >0 and ²u(r)/0(r)² <0 or diminishing marginal utility. Further, assume that the good can be costlessly redistributed between individuals. Prove that maximizing a Benthamite welfare function would lead to an equal utility welfare maximum. b) Now imagine some individuals have utility functions as above but others have bu(r) with b < 1 as they are a bit depressed. Would the welfare max with Bethamite be equal utility now? If so fully explain. If not, explain how it would differ from equal utility and why. 2) Say there are H people in the society and one good with a total endowment of X and that the utility functions are such that the UPF is bowed out from the origin. a) Assume that the utility function for each is identical Ui = u(¹) for i = 1,2 where Ju(r¹)/or* >0 and ²u(r)/0(r)² <0 or diminishing marginal utility. Further, assume that the good can be costlessly redistributed between individuals. Prove that maximizing a Benthamite welfare function would lead to an equal utility welfare maximum. b) Now imagine some individuals have utility functions as above but others have bu(r) with b < 1 as they are a bit depressed. Would the welfare max with Bethamite be equal utility now? If so fully explain. If not, explain how it would differ from equal utility and why.
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a If the utility functions are identical then the welfare function will ... View the full answer
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