Question

Anne and Bill are left stranded on a desert island with nothing else but some water x and bread y. There are 100 units available of each good. Suppose that initially Anne has all the water and Bill has all the bread. Anne and Bill have different preferences over the consumption of water and bread. Anne’s utility function is ??(?,?)=? raised 2/5 ? raised3/5, and Bill’s utility function is ??(?,?)=? raised 1/4 ? raised3/4. [30 marks] a) [3 marks] Is the initial consumption efficient in terms of consumption egalitarianism or welfare egalitarianism? (We assume that utilities are interpersonally comparable.) b) [10 marks] Derive Anne’s and Bill’s marginal rate of substitution of water for bread. Define the contract curve and draw it on the Edgeworth box. Is the initial allocation Pareto efficient? Justify your answer. c) [7 marks] Characterize the set of allocations of water and bread which Pareto improve 3 the initial allocation.

d) [10 marks] Now, suppose that Chuck and Dan are stranded on a different island, also with only water and bread. Their preferences are given, respectively, by ??(?,?)=???{?,? raised to 1/2} and ??(?,?)=???{?,?}. Suppose initially Chuck has all the water and Dan all the bread. Draw an Edgeworth box to represent this small exchange economy, locating the initial endowment and sketching the indifference curves passing through the initial endowment. What is the utilitarian optimal allocation? Is this allocation Pareto efficient?

Answer 1

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