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hw6 - Homework Assignment 6 Econ 121b Intermediate...

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Homework Assignment # 6 Econ 121b. Intermediate Microeconomics due March 30, 2011 Please put your discussion-section time on your answer. 1. Consider a pure-exchange economy with two consumers, A and B , and two goods, 1 and 2 . For each ` D 1 or 2 and i D A or B , write x i ` for consumer i ’s consumption of good ` . The utility functions are of Cobb-Douglas type: u A .x A 1 ; x A 2 / D .x A 1 / ˛ .x A 2 / 1 ˛ and u B .x B 1 ; x B 2 / D q x B 1 x B 2 ; where 1 2 < ˛ < 1 is a taste parameter. The endowments of consumers A and B are ! A D .! A 1 ; ! A 2 / and ! B D .! B 1 ; ! B 2 /; respectively. Finally, to ease the notation, write N ! 1 D ! A 1 C ! B 1 and N ! 2 D ! A 2 C ! B 2 : (a) What is the set of feasible allocations in this economy? (b) Draw the Edgeworth box for this economy. Label the axis appropriately, indicate the size of each edge and locate the endowment point. Draw a couple of indiffer- ence curves for each consumer. (c) What is a Pareto efficient allocation? (d) Explain why, in general, a feasible allocation .x A ; x B / is Pareto efficient if and only if the marginal rate of substitution (MRS) of consumer A at x A equals the MRS of consumer B at x B . (e) Solve for the contract curve , i.e. the set of all Pareto efficient allocations. (Hint:
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