Problem 2. There are two consumers with the following utility functions: x² + √√\x²₂ u¹ (x1, x²) u² (x²1, x²) x ²2. = = Total endowment is e = (1,1). (a) Calculate the set of Pareto optimal allocations (a convincing figure is enough). = (b) Assume that the planner wants to implement some Pareto efficient allocation (x¹, x²) ((x1, x²), (x², x²)) where x½ ‡ 0, as an equilibrium with transfers. Prove that any price vector such that 0 < p1 < 2√√x support that allocation (normalizing p2 = 1). can (c) What happens if the planner wants to implement precisely the allocation ((1,0), (0, 1))?

Problem 2. There are two consumers with the following utility functions: x² + √√\x²₂ u¹ (x1, x²) u² (x²1, x²) x ²2. = = Total endowment is e = (1,1). (a) Calculate the set of Pareto optimal allocations (a convincing figure is enough). = (b) Assume that the planner wants to implement some Pareto efficient allocation (x¹, x²) ((x1, x²), (x², x²)) where x½ ‡ 0, as an equilibrium with transfers. Prove that any price vector such that 0 < p1 < 2√√x support that allocation (normalizing p2 = 1). can (c) What happens if the planner wants to implement precisely the allocation ((1,0), (0, 1))?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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