3 The second welfare theorem Two agents meet to trade two goods. Agent 1 has utility function u¹(x¹) = ln x + ln x and endowment e¹ (3,4), while agent 2 has utility function u²(x²) = 2√x² + √√x² and endowment e² = (0,8). 1. Find a competitive equilibrium of this economy. 2. A social planner wishes to redistribute wealth so that both agents consume an equal amount of good 2. Find a competitive equilibrium with transfers which achieves this outcome. 3. Calculate a set of Pareto weights associated with each of the allocations you found in the previous two parts, with the normalization that each set of weights sums to 1.

3 The second welfare theorem Two agents meet to trade two goods. Agent 1 has utility function u¹(x¹) = ln x + ln x and endowment e¹ (3,4), while agent 2 has utility function u²(x²) = 2√x² + √√x² and endowment e² = (0,8). 1. Find a competitive equilibrium of this economy. 2. A social planner wishes to redistribute wealth so that both agents consume an equal amount of good 2. Find a competitive equilibrium with transfers which achieves this outcome. 3. Calculate a set of Pareto weights associated with each of the allocations you found in the previous two parts, with the normalization that each set of weights sums to 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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