(a) Provide a formal rigorous-proof of Sen's theorem that Liberalism and Pareto Optimality are incompatible. (b) Consider an economy with 15 consumers and 2 goods. Consumer 3 has utility function U³ = X₁ + X₂ At a certain Pareto efficient allocation, consumer 3 has an allocation (10, 0). What can you say about the competitive prices that support this Pareto Optimal allocation? Explain your answer.

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Q.3
(a) Provide a formal rigorous-proof of Sen's theorem that Liberalism and Pareto
Optimality are incompatible.
(b) Consider an economy with 15 consumers and 2 goods. Consumer 3 has utility
function U³ = X₁ + X2 At a certain Pareto efficient allocation, consumer 3 has
an allocation (10, 0). What can you say about the competitive prices that
support this Pareto Optimal allocation? Explain your answer.
Transcribed Image Text:Q.3 (a) Provide a formal rigorous-proof of Sen's theorem that Liberalism and Pareto Optimality are incompatible. (b) Consider an economy with 15 consumers and 2 goods. Consumer 3 has utility function U³ = X₁ + X2 At a certain Pareto efficient allocation, consumer 3 has an allocation (10, 0). What can you say about the competitive prices that support this Pareto Optimal allocation? Explain your answer.
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