Setup, from Q27 of the paper:
An economy has agents 1 and 2 and 3 units each of goods X and Y. An allocation is with left over. Each agent faces . Agent 1 (higher on the social ladder) chooses first to maximize ; Agent 2 then maximizes from the remainder. Which allocation is an equilibrium?
Let for Agent 2's utility function. Then, the equilibrium allocation in the above question is
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Setup, from Q27 of the paper: An economy has agents 1 and 2 and 3 units each of goods X and Y. An allocation is ((x₀,y₀),(x₁,y₁),(x₂,y₂)) with (x₀,y₀) left over. Each agent faces xᵢ≤ 3, yᵢ≤ 3, xᵢ²+yᵢ²≤ 12. Agent 1 (higher on the social ladder) chooses first to maximize u₁=x₁²y₁; Agent 2 then maximizes u₂=ax₂+y₂ from the remainder. Which allocation is an equilibrium? Let a=1 for Agent 2's utility function. Then, the equilibrium allocation in the above question is (A) Pareto efficient, because the slopes of the Agents' indifference curves are tangent at that allocation. (B) Not Pareto efficient, because the slopes of the Agents' indifference curves are not tangent at that allocation. (C) Pareto efficient, because there is a bound on Agent 1's ability to consume. (D) Not Pareto efficient, as Agent 2 can be made better off without making Agent 1 worse off.
Also written as: Setup, from Q27 of the paper: An economy has agents 1 and 2 and 3 units each of goods X and Y. An allocation is ((x_0,y_0),(x_1,y_1),(x_2,y_2)) with (x_0,y_0) left over. Each agent faces x_i<= 3, y_i<= 3, x_i^2+y_i^2<= 12. Agent 1 (higher on the social ladder) chooses first to maximize u_1=x_1^2y_1; Agent 2 then maximizes u_2=ax_2+y_2 from the remainder. Which allocation is an equilibrium? Let a=1 for Agent 2's utility function. Then, the equilibrium allocation in the above question is
Welfare economics and social choice has come up 62 times in 6 exams since 2004.
This question is on Pareto efficiency and Pareto improvements, part of Welfare economics and social choice in Microeconomics.
What it means for an allocation to be efficient, checked in exchange economies and other settings.
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Question from the DSE 2007 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.