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?
Now suppose Agent 2 is higher on the social ladder, so Agent 2 chooses first; . Which allocation is an equilibrium for this modified economy?
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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? Now suppose Agent 2 is higher on the social ladder, so Agent 2 chooses first; a=2. Which allocation ((x₀,y₀),(x₁,y₁),(x₂,y₂)) is an equilibrium for this modified economy? (A) ((0,0),(3,√3),(0,3-√3)) (B) ((0,0),(3-√(48/5),3-√(12/5)),(√(48/5),√(12/5))) (C) ((0,0),(0,3-√3),(3,√3)) (D) ((0,0),(2,3-√8),(1,√8))
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? Now suppose Agent 2 is higher on the social ladder, so Agent 2 chooses first; a=2. Which allocation ((x_0,y_0),(x_1,y_1),(x_2,y_2)) is an equilibrium for this modified economy?
General equilibrium and exchange economies has come up 69 times in 7 exams since 2004.
This question is on Competitive equilibrium in an exchange economy, part of General equilibrium and exchange economies in Microeconomics.
Finding the prices at which every consumer's chosen bundle clears the market.
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