In a two-person two-good exchange economy, agents are A and B and goods are 1 and 2, with utilities and . There are 5 units of each good (, ). Consider the allocation in which A gets 4 units of good 1 only, and B gets 1 unit of good 1 and 5 units of good 2.
Suppose an agent is said to envy agent if strictly prefers 's allocation over her own, and an allocation is a 'No-envy allocation' if neither agent envies the other. In that case:
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In a two-person two-good exchange economy, agents are A and B and goods are 1 and 2, with utilities u_A(x₁,x₂)=α x₁+x₂ and u_B(y₁,y₂)=y₁y₂. There are 5 units of each good (x₁+y₁=5, x₂+y₂=5). Consider the allocation in which A gets 4 units of good 1 only, and B gets 1 unit of good 1 and 5 units of good 2. Suppose an agent i is said to envy agent j if i strictly prefers j 's allocation over her own, and an allocation is a 'No-envy allocation' if neither agent envies the other. In that case: (A) the above allocation is always a No-envy allocation (B) the above allocation is never a No-envy allocation (C) the above allocation is a No-envy allocation if α≥ 5/3 (D) the above allocation is a No-envy allocation if α≤ 3/5
Also written as: In a two-person two-good exchange economy, agents are A and B and goods are 1 and 2, with utilities u_A(x_1,x_2)=alpha x_1+x_2 and u_B(y_1,y_2)=y_1y_2. There are 5 units of each good (x_1+y_1=5, x_2+y_2=5). Consider the allocation in which A gets 4 units of good 1 only, and B gets 1 unit of good 1 and 5 units of good 2. Suppose an agent i is said to envy agent j if i strictly prefers j 's allocation over her own, and an allocation is a 'No-envy allocation' if neither agent envies the other. In that case:
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Combining individual preferences into social judgements, and the limits of doing so.
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