Macroeconomics Exam Review 4

Macroeconomics Exam Review 4 - Solutions for Foundations of...

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Since there are no veto players ( 𝑇 = ), 𝑤 ( 𝑁 ∖ { 𝑖 } ) = 1 for every player 𝑖 𝑁 and 𝑗 = 𝑖 𝑥 𝑗 𝑤 ( 𝑁 ∖ { 𝑖 } ) = 1 which implies that 𝑥 𝑖 = 0 for every 𝑖 𝑁 contradicting (1.15). Thus we conclude that core = . 1.70 The excesses of the proper coalitions at x 1 and x 2 are x 1 x 2 { AP } -180 -200 { KM } -955 -950 { TN } -395 -380 { AP, KM } -365 -380 { AP, TN } -365 -370 { KM, TN } -180 -160 Therefore 𝑑 ( x 1 ) = ( 180 , 180 , 365 , 365 , 395 , 955) and 𝑑 ( x 2 ) = ( 160 , 200 , 370 , 380 , 380 , 950) d ( x 1 ) 𝐿 d ( x 2 ) which implies x 1 𝑑 x 2 . 1.71 It is a weak order on 𝑋 , that is is reflexive, transitive and complete. Reflexivity and transitivity flow from the corresponding properties of 𝐿 on 2 𝑛 . Similarly, for any x , y 𝑋 , either d ( x ) 𝐿 d ( y ) or d ( y ) 𝐿 d ( x ) since 𝐿 is complete on 2 𝑛 . Consequently either x y or y x (or both). is not a partial order since it is not antisymmetric d ( x ) 𝐿 d ( y ) and d ( y ) 𝐿 d ( x ) does not imply x = y 1.72 𝑑 ( 𝑆, x ) = 𝑤 ( 𝑆 ) 𝑖 𝑆 𝑥
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