Macroeconomics Exam Review 192

Macroeconomics Exam Review 192 - ? ( x ) Substituting...

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Weights { 123 } , { 124 } , { 34 } 1 / 2 , 1 / 2 , 1 / 2 { 12 } , { 13 } , { 23 } , { 4 } 1 / 2 , 1 / 2 , 1 / 2 , 1 { 123 } , { 14 } , { 24 } , { 3 } 1 / 2 , 1 / 2 , 1 / 2 , 1 / 2 { 123 } , { 14 } , { 24 } , { 34 } 2 / 3 , 1 / 3 , 1 / 3 , 1 / 3 { 123 } , { 124 } , { 134 } , { 234 } 1 / 3 , 1 / 3 , 1 / 3 , 1 / 3 3.266 Both sides of the expression e ? = ± ∈ℬ ? ± e ± are vectors, with each component corresponding to a particular player. For player ± , the ± ² component of e ? is 1 and the ± ² component of e ± is 1 if ± ² and 0 otherwise. Therefore, for each player ± , the preceding expression can be written ± ∈ℬ∣ ± ³ ? ± =1 For each coalition ² , the share of the coalition ² at the allocation x is ³ ± ( x )= ± ²´ ³ = e ± ˙ x (3.79) The condition ³ ? = ± ∈ℬ ? ± ³ ± means that for every x µ ³ ? ( x )=
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Unformatted text preview: ? ( x ) Substituting (3.79) e ? x = ? x which is equivalent to the condition ? e = e ? 3.267 By construction, 0. If = 0, ? ? ? = implies that ? = 0 for all and consequently ? ? ( ) ( ) is trivially satised. On the other hand, if > 0, we can divide both conditions by .) 201...
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