Macroeconomics Exam Review 71

Macroeconomics Exam Review 71 - 2.56 The cost allocation...

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Unformatted text preview: 2.56 The cost allocation game is not convex. Let = { , } , = { , } . Then ∪ = { ,, } = and ∩ = { } and ( ∪ ) + ( ∩ ) = 1530 < 1940 = 770 + 1170 = ( ) + ( ) Alternatively, observe that TN’s marginal contribution to coalition { , } is 1170, which is greater than its marginal contribution to the grand coalition { ,, } (1530 − 770 = 760). 2.57 is supermodular if ( 1 ∨ 2 ) + ( 1 ∧ 2 ) ≥ ( 1 ) + ( 2 ) which can be rearranged to give ( 1 ∨ 2 ) − ( 2 ) ≥ ( 1 ) − ( 1 ∧ 2 ) If the right hand side of this inequality is nonnegative, then so a fortiori is the left hand side, that is ( 1 ) ≥ ( 1 ∧ 2 ) = ⇒ ( 1 ∨ 2 ) ≥ ( 2 ) If the right hand side is strictly positive, so must be the left hand side...
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

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