Macroeconomics Exam Review 70

Macroeconomics Exam Review 70 - 2.54 Assume ( , ) is...

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Unformatted text preview: 2.54 Assume ( , ) is convex, that is ( ∪ ) + ( ∩ ) ≥ ( ) + ( ) for every , ⊆ For all disjoint coalitions ∩ = ∅ ( ∪ ) ≥ ( ) + ( ) is superadditive. 2.55 Rewriting (2.18), this implies ( ∪ ) − ( ) ≥ ( ) − ( ∩ ) for every , ⊆ (2.34) Let ⊂ ⊂ ∖ { } and let ′ = ∪ { } . Substituting in (2.34) ( ′ ∪ ) − ( ) ≥ ( ′ ) − ( ′ ∩ ) Since ⊂ ′ ∪ = ( ∪ { } ) ∪ = ∪ { } ′ ∩ = ( ∪ { } ) ∩ = Substituting in the previous equation gives the required result, namely ( ∪ { } ) − ( ) ≥ ( ∪ { } ) − ( ) Conversely, assume that ( ∪ {...
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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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