Macroeconomics Exam Review 37

Macroeconomics Exam Review 37 - By (1), is a cone. To show...

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Unformatted text preview: By (1), is a cone. To show that it is convex, let x and y belong to . By (1), x and (1 ) y belong to , and therefore x + (1 ) y belongs to by (2). is convex. Conversely, assume that is a convex cone. Then for every Let x and y be any two elements in . Since is convex, = 1 2 x + (1 ) 1 2 y and since it is a cone, 2 = x + y . Therefore + 1.188 We have to show that is convex cone. By assumption, is convex. To show that is a cone, let y be any production plan in . By convexity y = y + (1 ) for every 0 1 Repeated use of additivity ensures that y for every = 1 , 2 ,... Combining these two conclusions implies that y for every 1.189 Let denote the set of all superadditive games. Let 1 , 2 be two superadditive games. Then, for all distinct coalitionssuperadditive games....
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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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