Macroeconomics Exam Review 187

Macroeconomics Exam Review 187 - has no solution ∈ ℜ +...

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Unformatted text preview: has no solution ∈ ℜ + . If is the × n matrix whose rows are a , the latter system can be written as y = 3. By Gordan’s theorem, the system x > (3.78) has a solution ¯ x ∕ = . 4. Without loss of generality, we can take ∥ ¯ x ∥ = 1. (3.78) implies that a ¯ x = ¯ xa > for every = 1 , 2 ..., so that ¯ x ∈ ∗ a . Hence ¯ x ∈ ∩ =1 ∗ a 5. We have shown that for every finite set { a 1 , a 2 ,..., a } ⊆ , ∩ =1 ∗ a is non- empty closed subset of the compact set = { ∈ ℜ : ∥ x ∥ = 1 } . By the Finite intersection property (Exercise 1.116) ∩ a ∈ ∗ a ∕ = ∅ 6. For every p ∈ ∩ a ∈ ∗ a pa ≥ 0 for every a ∈ p defines a hyperplane ( a ) = pa which separates from . 3.253 The expected outcome if player 1 adopts the mixed strategy p = ( 1 , 2 ,... , ) and player 2 plays her...
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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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