Macroeconomics Exam Review 85

Macroeconomics Exam - 5 This implies that ˜ ≾ ˜ Therefore ˜ = ˜ ∈(˜ ˜ is a fixed point of 6 Since ⊆ ˜ = inf is the least fixed point

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Unformatted text preview: 5. This implies that ˜ ≾ ˜ . Therefore ˜ = ˜ ∈ (˜ ) ˜ is a fixed point of . 6. Since ⊆ , ˜ = inf is the least fixed point of . 2.116 1. Let ⊆ and ∗ = sup . For every ∈ , ∈ ( ). Since is increasing, there exists some ∈ ( ∗ ) such that ≿ . 2. Let ∗ = sup . Then (a) Since ≿ for every ∈ , ∗ = sup ≿ sup = ∗ (b) ∗ ∈ ( ∗ ) since ( ∗ ) is a complete sublattice. 3. Define ∗ = { ∈ : ≿ for every ∈ } ∗ is the set of all upper bounds of in . Then ∗ is a complete lattice, since ∗ = ≿ ( ∗ ) 4. Let : ∗ ⇉ ∗ be the correspondence ( ) = ( ) ∩ ( ) where : ∗ ⇉ ∗ is the constant correspondence defined by...
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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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