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Unformatted text preview: 1 3. (120 points) Consider the function z : ∆ × R → R 2 deFned by z ( p, α ) = 1 p 1 + α cos(2 πp 1 ) , − 1 + αp 1 cos(2 πp 1 ) p 2 ! Note that cos(0) = 1 and d dx cos x = − sin x . (a) ±or what values of α does the function z α ( p ) = z ( p, α ) satisfy the conditions of the DebreuGaleKuhnNikaido Lemma? (b) ±or what values of α does there exist p ∈ ∆ such that z ( p, α ) = 0? (c) Show that for every α ∈ R and every ε > 0, there is an exchange economy with two agents whose excess demand function agrees with z α on { p ∈ ∆ : p 1 ∈ [ ε, 1 − ε ] } . (d) Show that there is a set A ⊂ R of Lebesgue measure zero such that for every α 6∈ A , the economy with excess demand z α is regular. 2...
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 Spring '06
 ANDERSON
 Economics, walrasian equilibrium, Lebesgue measure, welfare theorem

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