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Unformatted text preview: found through the solution to the social planner’s problem. The allocations in the below problems are the optimal allocations from the social planner’s problem. We are trying to f nd the prices, p ∗ such that these allocations along with the prices constitute a valuation equilibrium. 1. Consumer’s problem, max x ∈ X U ( x ) ( 5 ) s.t. X t ( p ∗ 1 t x 1 t + p ∗ 2 t x 2 t + p ∗ 3 t x 3 t ) 2. Firm’s problem, max y ∈ Y X t ( p ∗ 1 t y 1 t + p ∗ 2 t y 2 t + p ∗ 3 t y 3 t ) ( 6 ) s.t. y 1 t = F ( − y 2 t , − y 3 t ) ∀ t Given this, derive a formula that links p ∗ 2 t , p ∗ 1 t and p ∗ 1 ,t +1 . Problem 7 Show that for the above problems where X, Y ⊂ L ⊂ R ∞ , First Order Conditions are the necessary conditions for optimality. 2...
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 Spring '08
 Staff
 Convex set, Topological vector space

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