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Unformatted text preview: 5. Trivially, x ∗ is a feasible allocation with endowments w = x ∗ and = p ∗ w = p ∗ x ∗ . To show that ( p ∗ , x ∗ ) is a competitive equilibrium, we have to show that x ∗ is the best allocation in the budget set ( p , ) for each consumer . Suppose to the contrary there exists some consumer and allocation y such that y ≻ x and py ≤ = px ∗ . By continuity, there exists some ∈ (0 , 1) such that y ≻ x ∗ and p ( y ) = py < py ≤ px ∗ contradicting (3.66). We conclude that x ∗ ≿ x for every x ∈ ( p ∗ , ) for every consumer . ( p ∗ , x ∗ ) is a competitive equilibrium. 3.229 By the previous exercise, there exists a price system p ∗ such that x ∗ is optimal for each consumer in the budget set ( p ∗ , p ∗ x ∗ ), that is x ∗ ≿ x...
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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.
- Fall '10