Unformatted text preview: P ( p , w ∗ ) , then there exists an x such that px ≤ px ∗ and u ( x ) > u ( x ∗ ) ≥ u ∗ . By continuity, for some nonnegative vector ε 6= 0, x − ε is a bundle such that u ( x − ε) > u ∗ and p ( x − ε) < px ∗ , contradicting the assumption that x ∗ is a solution to D ( p , u ∗ ) . The Hicksian Demand Function Assume that the dual problem D ( p , u ) has a unique solution. This is the case, for example, if u represents strictly convex continuous preferences. The Hicksian demand function h ( p , u ) is the solution to D ( p , u ) . This concept is analogous to the demand function in the prime problem....
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- Fall '10
- Utility, Prime number, Dual problem, Hicksian demand function