Unformatted text preview: p j . In order to establish suf±cient conditions for maximization, we require also that the preferences be convex. Claim: If % is monotonic, convex, continuous, and differentiable, and if at x ∗ • px ∗ = w , • for all k such that x ∗ k > 0, and for any commodity l , v k ( x ∗ )/ p k ≥ v l ( x ∗ )/ p l , then x ∗ is a solution to the consumer’s problem....
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- Fall '10
- Derivative, x∗, Convex preferences