Rubinstein2005-page73

Rubinstein2005-page73 - p j In order to establish...

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October 21, 2005 12:18 master Sheet number 71 Page number 55 Demand: Consumer Choice 55 Figure 5.1 (a) x is a solution to the con- sumer problem B ( p , w ) . (b) x is not a solution to the consumer problem B ( p , w ) . From the above we can derive the “classic” necessary conditions on the consumer’s maximization: Claim: If x is a solution to the consumer’s problem B ( p , w ) and both x k > 0 and x j > 0, then the ratio v k ( x )/ v j ( x ) must be equal to the price ratio p k /
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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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