Mathematical Properties
If the consumer's utility function is continuous and represents a locally nonsatiated preference relation, then the Hicksian demand correspondence satisfies the following properties:
i. Homogeneity of degree zero in p: For all, . This is because the same x that minimizes also minimizes subject to the same constraint.
ii. No excess demand: The constraint holds with strict equality, . This follows from continuity of the utility function. Informally, they could simply spend less until utility was exactly .
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