Editing Marshallian demand function (section)

== Continuity ==
The [[maximum theorem]] implies that if:
* The utility function <math>u(x)</math> is continuous with respect to <math>x</math>,
* The correspondence <math>B(p, I)</math> is non-empty, compact-valued, and continuous with respect to <math>p,I</math>,
then <math>x^*(p, I)</math> is an [[upper-semicontinuous]] correspondence. Moreover, if <math>x^*(p, I)</math> is unique, then it is a continuous function of <math>p</math> and <math>I</math>.<ref name=Varian/>{{rp|156,506}}

Combining with the previous subsection, if the consumer has strictly convex preferences, then the Marshallian demand is unique and continuous.  In contrast, if the preferences are not convex, then the Marshallian demand may be non-unique and non-continuous.