Editing Marshallian demand function (section)

== Homogeneity ==
The optimal Marshallian demand correspondence of a continuous utility function is a [[homogeneous function]] with degree zero. This means that for every constant <math>a>0,</math>
:<math>x^*(a\cdot p, a\cdot I) = x^*(p, I).</math>
This is intuitively clear. Suppose <math>p</math> and <math>I</math> are measured in dollars. When <math>a=100</math>, <math>ap</math> and <math>aI</math> are exactly the same quantities measured in cents. When prices and wealth go up by a factor a, the purchasing pattern of an economic agent remains constant. Obviously, expressing in different unit of measurement for prices and income should not affect the demand.