# What does it mean to have a strictly increasing transformation in consumer theory? [closed]

We're discussing utility functions

• A little more context would be helpful. In which context exactly did you encounter the term? – Michael Greinecker Oct 28 '18 at 23:38

If I'm understanding your question correctly, you are referring to increasing transformations of a utility function. Suppose I have a set of alternatives $$X$$, a rational preference relation $$\succsim$$ on $$X$$, and a function $$u:X \rightarrow \mathbb{R}$$ which represents this preference relation. Then it can be shown that for any $$v:\mathbb{R} \rightarrow \mathbb{R}$$ which is monotonically increasing, $$v \circ u:X \rightarrow \mathbb{R}$$ also represents these preferences. Try to prove this; it's a good exercise.