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

<p>So in classical economic theory, we never have a "unique" utility function which represents preferences. This is because we can always take an increasing transformation of the function and get something else which contains all the relevant information with respect to our preferences. </p>

CC BY-SA 4.0
2018-10-28T22:24:39.343Z
2018-10-28T22:24:39.343Z
NBm424
<p>We're discussing utility functions </p>

CC BY-SA 4.0
2018-10-28T23:38:09.373Z
A little more context would be helpful. In which context exactly did you encounter the term?
Michael Greinecker
<consumer-theory>
What does it mean to have a strictly increasing transformation in consumer theory?
Aloniad Loxas
# What does it mean to have a strictly increasing transformation in consumer theory?

(Asked by: username_0 on 2018-10-27)

We're discussing utility functions

**Tags:** consumer-theory
> **Comments:**
> **username_1**: A little more context would be helpful. In which context exactly did you encounter the term?  

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## 1 answers

### Answer by username_2 on 2018-10-28. Score: 1

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.

So in classical economic theory, we never have a "unique" utility function which represents preferences. This is because we can always take an increasing transformation of the function and get something else which contains all the relevant information with respect to our preferences.


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