# Inc Linear Transformation of Bernoulli Utility

According to MWG Proposition 6.B.2, it illustrates that the expected utility form is preserved only by increasing linear transformation.

What is the significance of this proposition?

The part I find challenging in connecting the dots is when right after the proof of this proposition, the authors claim that this proposition allows us to interpret meaning in differences of utilities. How are these two exactly connected?

In the other hand, there are representations os someone's preferences that are easier to work with, from the calculations point of view, or improve our understanding of the underlying economics of the problem. One example is when we have quasilinear preferences on good 1 (check MWG, chapter 3 for this example). When this is the case, we have that $U(x_{1},...,x_{I}) = x_{1} + \phi(x_{2},...,x_{I})$. Of course, if we take, say, the exponential of $U$, we will preserve ordering, but not this very useful representation.