Editing Marginalism (section)

==== Quantified marginal utility ====
Under the [[special case]] in which usefulness can be quantified, the change in utility of moving from state <math>S_1</math> to state <math>S_2</math> is
:<math>\Delta U=U(S_2)-U(S_1)\,</math>
Moreover, if <math>S_1</math> and <math>S_2</math> are distinguishable by values of just one variable <math>g\,</math> which is itself quantified, then it becomes possible to speak of the ratio of the marginal utility of the change in <math>g\,</math> to the size of that change:
:<math>\left.\frac{\Delta U}{\Delta g}\right|_{c.p.}</math>
(where "[[ceteris paribus|c.p.]]" indicates that the ''only'' [[Dependent and independent variables|independent variable]] to change is <math>g\,</math>).

Mainstream neoclassical economics will typically assume that
:<math>\lim_{\Delta g\to 0}{\left.\frac{\Delta U}{\Delta g}\right|_{c.p.}}</math>
is well defined, and use "marginal utility" to refer to a [[partial derivative]]
:<math>\frac{\partial U}{\partial g}\approx\left.\frac{\Delta U}{\Delta g}\right|_{c.p.}</math>