Marginal value

A marginal value is

(This third case is actually a special case of the second).

In the case of differentiability, at the limit, a marginal change is a mathematical differential, or the corresponding mathematical derivative.

These uses of the term “marginal” are especially common in economics, and result from conceptualizing constraints as borders or as margins. The sorts of marginal values most common to economic analysis are those associated with unit changes of resources and, in mainstream economics, those associated with infinitesimal changes. Marginal values associated with units are considered because many decisions are made by unit, and marginalism explains unit price in terms of such marginal values. Mainstream economics uses infinitesimal values in much of its analysis for reasons of mathematical tractability.

Assume a functional relationship

If the value of ${\displaystyle x_{i}}$ is discretely changed from ${\displaystyle x_{i,0}}$ to ${\displaystyle x_{i,1}}$ while other independent variables remain unchanged, then the marginal value of the change in ${\displaystyle x_{i}}$ is

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