In Economics

Economists are always asking how things would change when the parameters of a system are tweaked slightly. Whenever you see the word "marginal" come up in economics, it always means taking a derivative.

1. Suppose that $C(x)$ is the cost of making $x$ items. The marginal cost is $C'(x)$. This is often described as the cost of making one more item, namely $C(x+1) - C(x)$, but that's only a rough description aimed at people who don't know calculus! The cost of making $\Delta x$ more items is approximately $C'(x) \Delta x$, but isn't exactly that. (See the learning module on differentials and linear approximations.)


2. Likewise, if the revenue from making (and selling) $x$ items is $R(x)$, then the marginal revenue is $R'(x)$.


3. The profit from making $x$ items is $P(x) - R(x) - C(x)$, and the marginal profit is $P'(x) = R'(x) - C'(x)$. If the marginal profit is positive, you should increase production, while if the marginal profit is negative you should decrease production.