Actions in economics
Select examples from a book suggestion due to @markleeds, Optimal Control Theory with applications in Economics:

Polluting growth has action $\int(bz-\dot{z}+\ddot{z})dt$.
Optimal extraction of a natural resource has action $\int(C(-\dot{x},\,t)+q\dot{x})e^{-st}dt$.
Consumption vs rapid attainment of production capacity has action $\int[\dot{x}-x+q-a]dt$.
Resource extraction in an open economy has action $\int-U(\bar{c}-e^{rt}\dot{x}+ay-\dot{y})dt$.
Consumption versus investment can give rise to many actions, including:

$\int(\dot{x}-1)U(x)dt$
$\int e^{-\rho t}(\dot{K}+\delta K-f)U(K)dt$
$\int\frac{dt}{K-\dot{K}}$
$\int e^{\dot{K}-aK}dt$
$\int(\dot{K}-cK)^ae^{-bt}dt$