Actions in economics

Question

Mirowski 1989 argues economics and physics have frequently informed each other's theoretical development, and neoclassical economics has the same Lagrangian and Hamiltonian formalism frequently seen in physics. I don't know how mainstream this approach has ever been, but his account doesn't make explicit what would be an action in economics. For example, I can imagine a firm's profit maximization, or a portfolio's ROI variance minimization, being formalized as an extremal action principle, but only if such quantities are expressible in the form $int_a^bL(t,,q,,dot{q})dt$ or a suitable generalization. Are there any specific examples like that?

J.G. · Answer

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 $int(C(-dot{x},,t)+qdot{x})e^{-st}dt$.
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:

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

Actions in economics

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