Optimal regime switching and threshold effects: theory and application to a resource extraction problem under irreversibility

We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features ecological-like regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.