Dynamics versus optimization in non-convex environmental economics problems with a single welfare function

Economics has a well-defined notion of equilibrium. Unlike mechanics or thermodynamics, economics does not include explicit theories of dynamics describing how equilibria are reached or whether they are stable. However, even simple economics problems such as maximization of a welfare function might sometimes be interpreted as dynamics problems. Here we consider when dynamics is relevant to welfare optimization problems involving a single decision-maker, for example, a social decision-maker maximizing a social welfare function. We suggest that dynamics occurs in case a welfare maximum can only be known through a sequence of local computations. These local computations give rise to a dynamical system, and the welfare optimum is also equilibrium. On the contrary, if the welfare function is known, then dynamics is irrelevant and the maximum can be chosen directly. The importance of choosing the right metaphor for an economics problem is discussed.