Non-convexities in Production

From The Economics of Non-Convex Ecosystems: Introduction by Partha Dasgupta and Karl-Goran Maler:

The price mechanism is especially problematic in economic systems characterised by positive feedback processes. We now know that in such environments it may prove impossible to decentralise an efficient allocation of resources by means exclusively of prices. Efficient mechanisms would typically involve additional social contrivances, such as (Pigouvian) taxes and subsidies, quantity controls, social norms of behaviour, and so forth. This was proved formally in a justly famous article by Starrett (1972), who showed that for certain types of non-convexities associated with environmental pollution, a competitive price equilibrium simply does not exist: markets for pollution would be unable to equate demands to supplies.

The discussion in Section 4 demonstrates a link between gauge theory in physics and non-convexity theory in economics. Dasgupta and Maler "without rigorous justification" associate investment I with the time-derivative of capital stock K. Using the language of gauge theory, one would say that K is a "conserved current." When local symmetries of the system are broken over time or across space, such currents are no-longer conserved.