The optimal extraction of water along an arbitrarily configured river system

The fundamental problem for any scheme of water management that tries to maximise welfare across a river system is that of determining the optimal allocation at every point. The problem cannot, in general, be avoided by trading water rights because the price will not account for the effect of extraction at any one point on all other points. This article interprets the problem in terms of the indeterminacy that results from missing information on the value of water at internal junctions between rivers. It is then solved in an optimal control theory framework.