Constrained conjunctive-use for endogenously separable water markets: Managing the Waihole-Waikane aqueduct

An internal solution to an optimal control problem involving conjunctive-use of surface and groundwater may be inapplicable if water is not sufficiently fungible across space and time. We provide a more general solution and apply it to the problem of allocating a limited amount of water from the Ko'olau mountains to two Oahu water districts separated by those mountains. The solution involves initially allocating all of the mountain water to the district supplied by groundwater but eventually allocating all of the water to the district supplied by surface water. The conditions for an internal solution hold only in the intervening years when some mountain water is allocated to each district.