Allocation and pricing of water resources

Public intermediaries responsible for the management of uncertain water supply and demand face a number of decision problems. These include decisions with regard to water procurement and storage, capacity expansion, general operations, investment in demand side management programs, and pricing, among others. This thesis addresses two questions central to the water intermediary's management objective, both related to pricing. The first question is that of an optimal pricing policy in the presence of storage and both demand and supply uncertainty. There is an extensive literature treating the question of optimal public pricing in the presence of joint demand and supply uncertainty with specific application to the electricity sector (peak-load pricing). This literature assumes nonstorability of goods. The presence of storage is a defining feature of the water problem. We treat the pricing problem in the presence of storage, in a joint inventory-price control framework. We characterize the optimal pricing policy and investigate its sensitivity to a number of key model parameters, including the cost of water shortage. The second pricing model developed in this thesis treats option contracting in the water market. Reliance on option contracts is a relatively new phenomenon in the California water market. These contracts can be invoked to avoid costly shortfalls in supply faced by both urban and agricultural water agencies. As such, they can serve an important risk management role in the water market. Option contracts institute temporary transfers with lower transaction cost and lower institutional resistance than permanent transfers. Hence, in addition to providing a risk management tool, they may stimulate the water market by encouraging reliance on short-term water transfers. We price the water option contract from the seller's perspective and from a social planner's perspective. We then investigate the sensitivity of the contract prices and quantity to shifts in a number of contract parameters, including the presence of an outside option for the buyer and possible access to a spot market for water. Finally, we investigate changes to the contract prices and quantity in the presence of multiple buyers and sellers, where the latter requires consideration of strategic interactions between sellers.