Optimal Nonlinear Pricing and Contingent Contracts

Abstract

Rationing of output may be required to allocate resources when it is costly to operate a system of spot markets. In electric power markets, for example, interruptible service is the most frequently used form of capacity-sensitive allocation after time-of-use pricing. This paper examines the welfare properties and ease of implementation of alternative rationing rules and the pricing of contracts based on rationing rules. The model allows for both demand and supply shocks. The theoretical analysis is illustrated by application to curtailment rules and pricing in electric power markets. Rationing rules are a means of sharing risk and joint costs. Insurance provides a means of sharing the financial costs of random events. However, there are additional welfare gains to be obtained from pooling physical quantities of goods in the presence of random demand and supply, see Spulber (1985). By rationing goods, the common costs of production or productive capacity can be reduced while also reducing individual risk. This explains in part the extensive attention devoted to rationing of electric power. Electric power is subject to significant randomness in both supply and demand. Allocation mechanisms based on prices that adjust in real time, on complete contingent contracts, or on renegotiation of contracts in response to new information can involve prohibitive transaction costs. Avoidance of the need to ration would require inefficiently high capacity investment. Electric utilities must therefore employ rationing rules. These rules must be