rey auction for a type-bi consumer to obtain Therefore, since F1-k(b))=Q*(b) 9 For additional discussion, see Harris and Raviv (1981). In their setting, consumer types are discrete and capacity is perfectly divisible, as opposed to our setting, with a continuum of consumer types and capacity in discrete units. Networks in Telecommunications of allocating scarce capacity based on differences in how consumers value speed of delivery. In electricity and natural gas, customers paying a premium for higher priority are less likely to be curtailed given a shortage of transmission capacity. The discussion in the previous section derived a price schedule for reliability R(Q). This can be interpreted as a priority pricing scheme. Define pas the price of a unit of capacity, with a continuum of priorities ranging from p(0) = R(Q*(0)) to R(Q*(1)). The higher the price chosen by the consumer, the higher the priority. A consumer of type b will select a priority price, The firm will serve customers in order of priority prices starting from the highest price and continuing until all units of capacity have been exhausted. The Khighest- value consumers obtain a unit of capacity and have the same expected payment as in the case of the reliability schedule by construction. The priority pricing scheme is effectively a discriminatory auction in which every winning consumer pays his bid, with the highest K bidders winning a unit of capacity.10 C. Network Capacity Pricing with Congestion and Quality of Service Allocation of network capacity is substantially more complex than dividing a cake among potential consumers. The cause of this complexity is that usage of capacity can create congestion that drives down the quality of service. This means that whereas transmission capacity can be well defined in terms of quantity, changes in the level of usage affect customer benefits from using that capacity. The effects of congestion of telecommunications networks on quality of service have been widely recognized. Increases in usage for a given ca