rm's production and cost functions. 1. Allocating Multiproduct Costs The interconnection of services provided by a network has a number of formal implications. Because there are economies of scope, the total of the standalone costs of individual outputs necessarily exceeds the total cost of producing jointly, SO standalone costs are limited as a guide to dividing costs. The most that can be said is that the regulated revenue provided by a service Rj should not exceed its standalone cost, because consumers would then be better off if the service were supplied by a standalone facility: Rj S AC ((Qj). The standalone cost condition must hold for any subset of outputs. This condition is necessary and sufficient for a regulated rate structure to avoid cross subsidies. A regulated rate structure refers to revenues for each service that sum to equal total cost: The incremental cost of a service provides some guidance in dividing costs. To avoid cross subsidies, a regulated rate structure must have revenues that cover incremental costs: For a regulated rate structure, the requirement in equation (35) is equivalent to the condition in equation (33) that revenues not exceed standalone costs. If the firm earns a positive economic profit, revenues should still be greater than or equal to incremental cost. Otherwise the firm loses money on that service because the firm's profit could be increased by dropping the service. The cost reduction would exceed the lost revenue. The incremental cost condition must also hold for any subset of outputs. Networks in Telecommunications An important aspect of incremental costs is that if subsidy-free revenues exist, incremental costs must sum to less than total costs: A sufficient condition for the existence of subsidy-free revenues is cost complemen- tarities, 1,..., J. This is a stronger requirement on costs than economies of scope. Cost complementarities imply that the cost function exhibits economies of scope. Also, cost complementarities imply that the multiproduct cost function exhibit