The complete incremental cost test for cross-subsidies with a sub-modular cost function

The complete Incremental Cost Test for cross-subsidies can be difficult to apply to a multi-product enterprise because every possible subset of products must be tested. However, this combinatorial problem can be avoided when the enterprise’s cost function is sub-modular by identifying the smallest subset of products causing the maximum cross-subsidy. This subset contains all of the products, and only those products, that are responsible for the cross-subsidies left by a stipulated set of prices. In addition, the subset can often be identified with a simple and efficient Myopic Algorithm. The algorithm should be particularly useful as a method for detecting cross-subsidies in regulated enterprises and networks because the cost functions for these industries are typically sub-modular.