Consider economies with a continuum of small consumers, and a finite set of large oligopolists. Further assume that an oligopolist cannot make a joint transaction with a large set of consumers, but trades with them by offering them individual menus of transactions. These menus include transactions that are meaningful to an individual consumer, but are negligible relative to the market. The consumers, in turn, can choose repeatedly from these menus, and can trade among themselves in finite groups, using their endowments augmented by transactions made with the oligopolists. The theorem states that under these conditions linear pricing must prevail. On the other hand, when consumers can be involved in transactions with many participants and large quantities of goods, non-linear pricing may occur, indicating that the presence of friction is required for linear pricing.