Expanding distribution channels

We provide a model in which upstream producers, whose production cost is quadratic in quantity, sell their products through two distribution channels, a traditional channel and an external retailer. Some producers (called "large" producers) supply to both channels, whereas other producers (called "small" producers) are only able to supply to the traditional channel. All producers compete in quantity in the traditional channel. The external retailer offers a nondiscriminatory per unit payment to upstream producers. We show that distribution channel expansion executed by a small producer can decrease the producer's profit and the sum of the upstream producers' profits.