In recent years, there have been substantial interests in the joint production of ethanol and distillers grains (E&DG) from corn. At the same time, there have been corresponding increases in the production of animal feed based on distillers grains (DG). Under such circumstances, ethanol and DG are produced by an E&DG producer, and DG serves as input to feed production by a feed producer.The objective of this paper is to study the strategies of both producers in different models in order to maximize their own profit with more ethanol produced by consuming more DG in the feed market.

First, we investigate the economic relationships such as pricing between the E&DG producer and the DG-based feed (feed) producer under Stackelberg competition as well as under coordination when both producers have their own linear production costs, respectively. (1) Specifically, for competition, we construct a Stackelberg model with an E&DG producer as the leader and a feed producer as the follower, and examine the consequences in terms of profits, prices, and production and purchase quantities. As the DG fraction increases, the E&DG producer loses or gains more profit than the feed producer under different conditions. Under specific condition, as the DG fraction increases, both producers have higher profit with the higher quantity of DG as well as ethanol so as to help the increasing ethanol market. (2) For coordination, we consider a centrally coordinated model where producers are viewed as one group. Compared with the Stackelberg model, the centrally coordinated model has higher total profit to be shared by both producers as they are optimizing the total profit as a single company with more DG as well as ethanol produced.

Second, this paper extends Stackelberg model with a quadratic unit joint production cost for the E&DG producer. For this model, we investigate the economic relationships such as pricing, profit for both producers and compared with the euqilibrium solution in the Stackelberg model with a linear joint production cost for the E&DG producer.