Dual Coproduct Technologies: Implications for Process Development and Adoption

Many industries operate technologies in which multiple outputs (coproducts) are jointly produced. In some settings (vertical) the coproducts differ along a performance dimension and are substitutable. In other settings (horizontal) the coproducts differ in their applications and are not substitutable. In both cases, three important attributes of a coproduct technology are its processing cost, overall yield, and coproduct split, i.e., the proportion of each output produced. For both vertical and horizontal settings with deterministic market sizes, we characterize the optimal pricing and production decisions of a monopoly firm with two technologies. We establish the necessary and sufficient conditions for dual activation (i.e., using both technologies) to be optimal. Dual activation is driven by differences in marginal costs across the two technologies. There is an additional motive for dual activation in the horizontal setting: the desire to generate a product mix that better resembles the market mix. Building on the optimal production analysis, we characterize the optimal adoption-and-usage strategy of a firm with one incumbent technology considering a new technology. We establish the conditions for which a new technology will displace the incumbent or be used with the incumbent, and highlight some important adoption and usage differences between vertical and horizontal settings. Results are extended to the setting with uncertain market size(s).