Infrastructure sharing synergies and industrial symbiosis: optimal capacity oversizing and pricing

In this paper we show that Industrial Symbiosis (IS) being implemented in Eco-Industrial Parks (EIP) deals with both substitution synergies (exchange of waste materials, fatal energy and/or utilities as resources for production) and infrastructure/service sharing synergies. The latter is based on the intensification of use of an asset and thus requires to balance capital costs increase with economies of scale for its implementation. Initial investors must specify ex-ante arrangements (cost sharing and pricing schedule) to commit toward investments in infrastructure capacity and the associated transactions. In this way we propose a model that investigates the decision of 3 actors, 2 trying to choose cooperatively a level of infrastructure capacity oversizing to set a plug-and-play offer to 1 potential entrant. The latter has a capacity requirement which is randomly distributed. Capacity cost exhibits sub-additive property so that there is room for profitable overcapacity setting. The entrant's willingness-to-pay for the access to the infrastructure depends on its standalone cost and the capacity gap that must be completed in case the available capacity is insufficient ex-post (the backup cost). Since initial capacity choices are driven by the ex-ante (expected) entrant's willingness-to-pay we derive the expected complement cost function which helps us to define the investor's objective function. We first show that this curve is decreasing and convex in the capacity increments and that it is shaped by the distribution function of the potential entrant's requirements. We then derive the general form of solutions and solve the model for uniform distribution. Depending on the requirements volumes and the cost assumptions different capacity levels are set.