Circular economy: Joint dynamic pricing and recycling investments

In a circular economy, the use of recycled resources in production is a key performance indicator for management. Yet, academic studies are still unable to inform managers on appropriate recycling and pricing policies. We develop an optimal control model integrating a firm's recycling rate, which can use both virgin and recycled resources in the production process. Our model accounts for recycling influence both at the supply- and demand-sides. The positive effect of a firm's use of recycled resources diminishes over time but may increase through investments. Using general formulations for demand and cost, we analytically examine joint dynamic pricing and recycling investment policies in order to determine their optimal interplay over time. We provide numerical experiments to assess the existence of a steady-state and to calculate sensitivity analyses with respect to various model parameters. The analysis shows how to dynamically adapt jointly optimized controls to reach sustainability in the production process. Our results pave the way to sounder sustainable practices for firms operating within a circular economy.