Circular systems design is an emerging approach for promoting sustainable development. Despite its perceived advantages, the characterization of circular systems remains loosely defined and ambiguous. This work proposes a network optimization framework that evaluates three objective functions related to economic and environmental domains and employs a Pareto analysis to illuminate the trade-offs between objectives. The US polyethylene terephthalate (PET) value chain is selected as a case study and represented via a superstructure containing various recycling pathways. The superstructure optimization problems are modeled as a mixed integer linear program (MILP) and linear programs (LPs), implemented in Pyomo, and solved with CPLEX for a one-year assessment horizon. Solutions to the circular economy models are then compared to the corresponding solutions of linear economy models. Preliminary results show that the optimal circular network is advantageous over the optimal linear network for all objectives subject to the current market supply of raw materials and the total cost of production. However, when considering the present chemical processing infrastructure of the US economy and unrestricted biomass feedstock availability, a linear economy is favorable as an outcome of low operating cost and carbon sequestration.