In this paper, we investigate the remanufacturing problem of pricing single-class used products (cores) in the face of random price-dependent returns and random demand. Specifically, we propose a dynamic pricing policy for the cores and then model the problem as a continuous-time Markov decision process. We first design a basic model that does not consider the quality uncertainty of cores, and then extend our model to incorporate this factor. Besides proving optimal policy uniqueness and establishing monotonicity results for the optimal policy, we also characterize the impact of system parameters on the optimal policies, which can provide simple managerial insights. Finally, we use computational experiments to assess the benefits of dynamic pricing compared to static pricing and identify the impacts of specific parameters on the relative merits of dynamic pricing policy.