We consider the problem of allocating courses to students in post-secondary institutions. We propose a mechanism that assigns course seats based on student preferences and respects course priorities. This mechanism uses fake money and competitive equilibrium to allocate courses without transfers and has desirable theoretical properties in terms of stability, efficiency, fairness, and strategy-proofness. In simulations drawing from real-world university data, we demonstrate that its outcomes improve student satisfaction and allocation fairness over the outcomes of several celebrated mechanisms.