We propose a new set of mechanisms, which we call serial dictatorship mechanisms with individual reservation prices for the allocation of homogeneous indivisible objects, e.g., specialist clinic appointments. We show that a mechanism φ satisfies minimal tradability, individual rationality, strategy-proofness, consistency, independence of unallocated objects, and non-wasteful tie-breaking if and only if there exists a reservation price vector r and a priority ordering ≻ such that φ is a serial dictatorship mechanism with reservation prices based on r and ≻. We obtain a second characterization by replacing individual rationality with non-imposition. In both our characterizations r, ≻, and φ are all found simultaneously and endogenously from the properties. Finally, we illustrate how our model, mechanism, and results capture the normative requirements governing the functioning of some real-life markets and the mechanisms that these markets use.