We consider the problem of allocating indivisible objects to a group of agents. Multi-item auctions are a usual mechanism for such problems when monetary transfers are allowed. Demange et al. (1986) introduces an ascending multi-item auction with remarkable properties. It is known that, when the agents have quasi-linear preferences, this multi-item auction produces the minimum competitive equilibrium price vector of the market and an efficient allocation. Moreover, it is a generalization of the Vickrey auction (see for instance Roth and Sotomayor, 1990). Therefore, each agent is required to pay the social opportunity cost of allocating to him the object he receives under the auction. In this paper, we offer two characterizations of the multi-item auction introduced by Demange et al. (1986). When the number of agents exceeds the number of objects, it is known that the Vickrey rule is the unique rule satisfying strategy-proofness, individual rationality and efficiency (we refer to Holmström, 1979 and Ashlagi and Serizawa, 2012). Notwithstanding, this characterization does not hold when the number of objects exceeds the number of agents. We show that the multi-item auction rule is the unique rule satisfying strategy-proofness, individual rationality, efficiency and non-wastefulness in prices. For a second characterization, we drop strategy-proofness, individual rationality and efficiency and we characterize the multi-item auction rule with envy-freeness, non-wastefulness, price antimonotonicity and non-wastefulness in prices.