Digital preservation is a field of research focused on designing strategies for maintaining digital objects accessible for general use in the coming years. Out of the many approaches to digital preservation, the present research article is a continuation work of a previously published article containing a proposal for a novel object-centered paradigm to address the digital preservation problem where digital objects share part of the responsibility for self-preservation. In the new framework, the behavior of digital objects is modeled to find the best preservation strategy. The results presented in the current article add a new economic constraint to the object behavior. Now, differently from the previous paper, migrations, copies and updates are not free to use, but subject to budget limitations to ensure the economic sustainability of the whole preservation system, forcing the now-called cost-aware digital objects for efficient management of available budget. The presented approach compares two auction-based mechanisms, a multi-unit auction and a combinatorial auction, with a simple direct purchase strategy as possible efficient behaviors for budget management. TiM, a simulated environment for running distributed digital ecosystems, is used to perform the experiments. The simulated results map the relation between the studied purchase models with the sustained quality level of digital objects, as a measure of its accessibility, together with its budget management capabilities. About the results, the best performance corresponds to the combinatorial auction model. The results are a good approach to deal with the digital preservation problem from a sustainable point of view and open the door to future implementations with other purchase strategies.