Contracts versus salaries in matching: A general result

It is shown that a matching market with contracts can be embedded into a matching market with salaries under weaker conditions than substitutability of contracts. In particular, the result applies to the recently studied problem of cadet-to-branch matching. As an application of the embedding result, a new class of mechanisms for matching markets with contracts is defined that generalize the firm-proposing deferred acceptance algorithm to the case where contracts are unilateral substitutes for firms.