Contracts versus Salaries in Matching: A General Result. N.B.: This paper replaces Nr 13.09 "Contracts versus Salaries in Matching: Comment", (June 2013)

It is shown that a matching market with contracts may be embedded into a matching market with salaries under weaker assumptions on preferences than substitutability. 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 firms have unilaterally substitutable preferences.