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α: calibrated so average coauthorship-adjusted count equals average raw count
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.