When a job-seeker and an employer meet, find a prospective joint surplus, and bargain over the wage, conditions in the outside labor market, including especially unemployment, may have limited influence. The job-seeker's only credible threat during bargaining is to hold out for a better deal....

We develop a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions. We introduce a new "law of aggregate demand" for the case of discrete heterogeneous workers and show...