Labor market efficiency: output as the measure of welfare

We study the matching of workers to firms in which workers choose an observable and contractable effort after the match. If there are complementarities between a worker's ability and a firm's technology, positive assortative matching (PAM) is the only matching in any equilibrium and is the unique efficient matching. We investigate the effect of a policy that changes the matching of firms to workers from any matching to PAM, such as implementing a centralized clearing house. We characterize two sets of sufficient conditions on the production and cost functions under which the total output and welfare both increase. Under the first set of conditions, the increase in total output is an upper bound for the efficiency gain. In contrast, under the second set of conditions, the increase in total output is a lower bound for the efficiency gain. We identify a third set of conditions under which the total output decreases while welfare increases.