Production costs, scope economies, and multi-client outsourcing under quantity competition

Two game models are developed based on production costs and scope economies to investigate the widely observed multi-client outsourcing (MCO) phenomenon. Analytical results demonstrate that outsourcers' high in-house production costs and the advantage of scope economies motivate firms to outsource collectively to an independent vendor. Under certain conditions, if both firms make their outsourcing decisions simultaneously, collective outsourcing is one of the two equilibria; if both firms make decisions sequentially, collective outsourcing becomes the unique equilibrium. Furthermore, the comparative statics of the critical degree of scope economies are examined for the occurrence of MCO with regard to diverse market parameters. Finally, it is proved that market prices decrease as the degree of scope economies increases when MCO occurs. This research helps explain some widely observed phenomena such as malls, supply chain cities, and the China price.