In this paper, we present a pharmaceutical supply chain network model with outsourcing under price and quality competition, in both equilibrium and dynamic versions. We consider a pharmaceutical firm that is engaged in determining the optimal pharmaceutical flows associated with its supply chain network activities in the form of manufacturing and distribution. In addition to multimarket demand satisfaction, the pharmaceutical firm seeks to minimize its total cost, with the associated function also capturing the firm's weighted disrepute cost caused by possible quality issues associated with the contractors. Simultaneously, the contractors, who compete with one another noncooperatively in prices in the manner of Bertrand, and in quality, seek to secure manufacturing and distribution of the pharmaceutical product from the pharmaceutical firm. This game theory model allows for the determination of the optimal pharmaceutical product flows associated with the supply chain in-house and outsourcing network activities and provides the pharmaceutical firm with its optimal make-or-buy decisions and the optimal contractor selections. We state the governing equilibrium conditions and derive the equivalent variational inequality formulation. We then propose dynamic adjustment processes for the evolution of the product flows, the quality levels, and the prices, along with stability analysis results. The algorithm yields a discretization of the continuous-time adjustment processes. We present convergence results and compute solutions to numerical examples to illustrate the generality and applicability of the framework.