Trade in business services has been attracting attention from academic researchers, policy makers, and business journalists. While there are many anecdotes, there has been little in the way of formal theory applied to this issue. In this paper, we adapt a general model of fragmentation of production activities to try to capture the specific features of business services. Following a general discussion, we calibrate a numerical general-equilibrium simulation model to a situation in which both trade and foreign investment in services are initially banned to technically infeasible. We then compute three counter-factual scenarios: one in which trade but not investment in services is feasible or allowed, one in which investment but not trade is allowed, and one in which both trade and investment in services are allowed.