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Social Cloud Computing is an emerging online collaboration paradigm which is characteristic of many socially oriented electronic platforms. The operation of such a platform requires computational infrastructure to facilitate the platform itself as well as the services enabling its basic operation. While this infrastructure currently requires capital-intensive investments, we believe it is possible, and even advantageous, to use a co-operative model where the platform (i.e. its computational infrastructure) is provided by the users themselves. In this paper, we define a formal economic model for a co-operative infrastructure in the context of a socially oriented platform and analyze (through simulation) the model with respect to its feasibility and scalability. Using Social Clouds as a use case, we demonstrate in several scenarios that the co-operative approach does not only have advantages over dedicated infrastructures, but also is a particularly suitable model for providing core infrastructure in social (computing) platforms.