This paper empirically analyzes economies of scale and of scope in the production of research and technology transfer outputs in the Spanish public university system. We employ the flexible fixed cost quadratic function which relates total university R&D expenditure and the budget of the technology transfer offices with different outputs of research and technology transfer, from which we then compute the ray economies of scale, the specific economies of scale and the economies of scope. Our results indicate that ray economies of scale and research specific economies of scale hold up to 100% of current mean expenditure. The technology transfer product specific economies of scale hold up to 150% of current mean of the R&D expenditure. Our results also show that cost subadditivity acts a positive constraint, from which we infer the presence of economies of scope.