This paper estimates economies of scale and scope for 36 Australian universities using a multiple-input, multiple-output cost function over the period 1998-2006. The three inputs included in the analysis are full-time equivalent academic and non-academic staff and physical capital. The five outputs are undergraduate, postgraduate and PhD completions, national competitive and industry grants, and publications. The findings indicate that ray economies of scale hold up to about 120% of current mean output though product-specific economies of scale hold only for undergraduate teaching. Global economies of scope prevail in the sector, increasing with the level of mean output, while product-specific economies of scope arise for all outputs except publications. A cost efficiency index constructed using the sector benchmark indicates that the universities of Ballarat, Southern Cross and Flinders have a high level of cost efficiency, while New South Wales, Royal Melbourne Institute of Technology and James Cook are cost inefficient.