This paper investigates the existence of economies of scale in the Mexican petroleum industry as well as the direct and cross price elasticities of demand for its inputs by estimating translog cost functions for three subindustries: extraction of crude petroleum and natural gas, petroleum refining and derivatives, and basic petrochemicals. Our findings are consistent with the hypothesis that it would be possible to privatize each of the various subindustries in the Mexican petroleum industry where Pemex is the sole producer without giving up cost advantages from economies of scale. These results are least robust for the extractive industry, which is the part of Pemex least likely to be privatized.