We present a theoretical framework in which an elitist and a non-elitist university in a developed country compete by choosing admission standards and deciding whether or not to open a branch campus in a developing country. Students from a developing country attend university if either a branch campus is opened or, they can afford to move to the developed country. We find that the elitist university is more likely to open a branch campus. This result is reversed if the gain, in terms of prestige, to attend the home campus of the elitist university more than offsets a student’s mobility costs. A rise in the graduate wage increases the incentive for opening a branch campus, although this incentive is stronger for the elitist university.