As scientists are motivated by readership rather than by royalties, one might doubt that academic copyright is required for protecting the authors' property rights and for stimulating research. Consequently, the possibility of moving to an open access regime by abolishing academic copyright is currently intensively being discussed. We contribute to this discussion by focusing on the contest component of the publishing game. In our model, differently talented researchers compete for the limited space in top journals. We assume that publication fees when moving from a readers'-pay to an authors'-pay principle will fully be covered only by top universities. This yields an additional asymmetry in the Tullock-contest which reduces the quality effort incentives even for researchers whose fees are fully paid. We find that private research incentives may be either too high or too low. In the first case, open access is always superior. In the latter case, the welfare ranking of the two regimes depends on the model's parameters.