We examine the incentives of firms to form vertical research joint ventures (RJVs) which enable an upstream supplier to internalize the positive externality of its innovation on a downstream market, while giving the downstream members a cost advantage over their non-member rivals. Under the cost-sharing rules considered, the upstream member desires a larger RJV compared to the downstream members. RandD subsidies may be detrimental to social welfare. The optimal RJV size for the upstream (downstream) member decreases (increases) with RandD cost and increases (decreases) with the gains from innovation and the size of market. An increase in upstream competition has the effect of enlarging the optimal RJV.