European policy makers may have asked too much from regional policies: to decrease inequalities between regions, to increase efficiency at the national and European levels and to decrease inequalities between countries. This paper argues that these policies face a trade-off between equity and efficiency at the spatial level. If the existence of positive localised spillovers and of returns to scale explain the phenomenon of self-sustaining agglomeration, then agglomeration must have some positive efficiency effects. We also argue that because infrastructure financed by regional policies have an impact on transaction costs and therefore on the location decision of firms, the long-term effect of certain regional policies may be unexpected and unwelcome. Policies that finance infrastructure to reduce transaction costs on goods between regions lead to more agglomeration but higher growth at the national level. We show that policies that reduce agglomeration (transfers, financing of transport infrastructure inside the poor regions) may then also reduce efficiency and growth. On the contrary, a policy that reduces the cost of innovation or increases the diffusion of innovation reduces regional income inequality, agglomeration and increases growth.