In an AK model of growth with fixed and uniform labour supply but heterogeneous asset endowments by agents, we explore the conflict that arises in relation to the functional (labour-capital) distribution of output. Negative externalities make the competitive equilibrium inefficient. We develop the efficient utility frontier; we then analyse the outcomes in terms of growth and distributive (in)equality delivered by different ways of determining the labour (equivalently: capital) share. A clear order arises between various normative and positive arrangements such that Rawlsian is more egalitarian than utilitarian is more egalitarian than contractarian (Nash solution) is more egalitarian than median voter. We also propose a novel fourth concept of distributive justice (‘justice as minimal social friction') and show that it is more egalitarian than all except the Rawlsian solution.