We study competitive market outcomes in economies where agents have other-regarding preferences (ORPs). We identify a separability condition on monotone preferences that is necessary and sufficient for one's own demand to be independent of the allocations and characteristics of other agents in the economy. Given separability, it is impossible to identify ORPs from market behaviour: agents behave as if they had classical preferences that depend only on own consumption in competitive equilibrium. If preferences, in addition, depend only on the final allocation of consumption in society, the Second Welfare Theorem holds as long as any increase in resources can be distributed in a way that makes all agents better off. The First Welfare Theorem generally does not hold. Allowing agents to care about their own consumption and the distribution of consumption possibilities in the economy, the competitive equilibria are efficient given prices if and only if there is no Pareto-improving redistribution of income.