We analyze production economies with a linear technology and single peaked preferences. We first characterize the class of Pareto optimal (allocation) rules. We then characterize the subclass that additionally satisfies strategy proofness. Finally, we show that a uniform production rule uniquely satisfies Pareto optimality, strategy proofness, and equal treatment of equals. A similar result is obtained if equal treatment of equals is replaced with stronger fairness properties such as no-envy or anonymity. Our results can be applied to the problem of allocating central government funds among regional development agencies
