In many developing countries power demand is much greater than can be met, leading to routine load shedding. Some policy must be chosen for the fair and efficient rationing of power, however, transmission constraints and unreliabile generation can make it difficult to achieve a particular allocation of power. We develop methods to quantify the trade-off between maximising the total amount of power delivered and distributing the available power in a fairer way. To do so, we model a common situation in which the system operator minimises load shedding, subject to exogenous proportional allocation targets for different regions. We then explore how the level of permitted deviation from the target affects the level of load shedding. This minimisation problem is mathematically challenging, but we develop an efficient solution method for it based on Lagrangian decomposition. We apply our methods to a case study of the Nigerian Power system and analyse the Pareto frontiers between efficiency and fairness obtained under different specifications of the problem. In our case study, we show that current Nigerian policies reduce the total amount of power delivered by up to 5%, but that enforcing policies over a longer time horizon substantially reduces this efficiency penalty.