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Equitable bandwidth allocation is essential when QoS requirements and purchasing power vary among users. To this end, we present a mechanism for bandwidth allocation based on differential pricing. In our model, the QoS vs. cost trade-off induces a minimum acceptable allocation, a maximum acceptable allocation, and a unique optimal allocation for each user. We analyze the fairness and truthfulness properties of our mechanism from a game-theoretic perspective. We show that it produces allocations that provably satisfy a variant of the classical notion of max-min fairness. It ensures that flows with higher QoS requirements need to pay at higher rates to increase their likelihood of being served. Furthermore, the Nash equilibrium induced by our mechanism leads to allocations that are comparable to "socially optimal" allocations; hence users gain very little by being untruthful.