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In this paper, we study a two-echelon supply chain inventory system with a single manufacturer and a single buyer, considering price-dependent demand and variable lead time. Lead time can be reduced by added crashing cost. We first assume that the lead time demand follows a normal probability distribution and then consider the case where it is distribution free. We develop both the centralized and decentralized models and derive the optimal solutions by using profit maximization criterion. Feasibility and efficiency of the proposed models are justified through two numerical examples. We numerically investigate how the optimal decisions are affected by changes in various model-parameters. From numerical study, we observe that even though the lead time reduction diminishes the retailer's selling price, it enhances the system profit significantly. [ABSTRACT FROM AUTHOR]