An optimal quantity tax path in a dynamic setting

Following Ramsey, the existing literature on optimal quantity taxation only compares the pre and the post-tax market equilibriums in order to account for the efficiency losses. However, when the government imposes a quantity tax on the consumer, the buyer's price jumps to the pre-tax equilibrium price plus the amount of the tax, and the supply and the demand of the taxed commodity then adjust over time to bring the new post-tax market equilibrium. The existing literature does not take into account the efficiency losses during the adjustment process while computing the optimal quantity taxes. This paper derives an optimal quantity tax path in a dynamic setting minimizing the efficiency losses (output and/ or consumption lost) during the dynamic adjustment process as well as the post-tax market equilibrium.