Optimal Taxation under a Consumption Target

We consider a government facing a constraint on the total consumption of a specific good with varieties, and formulate an optimal commodity tax problem under a consumption target. We obtain a uniform pricing result (similar to the familiar uniform taxation rule): setting the same consumer price for all varieties constitutes a solution if, and only if, the compensated price elasticities of the varieties with respect to an untaxed good are all equal and non-negative. If, however, this elasticity condition does not hold, the optimal policy is at variance with the well-known inverse elasticity rule and with the Corlett–Hague rule.