# Optimal taxation under a consumption target

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## Abstract

While in the familiar problem of optimal commodity taxation the government faces a constraint on tax revenue, we consider the case of a consumption target on a group of commodities (i.e., a weak constraint on total consumption), instead. This optimal commodity tax problem with a consumption target brings about taxation rules that are mainly at variance with the standard results of commodity taxation. In our main theorem, we derive a general, though quite simple, rule of optimal commodity taxation under a target on total consumption: in particular, we establish that higher consumer prices should be charged for commodities with (1) high price elasticities of total demand and (2) low consumption shares in total demand. From this theorem we deduce three important corollaries: an anti-inverse elasticity result, an anti-Corlett–Hague result and a uniform-pricing result. All of these results are (generically) at variance with well-known rules of commodity taxation.

## Notes

### Acknowledgements

We are grateful to Ben Lockwood and two anonymous referees for their helpful and inspiring comments.

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