Optimum Commodity Taxation with a Non-Renewable Resource

Optimum commodity taxation theory asks how to raise a given amount of tax revenue while minimizing distortions. We reexamine Ramsey's inverse elasticity rule in presence of Hotelling-type non-renewable natural resources. Under standard assumptions borrowed from the non-renewable-resource-extraction and from the optimum-commodity-taxation literatures, we show that a non-renewable resource should be taxed in priority whatever its demand elasticity and whatever the demand elasticity of regular commodities. It should also be taxed at a higher rate than other commodities having the same demand elasticity and, while the tax on regular commodities should be constant, the resource tax should vary over time. The appropriate taxation rule depends on the governments revenue needs; the higher these needs, the closer the consumer price to the monopoly price. Reserves are a form of capital and royalties tax its income; our results contradict Chamley's conclusion that capital should not be taxed at all in the very long run. When reserves to be extracted are responsive to the taxation of extraction, in the absence of any subsidy to reserve discoveries, the optimal tax rate on extraction obeys an inverse elasticity rule almost identical to that of a commodity whose supply is perfectly elastic. As a matter of fact, there is a continuum of optimal combinations of extraction taxes and subsidies. When the government cannot commit, extraction rents are completely expropriated and subsidies are maximum. In general the optimum Ramsey tax not only causes a distortion of the extraction path, as happens when reserves are given, but also distorts the level of reserves developed for extraction. When that distortion is the sole effect of the tax, it is determined by a rule reminiscent of the inverse elasticity rule applying to elastically-supplied commodities.