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I thank, without implicating, Robert Flood, Michael Keen, and seminar participants in the IMF for helpful comments to previous versions.
The paper has less directly to say about the issue of taxing other fossil fuels, coal and natural gas. These markets fit less well with the model studied here: coal, used largely in electricity generation, is more costly to transport and tends to be consumed much more in the producer country; and natural gas often involves long-run price contracts due to heavy specific infrastructure investments in pipelines.
We are here ignoring the local externalities caused by petroleum consumption, which can in principle be corrected for by taxes and regulations in the countries themselves.
This obviously abstracts from the practical problem of agreeing on what is the correct value of the externality. This is difficult both due to great intrinsic uncertainty and because most benefits of carbon emission control will accrue to future, as of yet unborn, generations. We here also abstract from problems due to the environmental problem being due to a stock externality, while emissions are a current flow.
This of course ignores the specifics of considering petroleum an exhaustible resource; see Newbery (2005) and the discussion below.
See also Newbery (2005), who also derives estimates of optimal tariffs on petroleum, under different assumptions about price elasticities of demand for petroleum.
Bergstrom however does consider the strategic relationship between taxes set by importers and a monopolistic exporter, thus leading up to an analysis akin to ours in section 5.3 below.
This result is largely due to the combined assumptions of exhaustibility and zero extraction cost, which leads to a shift in the equilibrium future price path for the resource when an importer tax is imposed. By contrast, extraction costs here play a key role, while exhaustibility does not.
This assumption in effect embeds additional assumption that will not be discussed further here; in particular, all consumers of petroleum, in all consumer countries must be facing a uniform petroleum price, and all must behave atavistically in their respective markets. We are also, equally heroically, disregarding all distributional concerns, within or between countries.
When c1 represents the greenhouse-gas (GHG) related damage, it will typically involve a stock externality, as there will be an externality cost due to current emissions for all future periods. Such an interpretation of c is here permissible given that climate effects are linear in emissions, and with an infinite horizon and constant interest (and discount) rate. Then, in addition, damages from future emissions will be independent of the stock of accumulated GHG emissions, at any given time.
This follows when p0 > 0, and s > 0 at the optimal solution for exporters, as will be discussed further in the next subsection.
With n countries and N demanders of fossil fuels in each country, the externality effect to each demander, as a result of ones own demand for fossil fuels, will be of the order c/nN, which vanishes when N is large.
Note that there are no income effects on petroleum demand in this model, following from the assumption that the utility of petroleum consumption, from function (3), is independent of income.
In more realistic cases, the demand function is linear only as an approximation in the neighborhood of equilibrium, and not globally. The condition, under which t exceeds the Pigou level, is then that the value of the first petroleum unit as calculated from the linearized demand function, exceed the marginal externality cost; which will also hold unless c1 is extremely large.
A main difference is the current lack of auctioning of emission permits under EU ETS, with 95 percent of emission rights being given away to firms for free. Another difference is that the EU ETS only comprises a fraction (less than half) of carbon emissions in the European Union.
Another way to put this is to say that the exporter will always charge the highest price at which the total quantity of R would be sold to importers; this must be optimal for the exporter, since otherwise it would have selected a lower level of R.
Note that, also in this case of a “strong monopolist” that has the ability to set both output and price, but where the importer is a Stackelberg leader, it makes a great strategic difference for the importer whether he sets a quota or a tax, with preference for the latter.
There are several problems with the ETS. One of these is the high degree of free allocation of emission quotas to past emitters (at least 95 percent in the current trading period; and at least 90 percent for the 2008-2012 period), providing high windfall gains to emitters and robbing governments of potential tax revenue; see Goulder (2002) and OECD (2004). As argued by Böhringer and Lange (2005) and Rosendahl (2006), perhaps even more damaging is the system’s lack of ability to deliver carbon reductions over time, since future free quotas tend to depend on current emissions, and are expected to do so in the future.
The result can rather easily be generalized to the case where exporters do not act as a monopoly but instead in monopsonistic (Nash-Cournot) fashion or as a leader with a competitive fringe.
In recent years OPEC has, arguably, functioned more as an intertemporal regulator of supply than as a general suppressor, or has at least attempted to do so. Over the two years up to October 2006, when demand and price levels remained high, the group has generally not restricted supply. Over the last months there has again been some attempt by OPEC to regulate supply directly, in view of falling equilibrium oil market prices.
A large fraction of oil supply comes from companies that are directly government owned and where supply cannot be assumed to respond to price signals in a regular market-determined way. This raises the important and complicated, and so far unresearched, issue of what would be the exporter supply response from these companies, to petroleum taxes imposed by importer countries.
Note that the classical view of petroleum as an exhaustible resource may be challenged by development of new cost-competitive energy sources, such as biofuels, with the same functions as oil.