In order to understand the core of Sinn's argument, we will abstract from various complications that might weaken or strengthen his result, but that do not change the fundamental point that perverse CO2 emission responses are at least possible, even if not likely. That is, we will assume that resource extraction technology and the total stock of extractible resources (e.g. oil reserves in the ground), as well as the interest rate, are given and constant.
In that case, we can think about the problem of a resource producer, e.g. a global oil company, in the following way: If the oil producer leaves the oil in the ground today and sells it tomorrow, she gains if the price of oil increases in the meantime, so that she can sell it at a higher price tomorrow. The return of that is ΔP, the change in the oil price per time unit. If she extracts the oil today, she would have extraction costs c, earn price P, and then be able to invest the net profit for a per-period return of i(P-c). Thus, in any given period, the oil producer will adjust the resource extraction path until
i=ΔP/(P-c) (1)To see that this is true, consider what happens when this equation does not hold: For example, if the current price level is such that the expected increase in price over time, and therefore the return to leaving the oil in the ground is lower than the returns i that can be had elsewhere, then the oil producer will try and sell more oil now, in order to invest his money at those relatively favorable interest rates. However, this will increase the current supply of oil, which in turn lowers the oil price. As the amount of oil in the ground is fixed this means that there will be less oil left to be extracted in the future, which raises the future price of oil. As the current price of oil goes down and the future price goes up, the expected increase in the oil price per period increases, which raises the return to leaving the oil in the ground (the RHS of equation (1) above). This will continue until equation (1) holds, because at that point there is no gain to be had from transforming oil int eh ground into money that can be invested or vice versa.
In order to give an example of what this dynamic might look like, I have built a small model of the optimal extraction path (see footnote 1 for further details): Let's assume that the market price of the resource, say "Oil," is negatively related to the amount that is extracted in a given time period, but that the total amount of oil in the ground is fixed and that all oil will be produced within 10 time periods, with zero extraction cost, for simplicity's sake. All prices are assumed to end up at 10 in the last period, which is a stand-in here for the price of the last drops of oil right before the exhaustion of the resource. Moreover, the opportunity cost of keeping oil in the ground is assumed to be 10%, which means that the optimal extraction path following equation (1) will adjust extraction so that the increase in the oil price per period is also 10%. That optimal extraction path is shown as the dark green line R1 in Figure 1 below and the price path that it determines is the light green line P1. Note that the oil producer produces more oil in the beginning and less later, which is why the price rises towards the later periods.
Now, let's ask ourselves what would happen if we threatened the oil producer with constant taxes on oil extraction profits? Because the exogenous interest rate still determines the optimal price path, and remains unchanged at 10%, the extraction path R1 that we initially determined is still optimal. In some sense, as the tax is constant over time, the oil producer has handed over a share of his lifetime oil extraction profits to the government, but the problem of maximizing the value of his remaining share is the same as that of optimizing his extraction path if there were no tax. That is, a constant tax rate on oil extraction profits would not change CO2 emissions at all in this very simplified model. While the setup here is certainly unrealistic, it is not necessarily more so than most of the discussion in the media of climate change policy. And it suggests that at least under some conditions, taking into account the supplier's incentives can undo the intuition that might equate a rise in tax on oil production with a decline in CO2 emissions.
i=(ΔP/(P-c))-Δ/, (2)where is the level of the tax rate and the additional term on the RHS expresses the fact that any increase in oil revenue that can be had by leaving the oil in the ground for another time period will be mitigated by the increase in the share of profits that are taken away by the tax. Thus, if the interest rate on the LHS of equation (2) remains at 10%, but the tax rate grows by 15% every period, the price of oil would have to grow by 25% in order for the equation to hold. That is, the oil supplier will want the price path to be steeper to make it worthwhile for him to wait until she can sell his oil, if the future brings ever higher tax rates. Put differently, as later oil extraction will be less profitable due to rising taxes, she moves some of the extraction to earlier time periods to escape the higher future tax rates, and as a result current oil prices fall, while exhaustion price in period remains the same, steepening the price curve. This is shown in Figure 1 by the red extraction path R2 and the light blue price path P2, which result from using the same model as above, but replacing the required rate of price increase with 15%.
Let's note what this means: the policy of increasing carbon taxes over time, which is supposed to lead to lower carbon emissions than no taxes or constant taxes, in fact leads to more oil extraction in earlier periods, which means higher, not lower, carbon emissions than without the tax increases! Of course, this model abstracts from many things, among them the possibility of switching to new technologies, which is often one of the goals of carbon taxes. All I wanted to show here is that Sinn's paper suggests that including the suppliers' incentives in our CO2 emission policy analysis may lead to policies having the inverse of the intended effect in this simplified setting. As a result, when reading of any analysis of the impact of policy X on carbon emissions, it might be worthwhile checking whether the results take into account the incentives of resource producers, and, if not, take its policy recommendations with a grain of salt.
While Sinn's model assumes that the "resource suppliers" are a single entity that is free to alter its extraction path any time, the case of oil production would require us to model more complex market characteristics: most major oil producers are members of the OPEC cartel and therefore bound by production quotas that are intended to keep them from increasing their oil production unilaterally in a way that would lower the oil price received by all other producers. Then, the question becomes to what extent OPEC itself can be seen as an optimizing agent in Sinn's sense. On the other hand, there are other factors that might accelerate or decelerate oil production - some of which Sinn mentions: If a country faces an unstable political situation, the current government might not be able to profit from the national oil company's revenues after it loses power and therefore prefers earlier oil production to later oil production. Moreover, if a substantial share of the fiscal budget of a country comes from oil revenues, fiscal deficits may lead to an attempt to raise more revenues from oil production in the short run. In the end, the supply side response to expectations of the future profitability of oil extraction might be quite complicated, but that is no reason to ignore it.
1. The model used is the following: P=a-1.2*R, where a is chosen to ensure that (aggregate resource extraction)=(resource stock in the ground)=50.
2. i1=10% for the first pair of lines and i2=25% for the second pair of lines.
3. Then, equation (1) determines the price path, with exhaustion price set exogenously at P(t=10)=10.