Carbon prices in Canada are still low compared to where they need to be to combat greenhouse gas (GHG) emissions effectively. British Columbia's $30/tonne carbon tax is now followed by a similar tax in Alberta ($20/tonne in 2017, rising to $30/tonne in 2018) and cap-and-trade systems in Quebec and Ontario (with prices expected to fall in the $15-20/tonne range). There is one catch with carbon pricing. If other jurisdictions have much lower carbon prices or no carbon price at all, businesses that in Canada that face carbon prices will be at a competitive disadvantage. This problem is pronounced in energy-intensive trade-exposed (EITE) sectors of our economy. Among them are industries related to fossil-fuel production, processing, and refining, but also the cement and lime industry. Canada's Ecofiscal Commission has described some of these issues in its November 2015 report Provincial Carbon Pricing and Competitiveness Pressures. What can be done to alleviate the problem? Economic theory provides some insights and some ready answers as well.

The key economic insight is that a carbon price works at the margin: what matters is the cost of abating the next unit of carbon dioxide. This is the notion of marginal abatement cost (MAC). What makes carbon pricing economically efficient is that even though businesses all have different MAC curves, they will all increase their abatement effort until their MAC equals the carbon price. Ideally, that carbon price in turn reflects the marginal damage from GHGs. The problem is that a carbon tax equals carbon price times emissions, and thus may involve a large transfer of money from businesses to government. To offset the negative effect of this transfer, the BC carbon tax refunds a large part to businesses through lower corporate income taxes. This income tax reduction does not distinguish between EITE sectors and non-EITE sectors, and thus BC's revenue neutrality does not fix the problem with EITE firms.

Refunding money is obviously the key to solving the problem of EITE industries—but it has to be done in a way that does not lead to new distortions or creates unfair distributional outcomes. What is needed is a system through which the carbon price at the margin is high, where it determines abatement effort and emission levels. At the same time we need a system that keeps the average carbon price low so that it does not put emission-intensive industries at too large a disadvantage relative to its competitors. Efficient carbon taxes require a high marginal carbon price, while keeping Canadian industries competitive requires a low average carbon price. It sounds like squaring a circle. In fact, it is not very difficult to design a suitable mechanism to achieve both goals.

So what exactly is the difference between a marginal carbon price and an average carbon price? And how can we drive a wedge between the two in practice? To explain the different methods to achieve that, a little bit of economic theory is helpful. I will lay out a very simple model of a firm with abatement costs and a carbon tax and then introduce three different solutions to help EITE firms. The marginal carbon price is the carbon price a company faces for the next unit of emission, while the average carbon price a company faces is the total carbon tax divided by total emissions. There are mechanisms to keep the latter lower than the former.

A simple model with abatement cost and carbon tax

Consider a simple model of a firm with output \(q\), linear demand \(p=a-bq/2\), and emission intensity \(e\), The firm faces carbon price \(\tau\) on its total emissions \(e\cdot q\), but has the ability to abate at an increasing cost of \(s\cdot(\bar{e}-e)^2/2\) per unit of output, where \(\bar{e}\) is the unabated emission intensity. Note that the \(\bar{e}-e\) is emissions abated, the difference between the original level and the level the firm chooses. The square in the abatement cost function indicates that it gets harder and harder to achieve more emission reduction. Technically, this means that marginal abatement costs are increasing with the amount of abatement. Production costs have a constant marginal cost \(c\). With this set-up profits are revenue minus costs: \[ \pi = (a-bq/2)\cdot q-[c+s\cdot(\bar{e}-e)^2/2+\tau\cdot e]\cdot q \] The first-order condition for a profit maximum implies optimal emission level \(e^\ast\) and optimal emission abatement of \[\bar{e}-e^\ast=\frac{\tau}{s}\] and an optimal output level of \[ q^\ast= \frac{a-c}{b}-\frac{\tau}{b}\left(\bar{e}-\frac{\tau}{2s}\right) \equiv\frac{a-c-g(\tau)}{b} \] The expression in round parentheses is always positive, and thus \(g(\tau)\) has been introduced to simplify the effect of the carbon price in the equation; this function is increasing in \(\tau\) but at a diminishing rate. At \(\tau=s\bar{e}\), abatement is complete and emissions are reduced to zero. At that point output is reduced by \(s\bar{e}/2b\) units. The emission tax achieves its desired effect through two channels: output reduction and deploying abatement technolgy. Total profits are: \[\pi^\ast=\frac{(a-c)^2}{2b}-\left[\frac{g(\tau)(2(a-c)-g(\tau))}{2b}\right]\] As the emission price rises, profits fall. The expression in square brackets above is the total cost of the carbon policy to the firm: it includes the carbon tax as well as the abatement cost.

The expression in the square brackets is the problem we need to tackle: if it is "too large", it impedes the competitiveness of Canadian companies if their competitors abroad pay nothing. We need to find a way to reduce the amount in a neutral way that does not diminish the incentive to reduce emission. Of course, the moment we rebate money, the company will be better off and will tend to reduce prices and increase output. But this effect will be small unless demand is very elastic.

Solution 1: a best-of-class emission intensity rebate

Now assume that there is a best-in-class abatement technology with emission intensity \(0<\hat{e}<\bar{e}\), and that it is not possible to achieve further emission reductions. Emission reductions beyond implementing this technology can only be achieved through output reductions. The regulator decides to rebate the emission tax up to the point of the best-in-class technology so that the actual tax amount is now \(\tau\cdot(e-\hat{e})\cdot q\) instead of \(\tau\cdot e\cdot q\). Put another way, each firm receives a rebate equal to \(\tau\cdot\hat{e}\cdot q\) after paying the full carbon tax. This leaves marginal abatement cost still equal to emission price, but output is now slightly higher, as are profits. Whereas the average carbon price was equal to the marginal carbon price in the first scenario, in the new scenario the average price per unit of emission has now fallen to \(\tau\cdot(1-\hat{e}/e)\), which is lower than the marginal carbon price \(\tau\). For firms that actually implement the best-of-class technology, the emission tax will be zero, and the abatement cost will be \(q\cdot s\cdot(\bar{e}-\hat{e})^2/2\).

Refunding the carbon tax based on best-of-class emission intensity ensures that firms only pay for being a technological laggard. They do not get penalized for being more emission intensive than other industries simply based on what they produce. The remaining problem is then determining the best-of-class technologies in each industry. For most emission-intensive industries, this task is not too difficult. For example, the "gold standard" for LNG plants is the electric drive. In fact, the BC government has already recognized this principle in its new GHG Industrial Reporting and Control Act, which sets a benchmark of 0.16 tonnes of CO2 per tonne of LNG produced. Facilities that cannot meet this target are required to contribute to a technology fund for excess emissions. Clearly, the notion of best-of-class emission intensity rebated is already well understood in British Columbia. For future increases in the carbon tax it may well be worthwhile adopting the same principle more broadly.

Ideally, the actual \(\hat{e}\) chosen should exceed the best-of-class emission intensity a little bit in order to allow for further innovaton. It also needs to be revised periodically to catch up on technological advances. This makes sure that firms continue to have an incentive to "race to the top", and all pay at least a some amount of carbon tax.

Solution 2: a carbon conservation tariff

In my May 22 blog about "Electricity conservation tariffs: how do they work?" I explained how BC Hydro uses a locally-high marginal price to create an additional incentive to reduce energy consumption. The same method works for a carbon tax as well. Simply substitute the term "carbon tax" for "electricity tariff". The basic logic is simple. Define a baseline of the firm's carbon emission as a rolling average of the last three years. Continue to apply a carbon tax at the current rate of $30/tonne. Then offer to rebate, say, $60/tonne for emission savings up to 20% below the baseline and charge $60/tonne for emissions above up to 20% above the baseline. This means that in a range of +/-20% around the baseline, the (marginal) carbon price will be $60/tonne. However, the average carbon price will still hover around $30/tonne. As the baseline adjusts slowly over time, the surcharge or credit will gradually disappear. The downside of this model is that the cumulative benefits over a time horizon of decades will be smaller than from a high average carbon price. A carbon conservation tariff encourages small incremental improvements but does not provide large savings that may be necessary for abatement equipment with high up-front fixed costs.

I will return to the issue about the intensive and extensive margins of investing into abatement technology in a future blog.

Solution 3: grandfathered permits

The discussion above centered around carbon taxes. Ontario and Quebec are using a cap-and-trade system instead. In such a system one needs to rely on a quantity instrument rather than a price instrument to provide a rebate to EITE industries. Firms can be given a free allocation of permits instead of requiring them to purchase permits in an initial auction (from the government) or in the carbon market (from other firms). The number of grandfathered permits allocated to EITE firms can be proportional to their output and again the best-of-class emission intensity. The administrative problem is measuring output reliably. This is easiest when the output is a relatively homogeneous commodity—oil, or natural gas, or liquefied natural gas, or cement. It is rather difficult for industries that produce heterogeneous goods. This grandfathering method would not work well in that case. Fortunately, most EITE industries fall into the category of homogenous-good production.

What not to do to help EITE industries

It is possible to think of all sorts of other mechanisms to rebate money to firms. Many firms will indeed lobby for these, and many non-economists will probably find some of these appealing. Here is a short do-not-even-think-about-it list of policies that must be avoided.

The first bad idea involves paying firms "compensation" based on some sort of merit criteria. The devil is in such criteria. On one hand, they may be influenced politically rather than based on purely technological measures. On the other hand, criteria that may appear sensible can be flawed. For example, basing compensation on an industry's average emission intensity may reward industries that have failed to innovate. Basing compensation on a particular level of international trade exposure may also be unfair: firms that trade more with low carbon-price jurisdictions in Canada than with low carbon-price jurisdictions in the United States could find themselves disadvantaged.

The second bad idea uses arbitrary thresholds that group firms into eligible or ineligible within the same industry. This opens a can of worms for mining the system to meet the eligibility criteria. Good policies are "smooth" and avoid thresholds. Note that the best-in-class technology system explained above remains smooth even though it involves a threshold. The threshold is chosen in such a way that all firms are on the same side of the threshold. A best-of-class emission intensity is by definition the infimum of the set of emission intensities found in the industry. In other words, the emission tax still applies smoothly to all firms in that industry.

The third bad idea is to assess the need for help on the overall financial performance of firms. Obviously, some sectors enjoy higher returns than others, but this may change over the course of the business cycle. Any measure designed to provide relief to EITE industries must be independent of the business cycle and independent of structural change. The guiding principle for providing EITE relief must be to keep a level playing field across firms within the same industry, and minimize distortions.

Relief for EITE industries will be badly needed if the wedge between domestic and foreign (primarily: US) carbon prices widens. As much as we would like Canada to play a pioneering role in climate change mitigation, the reality of being a small open economy puts a limit on how far we can press ahead without damaging our trade-dependent economy. If the world wants to stay within the 2ºC limit embraced by the UNFCCC's Paris Agreement in 2015, we probably need a global carbon price that is at least at par with BC's current $30/tonne. Sadly, the signs do not look encouraging that this will happen soon enough. Because of delays in many countries to implement any significant climate policy at all, climate leaders will probably need to increase their carbon price beyond $30/tonne to compensate. Doing so without damaging the trade-exposed sectors of our economy will be challenging and will require fine-tuning our policy instruments.