## How much to pay for an additional tonne of sequestration compared to an avoided tonne of emissions

Many issues have been wrapped into this question, and various solutions proposed. Some would like to pay landowners up front for prospective storage once a foresta-tion project has been established. Worried that the carbon may not remain stored, the concept of 'discounted' tonnes has been created, whereby a fractional discount factor would be applied to account for possible return of carbon in the future - leakage. Others have proposed renting carbon storage - paying a price per tonne-year stored so that if the landowner chose to do something differently in the future, he or she could do so and would have received payment only for the time they actually stored the carbon. This is a solution to the problem of paying for a 'permanent' tonne only to have the landowner abandon the activity that is keeping it sequestered. Many of these approaches are based on solid economic analysis, recognizing that carbon storage is an investment problem, and can be analysed using the same formulas as for any investment. McCarl et al. (2005) and Lewandrowski et al. (2004) provide good reviews of different approaches.

Key to investment problems is the net present value (NPV) of the stream of returns. A landowner considering a sequestration project would compare the NPV of carbon storage to the investment cost plus the discounted stream of annual maintenance costs, just as he or she might compare the NPV of returns to installing irrigation to enhance crop production or establishing a forest for purposes of harvesting the wood. Herzog et al. (2003) offer one formulation of this NPV problem:

where p(t) is the price of carbon in year t, a(t) is the net amount sequestered or leaked in year t and r is the interest rate. They use the formulation to estimate a discount factor for ocean sequestration, imagining that the carbon would be sequestered in year zero and would gradually return to the atmosphere over a very long time. Thus in their problem a(0) is positive and a(t), for t = 1, . . . ยป, is negative. The same approach has been proposed for land use sinks, and for conceptual purposes the time periods could be of a length where all sequestration occurred in period zero - e.g. each period could be 10, 20 or 40 years - and leakage then might occur in later periods.

The simple and economically efficient approach for pricing carbon is to allow the market to price it once a cap has been established. A landowner who sequesters a tonne of carbon in period t may choose to sell the tonne at the full market price in time t or could hold it for future use or sales. Should the landowner at time t + n emit a tonne of carbon back into the atmosphere, he or she would then be responsible for purchasing a carbon allowance at the going price in year t + n or could use the banked tonne. This treatment is symmetrical to that of a fossil fuel emitter, say an electric power producer, who might be considering different power plant options that would have different streams of carbon emissions in the future. If the carbon stream were less than the allowance stream, the power producer could sell the extra allowances into the market or bank them against the possibility that it may not be of interest to continue the operation of the carbon-saving power plant indefinitely just as the landowner might decide to change his or her land use practice in such a way that carbon previously sequestered is released. The zero point on the axis, going from sink to source, has no special meaning in this trading environment. All that is important is how an entity's emissions or uptake compares with its baseline allocation of allowances so that it can determine whether it has allowances to sell or must acquire allowances.

Alternative solutions whereby there is an established rental price or an established discount for land use sinks lead to potential economic inefficiencies by asymmetrically treating fossil emitters and landowners. If we knew for certain future carbon prices and market rate of returns, and which sinks would leak at which rates, or at least the average leakage rate, one could establish an equivalency between rental rates, the carbon price and a discount factor.

Herzog et al. (2003) calculate the discount factor by calculating the NPV as in Eq. 8.3 and dividing it by the NPV of permanent storage (i.e. when a(t), for t = 1, . . . is zero). Lewandrowski et al. calculated a rental payment as a = rP (8.4)

where r is here the discount rate and P is the price of a tonne of permanently sequestered carbon. This result is derivable from a formulation like Eq. 3 under some highly simplified assumptions, namely that the price of carbon is constant over time. As Herzog et al. (2003) show, if the price of carbon rises at the rate of discount, the value of temporary storage is zero, and there are conditions under which we might reasonably expect the carbon price to rise at that rate. In particular, with a stabilization target and no backstop, efficient allocation of the reduction through time would require a constant discounted price - i.e. the actual price rises at the discount rate. We would not press the case that actual carbon price will necessarily rise at the discount rate but use this example to illustrate that the rental rate for carbon depends on what you assume about the future carbon price path - and, under some not implausible assumptions, the right rental rate could be zero.

The various formulations of: (i) sell or buy permits as you go, (ii) discounted tonnes, or (iii) renting carbon are all derived from the same basic formulation and so it would seem that any of these options could be used. Although the mathematics can be manipulated to derive one formulation from the other, problems arise because:

1. Calculating the discount factor or the rental price requires someone to know or estimate future carbon prices and the appropriate discount rate. If a public agency is to compute the discount factor or the rental value, they must make some projection of these.

2. Whether and when leakage occurs is not purely a phenomenon of nature that occurs with a known (or knowable) frequency, but rather is at least partly under the control of the landowner.

Problem 1 indicates that the public agency bears the risk of being wrong with rental calculations or with the discounted tonnes calculation, whereas when the fossil emitter's investment decisions require forecasting, the risk is on the private entity. One can make a case that the public agency should take steps to limit risk to private entities, but there is no good reason to have some segment of mitigators (fossil emitters) bearing the risk, and another segment (land use sequesters or emitters) not bearing the risk. Problem 2 indicates that an upfront discounted payment with no requirement to be responsible for the future of the carbon creates no incentive for the landowner to take actions that would prevent return of the carbon to the atmosphere. The rental formulation partly avoids this by only paying as you go, but because it produces incentives for sequestering but not avoiding emissions, it leaves land use emissions uncapped.

The 'disconnected tonnes' makes carbon sequestration less attractive - those landowners who might be willing to assure that the carbon had been permanently stored will be less willing to sequester at a discounted payment. If leakage were a purely natural and random phenomenon with no ability to know what its rate was for a specific parcel or to control it, the discount approach would on average credit the right amount. Since with these assumptions the landowner had no control over leakage, the lack of incentive to control it has no effect on leakage. However, these are unreasonable assumptions. The landowners who, a few years after accepting the payment, decide to do something else face no penalty for releasing the carbon. Realistically a programme of upfront payment would likely include conditions that would limit the landowner's actions, or penalize him or her for actions that led to sequestered carbon being emitted. But the efficient penalty is for the landowner to purchase carbon permits at the going price at the time the carbon is emitted. The notion of a penalty - that a wrong was committed - is mischaracterizing the decision. Simply allowing the landowner to essentially buy out of the commitment to store the carbon by purchasing credits preserves the option to use the land in another way if it is more economic. From a broader economic standpoint, preserving this option makes a lot of sense. If for some reason food is short and agricultural commodity prices rise, the landowner can switch to crop production. As long as carbon allowances are purchased to cover the emissions, the country will continue to be in compliance with its GHG mitigation targets; yet it allows land to be used to solve another pressing problem, food supply. There is no net leakage that is not covered by a reduction in emissions (or more uptake) elsewhere, and so there is no need to apply a discount to sequestered tonnes in the first place.

We have been careful to identify problems with tonne-years and discounting as a problem of a public agency implementing these formulas. All of the market approaches we see in capital and investment markets are likely to develop in a carbon market if it is set up as we propose - selling when sequestering at the then current price, and requiring allowances to cover emissions if at some point the carbon is released back to the atmosphere. In particular, landowners who wanted an upfront payment would probably find intermediaries prepared to pay some amount for the future stream of sequestration. The payment would reflect the intermediary's expectations of future prices of carbon, and a contract would need to be structured to describe who would bear the risk if the landowner was later found not to have sequestered the carbon. For this system to work, this requires that the sequestration agreement is legally enforced and the sequestration is monitored over time by a public agency. Landowners might simply bank credits they have created through sequestration, speculating that the price might increase and leave them in a difficult financial position if they wanted to do something that would release the carbon. Future prices and future contracts would likely develop, and intermediaries may be willing to rent carbon based on their speculation of what such temporary storage was worth - i.e. speculating on how carbon prices would change. Contracts and agreements between landowners and such intermediaries could be negotiated or might vary depending on the interests of the landowner, and the risks the intermediaries were willing to accept. In short, the market would quickly invent solutions to illiquidity or the need for upfront payments to cover investment, at a price, just as it has for other investments. Many concerns about the ability of landowners and markets to deal with carbon pricing over time have been expressed in the literature. However, investing in a forest for the sake of receiving payment in the future for the carbon stored is no different than the problem of investing in a forest with the goal of selling the timber in the future.