Pricing Theory

The holistic approach of the carbon pricing matrix could turn a systemic crisis into a systemic opportunity.

— Dr. Delton Chen (Founder)



This proposal for a Global Carbon Reward (GCR) is supported by the carbon pricing matrix. This is a new economic theory for carbon markets, and it is a relational diagram for describing the various possible options for pricing carbon in the economy (see Figure 1).

The carbon pricing matrix is framed by ‘carrot’ and ‘stick’ incentives. It explicitly defines four unique carbon pricing options: carbon taxes, cap-and-trade, carbon subsidies, and the proposed carbon reward. All four are recommended here for responding to the climate crisis.

The carbon pricing matrix is linked to the current proposal for optimal economic growth, defined on the homepage as an economic growth pattern that balances two objectives: (1) global energy efficiency, and (2) global carbon safety. A biophysical interpretation of optimal growth is provided in a separate section, called Biophysical Analysis (see the main menu).


Figure 1. The carbon pricing matrix appears like a monolith at the centre of the climate policy landscape.

The carbon pricing matrix is a relational diagram for pricing carbon. The matrix could turn a systemic crisis into a systemic opportunity.

The carbon pricing matrix appears like a monolith in the climate policy landscape (see Figure 1). The policy landscape includes market and non-market policies. Carbon offsetting exists as a metaphorical shadow, cast by the monolith, because offsetting doesn’t reduce carbon emissions at the source. Certain market policies—such as fee-and-dividend and fee-bates—are not explicitly mentioned in the matrix because they are adaptations of the four main policies that constitute the matrix. The non-market policies, which are not covered in this review, include planning laws, emissions standards, regulations, ecocide laws, political commitments, and Green New Deals.

The Technical Background to the carbon pricing matrix is presented below. This background includes a hypothesis that ‘carrot and stick’ incentives can be used to maximise social cooperation for managing the anthropogenic carbon balance. It is proposed here that the carbon pricing matrix — given its focus on cooperation and providing scalable finance — could turn a systemic crisis into a systemic opportunity.


Carbon Pricing Matrix

Video 1. Short introduction to the carbon pricing matrix (7 minutes)

Footnote to Video 1: see Carbon Currency for a description of the four functions of money.

The carbon pricing matrix is a relational diagram for understanding the different market policies that are available to tackle climate change. If this is your first time looking at the carbon pricing matrix, then it may be helpful to focus on the four policies presented in the matrix and their instruments. A short seven minute YouTube is provided left (see Video 1) to introduce you to the four policies.

Each of the four quadrants of the carbon pricing matrix represents a unique market policy. Each market policy employs an instrument. Each instrument has a unit of account — either ‘fiat’ or ‘carbon’ units — represented by the two columns of the matrix. Each instrument has a store of value — either as a ‘carrot’ or as a ‘stick’— represented by the two rows of the matrix.

The ‘unit of account’ and the ‘store of value’ are two of the four major functions of money, and this is relevant because market policies are based on monetary relationships. The matrix provides a framework for understanding the social and biophysical relationships that are expected to emerge when the four policies are implemented individually or jointly.

The first emergent relationship is the ability to manage the social cost of the anthropogenic carbon balance with carbon taxes (a type of stick). The second emergent relationship is the proposed ability to manage the climate-related risks of the anthropogenic carbon balance with carbon rewards (a type of carrot). The third emergent relationship is the capacity to improve cooperation when various kinds of carrots and sticks are implemented together (see Carrots and Sticks: Maximising Cooperation below).

Video 2. Long introduction the carbon pricing matrix (17 minutes)

A 17 minute YouTube video is provided (see Video 2) to introduce the key economic concepts and theories that are used to justify the four policies of the carbon pricing matrix, including the carbon tax, cap-and-trade, carbon subsidy, and the newly proposed carbon reward. Video 2 is somewhat more detailed than Video 1, and it explains why carbon offsetting is used, and how carbon offsetting relates to the carbon pricing matrix.

An explanation for why the carbon pricing matrix can/should be used to manage (a) social costs with sticks, and (b) climate-related risks with carrots, is provided in the Technical Background, Footnotes, and the section on Biophysical Analysis.


Technical Background

1. Carrots and Sticks: Maximising Cooperation

The mitigation of carbon emissions to achieve the 2015 Paris Climate Agreement will require unprecedented cooperation across all levels of society, from global to local. The Global Carbon Reward (GCR) will introduce a new global price for mitigated carbon, but can this improve cooperation?

Several scientific studies — including by Andreoni et al. (2003), Hilbe and Sigmund (2010), and Chen et al. (2014) — provide circumstantial evidence that financial rewards can improve cooperation. These studies found that cooperation amongst people involved in competitive games improved significantly when exposed to both carrot and stick incentives. This under-appreciated scientific finding is adopted as an emergent feature of the carbon pricing matrix.

It is claimed here that cooperation for mitigating the climate crisis is currently far below optimal because the standard theory on carbon pricing is heavily biased towards taxes and cap-and-trade (i.e. sticks). A key feature of the carbon pricing matrix is that it highlights the option to balance sticks with carrots as a major new way of improving cooperation and managing the anthropogenic carbon balance.


Figure 2. Group cooperation tends to maximise when ‘carrot’ and ‘stick’ incentives are combined.

The combination of carrot and stick incentives has a “profound effect” on cooperation (Andreoni et al., 2003) and it is “…a surprisingly inexpensive and widely applicable method of promoting cooperation” (Chen et al., 2014).

The recommended ‘carrots’ are the carbon reward and the carbon subsidy—which create a positive price for mitigated carbon. The recommended ‘sticks’ are the carbon tax and cap-and-trade—which create a negative price for emitted carbon.

The carbon pricing matrix and the theory for cooperation (see Figure 2) are also based on the following three presumptions: (1) there will be strong business interest in the profit opportunities that will be created by the carbon reward, (2) there will be strong market demand for the carbon currency given that it will be managed as an investment-grade currency with significant year-on-year appreciation, and (3) there will be much greater community involvement in climate mitigation based on the financial stimulus and new job opportunities created by the carbon reward, thereby shifting public opinion in favour of strong climate mitigation even if this involves higher carbon taxes and more stringent emissions regulations.


2. Costs and Risks: Car Driver Example

It is claimed that the carbon pricing matrix addresses the social costs and climate-related risks of the anthropogenic carbon balance [a]. But what exactly is a cost, and what is a risk?

The standard technical definition of risk is that it is “the effect of uncertainty on objectives” (ISO 3100). Many people simply define risk as the probability of an event multiplied by the impact of the event. The essential idea behind these definitions is that risks are unwanted events that are probabilistic in magnitude and/or their timing. Costs, on the other hand, usually refer to events that have predictable outcomes and can be planned for.

To help explain the meaning of costs and risks, some of the costs and risks of driving a car are presented in Figure 3. The yellow and blue wedges in Figure 3 are symbolic of the relative importance of the costs and the risks to the driver, respectively.

Figure 3. Responding to the costs and risks of driving a car with decisions and tools

Footnotes to Figure 3: (a) risk is the inverse of safety; and (b) the wedge diagram is based on efficiency (%) and probability (%) because these are non-dimensional values for describing problems and their solutions.

The yellow wedge is labeled “efficiency”, because choices that are made by the driver to manage costs are often made by comparing the efficiency of available options (i.e. high versus low efficiency). The blue wedge is labeled “probability”, because choices that are made for managing risks are often made by evaluating and addressing the probability of undesirable events (i.e. is the probability a concern?). The shape of the two wedges implies that all problems involve a combination of costs and risks in some proportion.

Problems and tools dominated by cost considerations are located close the left side of the wedge diagram in Figure 3; and problems and tools dominated by risk considerations are located close to the right side of the wedge diagram in Figure 3. Problems and tools that address a mix of costs and risks appear near the middle of the wedge diagram.

The driver uses two decision paradigms to manage the car as a system. One to maximise efficiency, and the other to manage probabilities.

Let’s consider an example of a cost. When the driver plans a journey from point A to point B, the most efficient route is typically the one that has the shortest distance (see Figure 3). A shorter route is usually more efficient because it requires less fuel and time. A tool that is often used to reduce these input costs is a roadmap or a GPS that displays the available routes. Given that a roadmap is a tool for managing efficiency, it is shown on the left side of the wedge diagram (see Figure 3).

Let’s consider the example of a risk. When driving on public roads, there exists a probability that the driver might collide with another vehicle. Collisions are a risk for all drivers. The driver in this example buys an air bag as physical insurance in the event of a collision. Given that the airbag is a tool for increasing the probability of surviving a car accident, it is shown on the right side of the wedge diagram (see Figure 3). The driver may also buy an insurance policy to convert the financial risk of accidents and collisions into a predictable cost (see Figure 3).

Although some tools may be useful for improving efficiency and for managing probabilities — such as a visiting a car mechanic (see Figure 3) — we should appreciate that certain tools are specialised for managing costs, by improving efficiency, and certain tools are specialised for managing risks, by influencing or responding to probabilities.

We may now describe the decision paradigms for managing costs and risks. The first decision paradigm is to improve efficiency, and the main example is to select the journeys with the highest efficiency, as follows:

Efficiency = Benefit of Arriving at a Destination (Output) / Cost of Driving (Input) Decision Paradigm 1


The efficiency-based decision paradigm (see above) may be called cost-benefit analysis (CBA). If the inputs and outputs can be expressed in the same units, then the efficiency can be expressed as a pure percentage (%).

With regards to the management of risks, the decision paradigm is to compare the probability (%) of unwanted events with the risk appetite of the driver, as follows:

Risk mitigation is needed if the probability of a dangerous event exceeds the driver’s risk appetite Decision Paradigm 2


The take-home message is that the management of costs and risks in common situations — such as when driving a car — typically requires two distinctly different decision-making approaches and distinctly different sets of tools.


3. Costs and Risks: The Trade-Off Problem

In everyday life, it is common for people to make decisions that involve conflicting criteria or objectives. In order to deal with such problems, a trade-off is required. In the management of complex systems, such as advanced engineered devices and entire economies, the need for a trade-off might not be immediately obvious.

One example of a trade-off between costs and risks — in a highly controlled artificial environment — is found in the control of a spacecraft when it docks with another spacecraft. According to Vinod and Oishi (2018), this trade-off problem involves a number of key factors, including the spacecraft’s trajectory, timing, measurement errors, and fuel needs. So a spacecraft pilot, just like a car driver (refer above), has to deal with costs and risks!

If the management of climate risk is expensive, then a loss of economic efficiency may be needed in a tradeoff to reduce the climate risk.

Another example of a trade-off between costs and risks is the world’s response to the COVID-19 pandemic. The risk was a function of the probability that the disease would spread among citizens. In this example, the governments of the world responded by imposing social distancing and other measures to reduce the probability of infection, and this introduced major constraints on many business operations, and thus its reduced economic efficiency in a trade-off. The IMF reports that real global GDP contracted by 3.3% in 2020 because of the constraints placed on certain kinds of trade.


4. Costs and Risks: The Climate Crisis

Now that we have a definition of costs and risks and an awareness of trade-offs (refer above), we may now examine the problem of managing the costs and risks of the anthropogenic carbon balance. Figures 4 & 5 aim to represent the system-level problems and decision paradigms that relate to the management of these costs and risks. Figure 4 represents the utility of the carbon pricing matrix, which proposes that four market policies, including “sticks” and “carrots”, should be used to manage the costs and risks of the anthropogenic carbon balance, respectively. Figure 5 represents the standard response to climate change. This response relies just on carbon taxes and cap-and-trade, called “sticks”.

Figure 4. Responding to the costs and risks of climate change with the carbon pricing matrix

Figure 5. Responding to the costs and risks of climate change with the standard theory on carbon pricing

Footnotes to Figures 4 & 5: (a) risk is the inverse of safety; and (b) the wedge diagram is based on efficiency (%) and probability (%) because these are non-dimensional values for describing problems and their solutions.

The decision paradigm for costs is represented in Figures 4 & 5 by the yellow wedge and is labeled “efficiency”. It requires cost vs. benefit analysis (Decision Paradigm 1). The decision paradigm for risks is represented by the blue wedge and is labeled “probability”. It requires a response to probabilities (Decision Paradigm 2).

The decision paradigm presented as the yellow wedge in Figures 4 & 5 is applied to the maximisation of economic efficiency. This decision paradigm is essential to the standard design of the carbon tax. The way that the carbon tax is evaluated, is with the method of Arthur Pigou (1920), which is to apply cost-benefit analysis (CBA), as follows:

Efficiency = Avoided Economic Damages (Output) / Carbon Tax (Input) Decision Paradigm 1


The decision paradigm for managing the risks associated with the anthropogenic carbon balance is symbolised by the blue wedge in Figure 4. This decision paradigm aims to compare the probability of unwanted climate change with the risk appetite of society, as follows:

Risk mitigation is needed if the probability of dangerous climate change exceeds the risk appetite of society Decision Paradigm 2


Figure 5 illustrates the status quo on carbon pricing, where the carbon tax is proposed for two objectives: (1) the maximisation of market efficiency (i.e. Decision Paradigm 1), and (2) addressing the 2015 Paris Climate Agreement which was formulated to limit the risks of dangerous climate change (i.e. Decision Paradigm 2). We know that the Paris Agreement is focused on risk management because the following statement appears in Article 2:


Holding the increase in the global average temperature to well below 2°C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C above pre-industrial levels, recognizing that this would significantly reduce the risks and impacts of climate change;

— (UNFCCC, 2015)


The explanation given here for the differences between Figures 4 & 5 is that the decision paradigm based on probabilities (i.e. Decision Paradigm 2) is overlooked in the standard theory for carbon pricing. The result is ‘mission creep’ for the carbon tax and cap-and-trade. This ‘mission creep’ is the result of proposing that taxes can/should be used to manage two criteria: (1) costs and (2) risks. There are two problems with this approach. First, the optimisation of costs and risks may be in conflict, requiring a trade-off between the two. Second, taxes are not suited to the task of managing systemic risks.

The differences between Figures 4 and 5 are discussed further in Footnote [b] in relation to the work of two leading economists, William Nordhaus and Nicholas Stern, and also in relation to multivariate optimisation.


5. Thinking Beyond Negative Externalities

The concept of a ‘negative externality’ is well-known to economists, and it is often mentioned in the mainstream media. An example of a negative externality is the economic damage caused by anthropogenic carbon emissions. The standard response of many economists and lawmakers is to try to limit these emissions by invoking the polluter pays principle.

With negative externalities being in the spotlight, society tends to ignore the opposite kind of externality: the positive externalities.

A positive externality is a spillover benefit that is enjoyed by a third-party who does not pay for the benefit. What creates a positive externality is a merit good. A merit good is a good or service that provides significant long-term benefits for many people in society. Two examples are education and preventative healthcare.

The carbon pricing matrix is a potential breakthrough in economics by proposing that ‘preventative climate insurance’ is a missing positive externality.

In the case of climate change, the merit goods that can create a positive externality are the climate mitigation services that will be undertaken by private actors. Technically speaking, this kind of positive externality is called a positive production externality. The omission of this positive externality in the mainstream narrative on climate change economics shows that there is a ‘blind spot’ in the standard economic theory.

Why do most economists focus on the negative externalities and the carbon tax? Two reasons are given here. First, the polluter pays principle is relatively simple to understand because it has a clear moral basis. Second, the polluter pays principle appeals to the notion of efficiency because it requires relatively simple administration and assessment procedures.

The ‘polluter pays principle’ states that the party that produces the pollution should bear the costs of prevention and rehabilitation if society or the environment are impacted. Social Principle for Addressing Costs


The polluter pays principle has some inherent limitations. First, it assumes that the actions of polluters are self-motivated. In fact, it is often the case that the producers and consumers of dirty energy act like ‘cogs in a wheel’, where the wheel is metaphorical for an economy that has a systemic growth bias and a rising appetite for energy. Another limitation is that pollution taxes do not address systemic risks very well (Decision Paradigm 2) because the standard theory for pollution taxes, based on the approach of Arthur Pigou (1920), is framed by efficiency maximisation (Decision Paradigm 1). These conceptual limitations are resolved in the next section on Managing the Risks of Carbon.

The above discussion presents a major question for the economists who presume that improving economic efficiency (Decision Paradigm 1) is the only reason for introducing market policies . The main reason why the carbon pricing matrix may be disruptive, is that it proposes that risk management (Decision Paradigm 2) is overlooked in the standard theory on carbon pricing.

Before we consider how to evaluate the carbon reward, we should first ask ourselves if there can/should exist a social justification for the missing positive externality. A social justification is proposed here, and it is called the preventative insurance principle:

The ‘preventative insurance principle’ states that humanity should be provided preventative insurance against dangerous climate change if the direct cost of the insurance can be transferred away from all stakeholders. Social Principle for Addressing Risks


We introduce the concept of preventative climate insurance because the climate mitigation services are analogous to preventative health care, where the aim of preventative health care is to avoid health problems that are incurable. The stakeholders in the preventative insurance principle refers to all citizens, businesses and governments. The direct cost of the preventative climate insurance is transferred away from all stakeholders using the monetary approach that is described in the section on Currency Demand. By transferring the cost away from all stakeholders, the preventative climate insurance qualifies as a positive externality according to the standard definition of a positive externality. Furthermore, by transferring the costs away from all stakeholders, the preventative climate insurance might attract favourable political support from stakeholders.



6. Managing the Risks of Carbon

To complete the technical background on the carbon pricing matrix, only one more step is required, which is to introduce a theory for setting a price for the carbon reward. As a reminder, the mechanism for setting the reward price will involve the coordination of central banks with a new international monetary policy, as explained in the section on Currency Demand.

The carbon reward price will be set based on the following principle: the reward price must be such that it can produce an amount of additional carbon mitigation (i.e. reduction and removal) that is sufficient to achieve a probabilistic climate objective.

The target mitigation rate (Q) should be evaluated from a probability density function (PDF) for successful mitigation based on the agreed climate objective. In the Paris Agreement, the objective is to limit global warming to a maximum of 1.5 to 2.0°C relative to the pre-industrial baseline, but without specifying the probability of success. In the current hypothetical example, the objective is to remain below 2°C of global warming with a 67% chance of success (i.e. a 33% chance of failure). The hypothetical PDF is presented in Figure 6a to illustrate how the ideal carbon reward is evaluated.

Figure 6. Hypothetical example of using a carbon reward to incentivise markets to remain below 2°C of global warming with 67% chance of success: (a) probability density function for successful climate mitigation, f(Q); (b) supply-demand curves for additional climate mitigation, P(Q); and (c) linking f(Q) with P(Q).

The theory for setting the carbon reward price is distinctly different from the standard theory for designing a subsidy. First, the reward price is evaluated from a probability density function (PDF) and not from cost-benefit analysis (CBA). The PDF does not refer to a single plan for additional climate mitigation, Q (t), because it is evaluated from a set of many different long-term plans for additional mitigation, Q(t). A rolling 100-year period is recommended as the planning horizon (i.e. t0 < t < t0 +100 years) for estimating the PDF for achieving a specific climate mitigation objective based on the various Q(t) plans.

A supply curve for the additional climate mitigation, Q(t), needs to be evaluated for each calendar year, to quantify the marginal abatement cost of Q over time (see Figure 6b). The supply curve for the additional mitigation should take into account the opportunity costs for market participants, the policy’s administrative costs, and the actual production/mitigation costs.

After the supply curves are assembled, the reward price for the additional climate mitigation, Q(t), should then be evaluated from the supply-demand curves (see Figure 6b). The reward price will vary with time, and it is termed the risk cost of carbon (RCC). The RCC is the counterpart to the social cost of carbon (SCC) when evaluating the ideal carbon tax.

This theory for assessing the RCC and setting the carbon reward price could/should have a major impact on our understanding of carbon pricing. The critical issue is that the supply-demand curves shown in Figure 6 do not include marginal social cost/benefit curves. They only show marginal private cost/benefit curves. The marginal social costs and benefits are not needed because they do not exist when considering risks as pure probabilities. From a technical/scientific perspective, the PDF for additional climate mitigation is the product of a risk assessment and not a cost-benefit analysis. Conventional SCC assessments (i.e. cost-benefit analyses) are a function of economic damages and preferred rates of time discounting. The RCC assessment, on the other hand, will be driven by an objective understanding of probabilities and biophysical systems. The RCC assessment will include a review of positive and negative climate feedbacks, of all types. These feedbacks and other trends will be factored into the PDFs for successful climate mitigation (see Figure 6).

The evaluation of the RCC and the ideal carbon reward is probabilistic and does not involve any explicit time discounting. Given that time discounting is not used in the evaluation of the carbon reward, the resulting price signal will help overcome the natural human tendency to respond too slowly, or too weakly, to the climate crisis. The RCC and the carbon reward are not assessed beyond the rolling 100-year planning horizon, and so events that could occur beyond 100 years into the future are time-discounted implicitly. The validity of using a rolling 100-year planning horizon is based on critical path analysis, in which it is presumed that events during the next 100 years will disproportionally impact events during the following thousand years. The critical path analysis takes into account that certain climate damages will be irreversible (e.g. species extinction and ecosystem collapse) and that tipping points could be crossed. It also includes an expectation that significant technological advances and societal re-organisation can take place over a 100-year period. It is presumed that humanity will develop a significantly greater capacity to mitigate climate change during the rolling 100-year planning horizon.

The above theory for assessing the ideal carbon reward addresses several macroeconomic issues, but there are microeconomic issues to contend with too. Important is that the building of the supply curve for additional mitigation (see Figure 6b) will require the gathering of information that represents the full spectrum of low-carbon technologies and methods. Interpreting this information will require a subjective interpretation of the emissions baselines for the estimation of the the mitigated carbon, by mass, for each of the low-carbon technologies and methods.

Three broad systems — societal, built and Earth — should be taken into consideration when assessing the PDFs and the supply curves for additional mitigation (see Table 1). Built systems include the full spectrum of technologies and methods that can be used to reduce carbon emissions and remove carbon from the ambient atmosphere. It is important to note that carbon rewards do not pick technology ‘winners and losers’ because the rewards are only provided for successful outcomes. For this reason the market participants will be expected to carry the financial risk created by their projects.

Table 1. Systems that have an impact on the probability of mitigating climate change.

1. Societal Systems

    • Financial
    • Political
    • Institutional
    • Legal
    • Educational
    • Media
    • Family Planning

2. Built Systems

    • Energy Production
    • Food Production
    • Buildings & Cities
    • Land & Sea Use
    • Transport
    • Materials Production
    • Carbon Dioxide Removal (CDR)

3. Earth Systems

    • Atmosphere (Air)
    • Hydrosphere (Water)
    • Cryosphere (Ice)
    • Biosphere (Ecosystems)
    • Pedosphere (Soil & Rocks)

Footnote to Table 1: The probability density function (PDF) for successful climate mitigation is a function of the rate of additional climate mitigation (Q) by mass. The PDF will be influenced by human interference with the Earth’s albedo, however such influences should be treated as independent variables and managed outside of the carbon pricing matrix. Solar radiation management (SRM), if it is needed, will likely require new top-down not-for-profit policies and global governance (refer Biophysical Analysis).

The probability density functions (PDF) for additional mitigation (Q) and the supply curves will be estimated from a review of the items listed in Table 1. The first list in Table 1, called “societal systems”, includes the item “financial”. This refers to the various financial trends that encourage dirty economic growth, such as rising debt, profits, and associated energy demand. It also refers to the typical behaviour of the commercial banking system and financial markets. The item “political” refers to each government’s nationally determined contribution (NDCs) under the Paris Agreement, and other political trends, such as trends towards globalism, nationalism, xenophobia, fascism, liberalism, democracy, etc.

The second list in Table 1, called “built systems”, refers to the feasibility of building, retrofitting and replacing infrastructure to achieve net-zero or net-negative carbon emissions. This refers to the cost of retrofitting/replacing energy networks, transport systems, buildings, manufacturing processes, and food production systems—which tend to lock society into dirty patterns of behaviour. The associated capital costs pose a risk that is sometimes called the ‘carbon lock-in effect‘.

The third list in Table 1, called “Earth systems”, refers to the various Earth system responses, including climate sensitivity to greenhouse gases and the emergence of positive climate feedbacks that amplify the drivers of climate change. Positive feedbacks may result from disturbed vegetation, warming soils, permafrost thaw, ocean thermohaline instability, etc. The breakdown or collapse of certain marine and terrestrial ecosystems might possibly result in chaotic feedbacks with non-linear impacts on climate change through a loss of biological function and carbon absorbing capacity. 

As a final note, the assessors of the ideal carbon reward may wish to consider the possibility of a ‘domino effect’ between the items listed above for the three kinds of systems. For example, food supplies may be impacted by extreme weather, and this could lead to human migration and political instability that may force some governments to neglect their climate commitments under the Paris Agreement.


Updated 9 January 2022


aSAFETY & RISK: Throughout this website the term ‘risk” is used in preference to the term ‘safety’. Risk is considered here to be the inverse of safety. The reason why the term ‘risk’ is used, is because the standard practice is to provide and improve safety with risk management principles and methods.
bWILLIAM NORDHAUS & NICHOLAS STERN: To explain the discrepancies between Figures 4 and 5, the work of two leading economists—William Nordhaus and Nicholas Stern—is considered here. It is well-known that Stern et al recommend a higher carbon tax than does Nordhaus. Important is that Nordhaus and Stern et al employ somewhat different approaches in the evaluation of the ideal carbon tax. Nordhaus recommends a carbon tax that maximises market efficiency based on cost vs. benefit analysis (see Nordhaus’s Nobel lecture presentation; see also the left side of Figure 5 and Decision Paradigm 1). His method is to evaluate the social cost of carbon (SCC) using integrated assessment models (IAMs). Critics of Nordhaus’s estimate of the ideal carbon tax usually focus on his estimate of the damage function and his prescribed rates of time discounting. Steve Keen provides a review of Nordhaus’s damage function arguing that it “drastically” underestimates climate damages because of the simplifying assumptions and data points that were employed by Nordhaus.

Stern and his colleagues at the High Level Commission on Carbon Pricing recommend a carbon tax that targets the Paris Agreement. The framing of their assessment is ambiguous with regards to the decision paradigm (see this report and the right side of Figure 5). On the one hand, Stern et al’s decision paradigm is based on addressing the Paris Agreement (i.e. Decision Paradigm 2). On the other hand, it appears that Stern et al have assumed that the market theory of Arthur Pigou (1920) should support the Paris Agreement (i.e. Decision Paradigm 1). It is claimed here that this ambiguity is the result of ‘mission creep’ because the most efficient economic outcome does not necessarily correspond to the Paris Agreement. Moreover, it is claimed here that the carbon tax is inherently inappropriate for managing climate-related risks because it does not solicit sufficient cooperation from market participants and it has other limitations.

By comparing Figures 4 and 5, we can see that there is an alternative explanation for the discrepancy between the advice of Nordhaus and Stern et al. Although the damage function in Nordhaus’s analysis could be overly optimistic, the point of most importance is the current interpretation of “carrot and stick” carbon pricing, as depicted in Figure 4. In this revised interpretation, the resolution is the carbon pricing matrix with the second decision paradigm and the carbon reward for responding to the systemic risks of climate change.

Nordhaus and Stern et al have only utilised one formal theory for making and enforcing decisions. This theory is based on Arthur Pigou’s (1920) theory for the maximisation of allocative efficiency with the re-pricing of private production to account for externalities (i.e. Decision Paradigm 1). The signing of the Paris Climate Agreement in 2016 was a milestone for risk management (i.e. Decision Paradigm 2). The Paris Agreement stands in contrast to the theory of Arthur Pigou (1920) because it ignores economic efficiency for the purpose of managing risk.

cDYNAMIC MARKET FAILURE & PHASE SPACE: From a technical perspective, we may critique the market failure in carbon in terms of optimisation theory and thermodynamics. A major feature of the standard theory on carbon pricing is that it assumes that the market failure is a univariate optimisation problem, with the ideal carbon tax providing the optimal ‘solution’. The technical resolution that is provided here is to treat the market failure in carbon as a “dynamic market failure” due to the strong physical/chemical coupling that exists between carbon and energy, and to then introduce more controllers to match the degrees-of-freedom for the biophysical system. How many degrees-of-freedom are there likely to be? From classical thermodynamics, we should expect at least three degrees-of-freedom. The first two degrees-of-freedom correspond to the two governing laws: the first and second laws. A third degree-of-freedom is needed to account for the fact that the global system (i.e. the civilisation-Earth-climate continuum) has a changing energy balance caused by the enhanced greenhouse effect and changes in albedo. The outer boundary of the global system is the edge of space, and this boundary is called a “closed boundary” because mass fluxes are negligible whereas energy fluxes are significant.

It is claimed here that the climate crisis should be understood as a trivariate optimisation problem, based on the presumption of three degrees-of-freedom. If the Earth’s energy balance were stable, then the market failure in carbon might be understood as a bivariate optimisation problem, based on carrot and stick carbon pricing. Carrots and sticks are two of the three required controllers, with the third controller relating to the Earth’s albedo, which can change significantly over timescales of centuries or decades. Hence, the proposed policy resolution is to take control of the carbon balance using two explicit prices on carbon, namely (sticks) taxes on emitted carbon, and (carrots) rewards for mitigated carbon; and to address the albedo problem with a separate international policy that is optimal for managing the Earth’s albedo.

Given that warming of the Earth’s climate system is prone to positive feedbacks — including changes in surface albedo, cloud albedo, and possible climate tipping points — it is likely that solar radiation management (SRM) technologies will be needed, and this is consistent with the notion of the three-dimensional phase space (refer Footnote [e]). If the Earth’s albedo needs to be managed, then it becomes apparent that the survivability of global civilisation is a trivariate optimisation problem based on three global variables: (1) the average energy efficiency of producing goods and services, (1) the probability of achieving a preferred carbon balance for climatic and ecological safety, and (3) the average surface albedo of the Earth.

Note that the three key variables — (1) efficiency (%), (2) probability (%) and (3) albedo (%) — are non-dimensional and are expressed as percentages. It is proposed here that these three variables constitute the three-dimensional phase-space of the civilisation-Earth-climate continuum and can be used to define the conditions that are necessary for the survival of civilisation as a self-organising system. The phase-space concept originated in the discipline of physics, and more specifically in classical thermodynamics. The three-dimensional phase space that is proposed here (i.e. based on efficiency, probability and albedo) does not appear in the literature because it is a newly proposed phase-space and is specific to complex living systems.

A theory that supports the three dimensional phase-space for civilisation (and the dynamic market failure) is introduced in the section termed biophysical analysis. The biophysical analysis is focused on describing the economy and living organisms as biophysical systems. The analysis links the behaviour of these living systems to the laws of thermodynamics and associated concepts, however the complete theory is not presented on this website for reasons of brevity.

If the hypothesis for a dynamic market failure (and the phase space) holds true, then the neoclassical framework for market externalities and carbon pricing should be revised accordingly.

d COASE THEOREM: An important feature of the carbon reward is that it will be delivered with the carbon currency. The new currency will be issued as a proportional reward for climate mitigation services. So a robust administrative system will be required to ensure that the supply of the carbon currency is constrained by the quantity of carbon that is mitigated over the long-term. Although the initial supply of the carbon currency will be relatively expensive to produce because of the administrative overhead, the trading of the carbon currency (after it is created) will not be expensive. The carbon currency will be traded as private property and with low transaction costs. The Coase theorem is applicable in this situation, such that a Pareto optimum will be achieved with the trading of the carbon currency among currency traders. The economic value of the carbon currency will, in theory, represent the insurance cost (i.e. the cost of the preventative climate insurance), and this insurance cost will be experienced as a profit opportunity for currency traders since a floor price for the carbon currency will rise for many decades with the support of the world’s central banks (see Figure 1 in the section on Carbon Currency).
eMANAGING THE EARTH’S ALBEDO: An important climate variable is the Earth’s albedo. Factors that impact albedo include ice melt (i.e. falling albedo), atmospheric aerosols, and changing cloud dynamics (i.e. rising or falling albedo). The various policies in the carbon pricing matrix do not reward or penalise market actors for increasing/decreasing surface albedo or atmospheric albedo. This is because the focus of the carbon pricing matrix is the anthropogenic carbon balance, and the matrix does not directly affect the Earth’s radiation balance. This limitation of the carbon pricing matrix is intentional because direct interference with the Earth’s radiation balance should be addressed with a separate policy that is specifically designed to deal with solar radiation management (SRM). It is acknowledged here that the carbon pricing matrix might not suffice if the ideal taxes and rewards need to rise exponentially after passing a climate tipping point. In order to avoid a runaway global warming scenario, it may be necessary to implement SRM in concert with the carbon pricing matrix and non-market policies. Even before a tipping point is passed it may be advantageous or necessary to implement SRM (refer Footnote [c]). This specific issue is addressed in the Biophysical Analysis.