The Global Capital Reservoir

The Global Capital Reservoir

In this model, Global Capital is a reservoir that represents all the goods and services of the global economic system; so this is much more than just money in the bank. This reservoir increases as a function of investments and decreases due to depreciation. Depreciation means that value is lost as things age, and the model assumes a 10% depreciation per year; the 10% value comes from observations of rates of depreciation across the global economy in the past. The investment part is calculated as follows:

Investment = Savings Rate x ( GDP - Abatement Costs – Climate Damages )

Abatement Costs

The Abatement Costs are the costs of reducing carbon emissions and are directly related to the amount by which we reduce carbon emissions. If we take steps to reduce our carbon emissions, either by switching to renewable energy or improving efficiency or by direct removal of CO2 from the atmosphere, then there are costs associated with these steps. The model includes something called the abatement cost per GT C — this is the cost in trillions of dollars for each gigaton of carbon removed, and it can be changed over time. The default value is \$3 trillion/GT C, which is a lot because it also includes the costs of large battery systems and new electrical transmission lines. But, the good thing about these costs is that once you pay for a GT of C removed, you don’t keep paying for it. If we were to completely cut all carbon emissions (currently around 10 GT C/yr) and do it in one year, it would cost \$30 trillion or about 1/3 of the global GDP.

The diagram below shows how the abatement costs each year are figured out.

abatements costs for each year, see caption for details

The red curve shows a history of carbon emissions with no abatement; the green curve shows lower emissions due to abatement efforts. The vertical double-headed arrows show the amount (GT of C) of emissions reductions at two points in time. The difference in those two emissions reductions values represents new abatement that has to be paid for in that time period. What this means is that each year, we are only paying for the new emissions reductions — we don’t keep paying for it in later years.

The image is a line graph illustrating the concept of carbon emissions over time with and without abatement measures. Here's a detailed breakdown:

  • Axes:
    • The x-axis is labeled "Time" and represents the progression of time without specific numerical values.
    • The y-axis is labeled "Emissions in GT C/yr" (Gigatons of Carbon per year), representing the amount of carbon emissions.
  • Curves:
    • Emissions with no abatement: This is represented by a red curve that rises steeply over time, indicating an increase in carbon emissions if no measures are taken to reduce them. Emissions with abatement: This is represented by a green curve that rises more gradually compared to the red curve, indicating reduced carbon emissions due to abatement efforts.
  • Key Points:
    • There is a vertical black arrow labeled "GT C reduction due to abatement" between the red and green curves, pointing from the green curve upwards to the red curve. This shows the amount of carbon emissions that have been reduced due to abatement efforts.A note between the curves reads, "the difference between these represent the new abatement that has to be paid for in that time period," explaining that the gap between the two curves indicates the additional abatement efforts required during that time frame

This graph visually demonstrates how abatement strategies can significantly lower the trajectory of carbon emissions over time compared to a scenario where no such measures are implemented.

Credit: David Bice @ Penn State is licensed under CC-BY-NC-4.0

Climate Damages

Climate Damages are the costs associated with rising global temperatures, including the costs of dealing with sea level change along coasts, extreme weather events (hurricanes, flooding, droughts, wildfires, etc.), labor (reduced productivity at higher temps), and increased human mortality (loss of workers hurts the economy). In the model, the climate damages are calculated as a fraction (think of this as a percentage) of the GDP. The fraction is a quadratic equation that looks like this:

d a m a g e f r a c t i o n = s l o p e × Δ T + c o e f f i c i e n t × Δ T exp ⁡ o n e n t  

The Δ T  is the global temperature change in °C. Both the slope and exponent can be adjusted in the model; the coefficient is set at 0.003. The default slope is 0.025 and the exponent is 2, which means that if we have a global temperature change of 4°C, damages equal to 15% of GDP; this rises to a devastating 55% for a temperature increase of 10°C. The diagram below shows what this damage fraction equation looks like, plotted as a function of temperature change in °C.

graph temperature vs damage fraction

Damage fraction as a function of temperature change

The image is a line graph illustrating the relationship between temperature change and damage fraction. Here's a detailed breakdown:

  • Axes:
    • The x-axis is labeled "Temperature Change" and ranges from 0 to 10 units.
    • The y-axis is labeled "Damage Fraction" and ranges from 0.00 to 0.80.
  • Data Series:
    • A single red line represents the relationship between temperature change and damage fraction. This line starts at the origin (0,0) and curves upwards, indicating an exponential or non-linear increase in the damage fraction as temperature change increases
  • Trend:
    • As the temperature change increases from 0 to 10, the damage fraction rises from 0.00 to 0.80. The increase is not linear; it starts off slow but accelerates, showing a steeper rise especially after a temperature change of about 4 units

  • Legend:

    • Located at the bottom of the graph, it identifies the red line as "Damage Fraction.

    This graph visually represents how the fraction of damage increases with rising temperatures, suggesting that the impact of temperature change on damage becomes more severe as the temperature change grows larger.

Credit: David Bice @ Penn State is licensed under CC-BY-NC-4.0

Relative Climate Costs

It will be useful to have a way of comparing the climate costs — the sum of the Abatement Costs and the Climate Damages — in a relative sense so that we see what the percentage of these costs is relative to the GDP of the economy. The model includes this relative measure of the climate costs (in trillions of dollars) as follows:

Relative Climate Costs = (Abatement Costs + Climate Damages) × GDP/initial GDP

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