Module 10: Economics

Module 10: Economics jls164

Module 10 Overview

Don’t even think about going to the bathroom in your neighbor’s driveway—you may not do so legally. The government has passed rules and regulations that outlaw such actions. But, this is not the only way to handle pollution. Another approach is to find out how much damage would be done to your neighbor, or to all of your neighbors if you went to the bathroom in one of their driveways, and then allow you to do so if you paid for the damages. But, how would you estimate the damages, and who would be paid?

The value to society of burning fossil fuels is much greater than the value to you of going to the bathroom in someone else’s driveway. So, little consideration is given to immediate rules to outlaw emission of fossil-fuel CO2 (although some rules to reduce CO2 are being enacted). Much consideration is being given to ways to estimate the damages caused by the CO2, and raise the cost of fossil fuels to reflect those damages.

This module looks at the economic side of estimating those damages. Most of the damages will happen in the future because the costs of climate change go up exponentially as the temperature rises, and the temperature will remain elevated for a long time if we don’t take actions. So, some way is needed to estimate the present value of those future damages.

Economists typically do this with integrated assessment models, which allow for the use of money to reduce the damages of warming now or in the future, and all of the other uses of money, such as investing to help future generations be wealthy and have the resources to deal with the damages of climate change.

These analyses show that emitting CO2 to the air does have costs for society. Following usual economic assumptions about getting the most good for people from the things they consume, a response to reduce CO2 emissions is economically justified. But, because other uses of money are also valuable, the optimal response starts slowly, doing a little about climate change now and doing more later, while still allowing much climate change to occur. Many uncertainties are associated with these calculations, and it appears that most point to doing more now to reduce warming than this economically efficient path.

Goals and Objectives

Goals and Objectives azs2

Goals

  • Recognize the role of human actions in determining the future of our climate
  • Explain scientific concepts in language non-scientists can understand
  • Find reliable sources of information on the internet
  • Use numerical tools and publicly available scientific data to demonstrate important concepts about the Earth, its climate, and resources

Learning Outcomes

By the end of this module, you should be able to:

  • Recognize that there is a cost to future society of emitting CO2 to the air today.
  • Describe how one might balance immediate needs against protection from future losses.
  • Explain why growth cannot be infinite in a world of finite resources.
  • Use an Integrated Assessment Model to determine the most economically beneficial approach to dealing with emissions and climate change.

Roadmap

Roadmap azs2
Module Roadmap
What to doTask

Due

To ReadMaterials on the course website (Module 10)

A.S.A.P.

To DoComplete Summative Assessment

Quiz 10

Due Following Tuesday

Due Sunday

Questions?

If you have any questions, please post them to Help Discussion. We will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.

Paying the Piper

Paying the Piper jls164

Earth: The Operators' Manual

In case you want to remind yourself of where we might be going with renewables, here is a 7-minute roundup.

Video: Renewables Roundup (7:24)

Renewables Roundup

DR. RICHARD ALLEY: Can low-carbon solutions really give us enough energy to power the planet and a growing population? Let's put some numbers on how much energy we can get from non-fossil fuel renewables... Today, all humans, everywhere on earth, use about 15.7 terawatts of energy. That's a big number. In watts, that's 157 followed by 11 zeroes, or one hundred fifty-seven billion of those 100 watt light bulbs we used as a reference. To show what's possible let's see if we can get to 15.7 terawatts, using only renewable energy. I'm here in the Algodones Dunes near Yuma, Arizona. The "Guinness Book of Records" says it's the sunniest place in the world. There's barely a cloud in the daytime sky for roughly 90% of the year. Zero point zero one percent... one one-hundredth of one percent. If we could collect that much of the sun's energy reaching the Earth, it would be more than all human of use today.

Today's technologies have made a start... This was the world's first commercial power station to use a tower to harvest concentrated solar energy. Near Seville, Spain, 624 mirrors stretch over an area of more than 135 acres... beaming back sunlight to a tower nearly 400 feet high. Intense heat produces steam that drives a turbine, which generates electricity. When completed, this one facility will be able to power 200,000 homes, enough to supply the entire nearby city of Seville. Remember our target of 15.7 terawatts? Well, the sun delivers 173,000 terawatts to the top of Earth's atmosphere... eleven thousand times current human use. No way we can capture all of that potential energy at Earth's surface, but the deserts of America's southwest, with today's technology, have enough suitable land to supply 80% of the entire planet's current use. Of course, there's one big problem with solar power... night.

But with more efficient transmission lines, and as part of a balanced renewable energy portfolio that includes storage, the sun's potential is vast. In tropical nations like Brazil, the sun heats water, makes clouds and unleashes rainfall that feeds some of the planet's largest rivers. Iguacu Falls is a tourist attraction, one of the most spectacular waterfalls on earth, where you can feel the immense power of falling water. The nearby Itaipu Dam, on the border of Brazil and Paraguay, produces the most hydroelectric power of any generating station in the world. This one dam supplies most of the electricity used in Sao Paulo, a city of more than 11 million. Sao Paulo is 600 miles away, but Brazil made the decision to build innovative high voltage direct current transmission lines to minimize energy loss. The Itaipu to Sao Paulo electrical grid has been in operation since 1984, and shows that renewable energy can go the distance. Dams can't be the answer for every nation... they flood landscapes, disrupt ecosystems, and displace people. But hydropower gives Brazil, a nation larger than the continental United States, 80% of its electricity. And world-wide, hydro-power could contribute 12% of human energy use... ready at a moment's notice, in case the sun goes behind a cloud.

Brazil is also using its unique natural environment in another way. Its tropical climate provides ideal conditions for sugarcane, one of the earth's most efficient plants in its ability to collect the energy of sunlight. Plantations like this one, harvest the cane for the production of sugar and the biofuel called ethanol. The U.S. is actually the number one producer of ethanol in the world, mostly using corn instead of cane. But ethanol made from sugarcane is several times more efficient at replacing fossil fuel than corn-based ethanol. Modern facilities like this one pipe back wet waste to fertilize the fields and burn the dry waste, called bagasse, to generate electricity to run the factory. For Brazil, at least, ethanol works. Today, almost all cars sold in Brazil can use flex fuels. Drivers choose gasoline blended with 25% ethanol, or pure ethanol, depending on price and how far they plan to drive. Local researchers say that if all the gasoline in the world suddenly disappeared, Brazil is the only nation that could go it alone and keep its cars running.

Using food for fuel raises big questions in a hungry world. As of now, sugarcane ethanol hasn't affected food prices much, but there are concerns with corn. So here in the U.S., government labs like NREL, the National Renewable Energy Lab, have launched programs to see if biofuels can be made from agricultural waste. It does work, and researchers are trying to bring the cost down. So with plants capturing roughly eleven times human energy use, they're a growing opportunity.

New Zealand takes advantage of another kind of energy. These are the geysers and hot springs at Rotorua on the North Island. Once they were used by the native Maori people for cooking and bathing. Now geothermal power plants harvest heat and turn it into as much as 10% of all New Zealand's electricity. Many power projects are partnerships with the Maori, benefiting local people and avoiding the "not in my backyard" problems that often complicate energy developments. Globally, geothermal energy offers three times our current use. But we can mine geothermal, extracting the energy faster than nature supplies it, cooling the rocks deep beneath us to make power for people. This energy exists even where you don't see geysers and mud pots, so it can be extracted without harming these natural wonders. A study by MIT showed that the accessible hot rocks beneath the United States contain enough energy to run the country for 130,000 years. And like hydroelectric, geothermal can provide peaking power, ready to go at a moment's notice if the sun doesn't shine and the wind doesn't blow.

Source: Earth: The Operators' Manual. Renewables Roundup. YouTube. April 9, 2012.

Investments typically grow over time. But, if you don’t solve them, problems often grow too. And solving problems takes money, which could be invested now to solve problems later. Solve? Invest? Solve a little and invest the rest? Throw a party and worry about it later? What is a poor confused society to do? Call an economist!

Short version:

Using a calculation called discounting that is similar to interest-rate calculations, it is possible to estimate the present value or cost of future events. The discount rate, which is the real return you could get if you invested your money, is a function of the growth rate of the economy, as well as our preference for having things now rather than later (and thus us behaving as if our generation is more important than future generations). Actions to reduce CO2 emissions have costs now but benefits in the future. Thus, discounting is an important part of the economic models, called "integrated assessment models," used to compare possible paths to the future. The path that optimizes the tradeoff between these costs and benefits calls for beginning now to slow global warming, but in a measured rather than panicked way.

Friendlier but longer version:

We all face choices between today and tomorrow. Should I buy an apple now, or invest the money and have enough to buy two apples in a few years? Should I throw a party, or save the money to help support future generations of my family? Should I pay off the dangerous person who has suggested that if I don’t pay him, he will punch my teeth out, or put the money into the hot new investment that will make me so wealthy that false teeth will seem cheap?

Close up of tree branch with red apples Laptop screen

Apples on Tree Branch (Top). Laptop screen (Bottom).
Photo Credit: Richard B. Alley © Penn State is licensed under CC BY-NC-SA 4.0

Economists have built a powerful intellectual framework for dealing with questions of this sort. The topic is usually discussed as discounting.

You can think of discounting as a tool to estimate the value or cost today of various future events. This allows you, or society, to compare the future results of possible decisions you could make today, and so choose the path that is least expensive or most beneficial overall.

Starting on the next page, we explain discounting with a little math. Note that we do not require that you master the math, or use it to calculate anything, but we owe it to you to show you how it goes. (And, we have found that knowing the math often helps, in many ways.) We then will apply the results to climate change.

Enrichment

Want to learn more?

Read the enrichment titled Discount Rate.

We can choose to spend money now to head off future climate change. Or, we can ignore climate change and just go about our business, spending money on things we consume now, but also spending some money on investments for the future. Then, our descendants can use their great wealth from those investments to deal with the problems caused by climate change. We will find that the economically optimal path takes a middle road, spending some money to reduce climate change but investing some money to make our descendants wealthy and letting them deal with the problems of climate change. This raises many other questions, some of which we will address. But, hard-nosed economics recommends some actions now to head off climate change.


Interesting Discounts

Interesting Discounts jls164

Suppose you go to a bank and deposit one thousand dollars (or euros, or yuan, or whatever currency you prefer), which the bank promises to return to you at some time in the future. You will expect the bank to return more than you deposited. Say they promise to give you $1040 in a year. The difference, 1040  1000 = 40 , is your interest. To get the interest rate, you need to divide the interest you received by the amount you put in the bank at the start, 40 / 1000 = 0.04 . Most people dislike talking about an interest rate of 0.04, so they multiply by 100 and say the interest rate is 4%. Your bank probably had a big sign out front advertising “4% interest rate on savings!” Clearly, if you had deposited more, you would have gotten more interest at the same interest rate—put in 1,000,000, get back 1,040,000, the interest is 1 , 040 , 000  1 , 000 , 000 = 40 , 000 , and the interest rate is 1 , 040 , 000  1 , 000 , 000 = 40 , 000  or 4%, just as before.

But, there is no requirement that you compare the interest to the amount you started with. Suppose instead that you divided by the amount you finished with. Go back to your original investment of 1000 that becomes 1040 in a year, with interest of 40, and calculate 40 / 1040 = 0.038  or 3.8%. That is the discount rate. (In the ENRICHMENT linked below we show that we could have set up the example so that the discount rate came out to be a nice easy number, with the interest rate harder to remember—a 4.17% interest rate gives a 4% discount rate, for example.)

Enrichment

Want to learn more?

Read the enrichment titled Interesting Discounts.

Next, suppose you see a problem. Say, the roof on your house is leaking. Fixing the roof today will cost you the $1000 that you happen to have in your wallet. If you don’t fix the roof, then in 20 years the roof will still cost $1000 to fix. (We have ignored inflation because economists can correct for it before making the calculation, as described in the ENRICHMENT. And, you could spend the $1000 on many other things, including a party or a vacation, a point to which we’ll return soon. Just go along with us for now.) But, if you wait 20 years to fix the leak, the dripping water will cause another $1000 in damage to your house, so the total repair will cost $2000 in 20 years. Should you spend the money from your wallet to fix the leak now, or invest the money and fix the leak in 20 years?

House with roof under repair.

Dr. Alley’s family paid for workers to fix their roof. (The cat Prancer normally stays inside the house, but came out for just a minute to inspect the work from a safe position on the sidewalk.)
Credit: Richard Alley © Penn State is licensed under CC BY-NC-SA 4.0

To answer this question, you can calculate how much money you would need to invest now so that you have $2000 in 20 years to fix the roof—this is often called the present value of the future cost. If this present value is less than the $1000 needed to fix the roof now, then you could invest the present value in a “fix the roof in 20 years” fund, and have the rest of your $1000 to spend on other things; however, if the present value is more than $1000, you would be better off economically to fix the roof now.

In our example, with a 4%=0.04 discount rate and a future cost of $2000 in 20 years, the present value is 2000 / ( 1 + .04 ) 20 = 913 . Hence, you can invest $913 in your “fix the roof in 20 years” fund, and use the rest of your $1000 for other things now. (If you prefer an equation with symbols, let the present value be P, the future cost F, the discount rate be D%, the number of years be t, and the equation is P = F / ( 1 + D / 100 ) t . D/100 turns the 4% into .04, add that to 1, raise the resulting 1.04 to the t th power, and divide F by all of that.)

The issue is similar for society dealing with fossil fuels. Fossil-fuel CO2 emissions cause damages that are costly to us and to other people in the future, and those damages increase as more CO2 is emitted. So, just as for your leaky roof, we could avoid future costs by spending money now to reduce CO2 emissions. But, money spent reducing CO2 emissions is money that is not used for other purposes, such as investing in growing the economy so that our grandchildren and their grandchildren are much wealthier than we are and can afford to solve the problems caused by the CO2. The decision whether to fix the roof now or later is similar to the decision whether to reduce fossil-fuel emissions now or pay to fix the damages later.

If the discount rate is high, then the troubles our CO2 causes for future generations of people have very little present value; then, if we behave in an economically optimal manner, we should spend only a little money trying to reduce our CO2 emissions. If the discount rate is low, then optimal behavior now involves spending more to reduce CO2 emissions.

We’ll discuss how this calculation is made later. But first, let’s take a closer look at what sets the numerical value of the discount rate—1% or 4% or 7%—because it is the most important control on what behavior is economically optimal if we look at the problem in this way.

Forever, and Ever

Forever, and Ever jls164

The discount rate is usually taken to be equal to the real rate of return you can get from investments. And this is based on three parts: growth of the economy, how quickly more stuff satisfies our desire for still more stuff, and our preference for having stuff now rather than later. For a slightly more technical discussion, see the ENRICHMENT.

Enrichment

Want to learn more?

Read the Enrichment titled Discount Rate.

Economists know that sometimes recessions or depressions happen, the Dark Ages really did engulf Europe, and civilizations have fallen in many places. But, with a sufficiently broad view, the economy has always regrown even stronger from these setbacks, as people produced more and more goods and services. Some of this growth is linked to population growth—we have more workers—but some of the growth is the increase in economic productivity per person.

Video: World GDP Per Capita (1:17)

World GDP Per Capita

DR. RICHARD ALLEY: This figure from Qwfp at Wikipedia.org-- the source is down here on the lower left-- shows the history of the size of the world economy per person. So more dollars or more economic activity goes up against time starting in the year 1500 on the left and running up to 2,000. And then growth has continued.

And what you'll notice is that the economy per person as grown fairly steadily even with all the wars. Even with all the plagues and everything else, we've seen growth. This growth looks like what we call an exponential. Except, what we know is that an exponential goes to infinity and we are confident that you can't make something infinite.

The really interesting questions are whether the future eventually flattens out or whether the future might flatten out and then come down gradually, or whether the future might go way up and then crash into something horrible. And this is a subject that has to interest a lot of people in a lot of ways

Estimate of the world’s gross domestic product per person per year—the total market value of goods and services produced and sold or traded in the world per year, divided by the number of people—over the last 500 years. The economy really has grown over long times.

In mainstream economics, the assumption is often made that this growth per person will continue for a long time, so that we are so far from any limits on growth that they do not have a meaningful effect on economic activity now. If you expect the economy to grow rapidly, then the discount rate is high—your grandchildren will have the resources to address problems from climate change even if you don’t invest much to help them. (Some economists have explored alternatives to this; we’ll visit such issues soon.)

Next, a single apple is more valuable to a starving person than to an overfed billionaire; the apple may be as valuable to the poor person as a yacht is to the billionaire. If you believe that economic growth per person can continue for a long time, then investing now to help future generations means that you’re taking apples from you, a poor person, and giving apples or yachts or dollars to your incredibly wealthy grandchildren. If this transfer of money to wealthier future generations doesn’t bother us very much, then the discount rate is low and we try to help them; if we object to giving money to rich people, then the discount rate is high, and we tend to spend more on us now.

Finally, we tend to behave as if now is more valuable than later, and our generation is more valuable than future generations. We won’t give the bank a dollar unless they promise to give us more than a dollar back, and we demand a greater extra payment than can be explained by the expected growth of the economy and our objections to giving money to the wealthy, even if the “wealthy” person is just us getting our money back from the bank a year later. This extra demand is just us saying that we matter most. The more we are focused on us, the higher the discount rate, and the less we invest to help the future. This is sometimes called the “pure rate of time preference”. For a person, preferring a reward now to the same reward sometime in the future is well-known. But when we choose the reward rather than giving it to future generations, some people harrumph and refer to it as “selfishness”.

Economists do NOT tell us that this is good or bad; they tell us that they have watched people buying and saving in the real world, and this is how we behave. Rather clearly, this raises large ethical issues, which we will consider later in the course—regardless of whether you call it “pure rate of time preference” or “selfishness”, some people don’t like it. For now, please don’t worry about the ethics, or the limits to growth. Because, perhaps surprisingly, even if we assume that the economy can grow forever, and we don’t want to help the future generations very much because they will be so wealthy, and we are more important than they are anyway, we still should be spending money to head off global warming if we wish to be economically efficient!

All Together Now... Integrated Assessment

All Together Now... Integrated Assessment jls164

So, we have a framework to help us choose today the path that gets the most economic value (the utility of consumption) by estimating the current value of various future events. With the appropriate numerical model, a skilled economist can test various possibilities to find the optimal path, the one that gives the most good from the things we use.

The modeling is normally done with integrated assessment models. We enjoy consumption today, but investing rather than consuming now gives more consumption in the future. Writing the equations for this, as they work through the whole economic system, is a well-developed branch of economics. The integrated assessment models add a representation of the climate system, its response to the CO2 generated by the greenhouse gases that now power most of the economy, and how those climate changes, in turn, affect the economy.

Video: Earth System (1:29)

Earth System

DR. RICHARD ALLEY: This complicated figure comes to us from the US Global Change Research Program-- USGCRP-- in 2006. And this is a diagram showing an integrated assessment model. And we talk a good bit in the course about what integrated assessment models are and what they do.

This is a cartoon of one of them. And what it does is to take natural causes of climate change-- but also human causes of climate change, such as CO2 and other things-- and ask, how do these interact with the ocean, with the land, with the living things, with the atmosphere, with air pollution, and with the things that we grow to eat, the logging we do, and other things to make economic activity that in turn affects so many of these other things? What you end up with out of this are estimates of what is happening to living things, what is happening to the world's climate, and what is happening to the economy as they interact with each other?

You should not try to memorize all the pieces of this. But you should see what goes into providing us the knowledge base to make wise decisions about these things.

A diagram of the elements of an Integrated Assessment Model. Do not worry about the details, but notice how much goes into such an effort.
Source: US Global Change Research Program, 2006. Image from Our Changing Planet FY 2006 Integrated Assessment Models
Credit: Dutton Institute. EARTH 104 Module 10 Earth System. YouTube. January 13, 2015

For example, if we decide to ignore climate change, then the economy will hum along making greenhouse gases, we will initially consume a lot (good, in the model). But, the damages from the CO2 will cause economic losses that rise rapidly, so as the model is run into the future it projects greatly reduced consumption (bad, in the model). Hence, ignoring climate change is not an optimal path.

However, if we outlawed fossil fuels today, thus avoiding much future climate change and its associated costs, we would greatly reduce economic growth. (Actually, we would have an economic crash.) This would lower consumption (bad, in the model). So, the optimum must be somewhere between do-nothing and do-everything to stop climate change from our greenhouse gases. (We’ll return in Module 11 to the possibility that modern policies are actually serving to accelerate global warming by promoting fossil fuels, and thus are further from the optimum than simply doing nothing.)

Looking at all the possible choices (or at least a representative sample, using sophisticated techniques to narrow the search) between consuming, investing in actions that will slow climate change, and investing in other ways, the integrated assessment models can be used to find the best path. In the great majority of published cases, and including cases that explore the uncertainties in our knowledge, the models find that a measured response to reduce global warming is best. The result from William Nordhaus’ DICE model is probably the best known and is quite representative: put a small price on emitting carbon dioxide into the atmosphere now, and increase it at a specified rate per year (2-3% in recent work). In his book A Question of Balance (Yale University Press, 2008), this spends $2 trillion to avoid $5 trillion in damages but allows $17 trillion in damages to occur. (We will revisit these issues! Bear with us. And, all of this is in present value.)

Please note that because the model attempts to simulate the whole economy, other possible uses of that $2 trillion (curing malaria, or feeding starving children) are implicitly included in the assessment. If curing malaria is an investment (it would greatly increase the economy, for example), it is part of the investment portfolio; if we want to spend more on curing malaria than would be justified on purely economic grounds, that is a choice we make and so is a type of consumption. Any use of money, whether it is curing malaria or heading off climate change, can be treated in the same way, as long as the use is not a large fraction of the whole economy. Thus, use of the $2 trillion to head off climate change over the coming decades is appropriate because other money is available from the whole huge economy to do other things.

Activate Your Learning

Whether or not to invest $2 trillion to reduce climate change more or less depends on the discount rate used. Let’s go back to your house, as a simpler case, and suppose instead of 20 years, we think about 100 years, a time-scale that matters in climate change. Suppose that there is a problem in your house that in 100 years will cost $1000 to fix. Our equation for calculating present value, from above, is P = F / ( 1 + D / 100 ) t . With t=100 years, and F=$1000, if the discount rate is D=4%, then the present value is $19.80. Bizarre as it may seem, spending $20 now to fix a problem that will cost $1000 is not a wise investment; better to invest the money and let future generations solve the problem with the wealth you give them. Raise the discount rate to 7%, and the current value is down to $1.15; if you have a pocket full of change, you would be economically inefficient if you spent it to head off a $1000 problem. But, drop the discount rate to 1%, and you should spend as much as $370 to head off the problem. Changing the discount rate from 1% to 7% changes the current value more than 300-fold. And, you can find reasons why either value might be used.

This highlights the reality that in these integrated-assessment economic-optimization exercises, the discount rate is typically the most important issue. We will look at that soon, including the perhaps surprising result that our uncertainty about the discount rate translates into a lower discount rate over longer times. But first, a word about costs of emitting carbon.

Fees to Flush

Fees to Flush azs2

In most of the world, it is absolutely illegal to go to the bathroom in your neighbor’s yard. Instead, people are legally required to do such things in special places (bathrooms, loos, water closets, toilets, or whatever you want to call them), and pay for sewer or septic services to assure safe disposal. Similarly, most people are required to pay someone to haul away household trash (just under 1000 pounds or 500 kilos per person per year in the US), and businesses are required to pay to dispose of their wastes. Dumping your waste in your neighbor’s yard is strictly forbidden.

If your wind turbines or solar cells break and you can’t fix them, you must pay to recycle or dispose of them. But, the roughly 20 tons of CO2 per person per year from the US economy are dumped into the air with no cost at all to the people or businesses that produce CO2. The same is true for much of the world, although some places have used policy actions to place taxes or fees on CO2 emissions, but still generally less than the damages caused (see below). And, we have high confidence that the CO2 does hurt other people.

The ability to use discounting to estimate the present value of future events means that the costs or benefits associated with emitting CO2 can be estimated. CO2 does fertilize plants, and in especially cold places warming may be economically beneficial, but the costs come to dominate. The cost today of the damages caused by emitting CO2 is called the social cost of carbon.

The 2007 IPCC (Working Group 2, ch. 20 and Summary for Policymakers) reported on more than 100 estimates of this social cost of carbon, running from $-2 per ton of CO2 (very slight benefit) to $86 per ton of CO2 (moderately large cost). For comparison, burning just over 100 gallons of gasoline will release 1 ton of CO2. Recently in the US, this has been about $300-$400 in gasoline. A car getting 25 miles per gallon and driven 10,000 miles per year would make 4 tons of CO2 per year, costing the driver about $1500 for gasoline and costing society perhaps 10% of that, if you take the average of the high and low values just above. (The numbers here are all in 2000-pound short tons of CO2. You will see different numbers if you go look at the IPCC report because they were quoted in 1000-kg metric tons, and were for tons of carbon instead of tons of CO2; we have made the conversions for you.)

Additional estimates noted by the IPCC were as high as almost $400/ton for the social cost of releasing CO2. Many factors contributed to this large range; again, the discount rate is often the most important control. In 2013, the US government reevaluated the cost of carbon used in calculations, and found that the cost of emissions in 2020 (not that far in the future) would be $12/ton for a 5% discount rate, $43 for 3%, and $65 for 2.5% (in 2007 dollars) and rising for emissions further in the future. The government also checked what would happen if the parameters in the calculation are near their most-expensive end rather than in the middle of the possible range, and found with the 3% discount rate a cost of $129 per ton.

Video: Social Cost of Carbon Graph (1:44)

The US Government recently updated their estimates of the social cost of carbon, using various scenarios and models to get distributions of possible costs and then summarizing those results, as shown here.

DR. RICHARD ALLEY: This figure from the US Government in 2013 shows the estimates of the social cost of carbon, how much damage is caused to society by emitting a ton of CO2 to the atmosphere. It's done with various uncertain parameters, and so they did a range of simulations of possible outcomes. And so you get a distribution in the number of simulations, they give a different number as shown here.

If we start out with the blue one, which is the discount rate of 5%, which is the future doesn't matter much, so you're basically just concerned about now, then what you end up with is a very low social cost of carbon, which you might actually be zero, but probably is a little bit above zero. However, as you go through the green into the red, which is, essentially, that the future matters a lot, what do you end up with is a much higher social cost of carbon. You estimate that when you emit carbon to the air, it costs society a whole lot.

There's a very slight chance that it's low, but there's also a larger chance that it's actually really high. And it could be very, very high. This sort of distribution-- there's a best estimate it could be a little less, a little more, or a lot more-- is very common in these. But it's clear that when we emit carbon to the atmosphere, we are causing damage to society. And allowing that carbon to be emitted to the atmosphere without paying for it is a sort of subsidy for fossil fuels.

Source: Technical Support Document: Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis, Under Executive Order 12866, Interagency Working Group on Social Cost of Carbon, United States Government, May 2013.

The IPCC also noted that it is likely that all of these estimates of the cost of carbon are too low (which would probably shift the slight benefit estimates to being costly as well), because many of the damages of CO2 are not “monetized”. Suppose, for example, that climate change from rising CO2 causes the extinction of species that are not being used commercially. Some of those species may have had economic value that had not yet been realized, and many people may have valued those species for other reasons. But, if those species are not contributing to the economy now, their loss is not a cost of global warming in these studies. Other issues, such as the possibility of long-term catastrophic events (making the tropics uninhabitable for unprotected large animals, for example) are also not included in the costs of global warming. The IPCC notes that the calculated costs are based on only “a subset of impacts for which complete estimates might be calculated” (ch. 20, WGII, p. 823, 2007).

Video: 10 Pikas (3:22)

Pikas are cute and are endangered in much of their range if warming continues. The loss of pikas in these places would make many people unhappy but is often not “monetized” and so not counted as part of the cost of global warming.

DR. RICHARD ALLEY: (VOICEOVER) American Pika's live in though Western US and Canada, and except in very special circumstances, they have to live in cold places. They're related to other pikas, and to rabbits and hares. They're lagomorphs.

Pikas don't hibernate despite living in cold places. They spend the summer making hay. They run around gathering up flowers and leaves, grasses, and what they can, and they stow them in a space under a rock. And then they can hide in this hay and stay warm during the winter and eat it, and they're having a very good time there.

Many people think pikas are really cute. On one of our early family vacations, finding a pica was a goal, and we went out of our way looking for pikas, and we found them and we had a ball doing it.

Because pikas like cold climates, many populations are being placed in danger by a warming climate. This figure shows in the bluish areas the suitable habitat for pikas recently in the US. And then the little red areas in the centers there show the habitats that are expected to remain around the year 2090-- one human lifetime from now-- if we follow a high CO2 emissions path.

Some populations of pikas out in the Great Basin are already endangered or have disappeared. We looked at the economic analyses of global warming, which compare cost of reducing climate change to the cost of the damages if we allow change to continue. And which show that we will be better off if we take some actions now to reduce warming.

But in general, such economic analyses do not include pikas. Loss of populations of pikas, even extinction of the pika has little or no economic value. We personally spent money on tourism that involved pikas. But we probably would have gone to see something else if pikas hadn't been there.
Pikas aren't really monetized. They haven't been turned into their monetary value. And so the loss of pikas isn't monetized either in these calculations, nor would be loss of polar bears or many, many other species.

If you believe that pikas are valued, that if you pay a little money to save pikas, or if you believe we have an ethical or religious obligation to preserve creation, including pikas, then the optimum path for you would involve doing more now to slow global warming.

If you don't believe pikas are a value, the economic still says that we should do something to slow global warming if we want to be better.

Credit: Dutton Institute. EARTH 104 Module 10 Pikas. YouTube. January 13, 2015

The social cost of carbon, if it is not offset by a tax or other fee on emitting the carbon, is essentially a subsidy from society for fossil-fuel use. We will return to this topic when we consider policy options in the next module.


Dithering with the Discount Rate

Dithering with the Discount Rate azs2

Recall that the discount rate is often taken as being large if the economy is expected to grow rapidly, or if we behave as if we don’t like giving money to future generations because they will be so much richer than we are, or if we prefer things now rather than later (so, essentially, we behave as if we are more important than future generations). The last of these is often the starting point for ethical critiques of such modeling, and will come up again in Module 12. We won’t say too much here about our willingness to transfer money to wealthier people in future generations; but, that willingness won’t matter if future generations aren’t wealthier than we are. So, let’s take a look at the assumption of continuing economic growth.

Economists are surely correct—if you take a sufficiently broad and long view, the economy always has grown, as we have become better and better at providing goods and services for each other. Local reversals occurred, but the broadest trend has been upward.

The mere existence of this trend does not prove it will continue—when Dr. Alley was 20, he had been getting stronger and faster his whole life, and merely extrapolating those trends to today would make him a world-record holder in numerous athletic events, which did NOT occur.

But, economists not only see the trend, but they understand how new scientific discoveries and commercial innovations make economic progress possible as we invent and build, and pass on to future generations the roads and buildings, and the knowledge. Think of a smartphone, which is nothing but a little sand, a little oil, and a few appropriate rocks, plus an immense amount of accumulated know-how. Even with the recent shortage of rare-earth elements, there is little doubt that the world can produce far more smartphones than have been made to date, with more apps, contributing to economic growth in many ways.

However, some parts of the economy, such as fishing and forestry and farming and fossil fuels, are supported by much larger parts of the Earth. We have already seen that our energy system is grossly unsustainable—if we keep doing what we’ve been doing, the highly concentrated fuels that yield more energy than needed to extract them will run out as practical resources, possibly in decades, almost certainly before many centuries pass. Economists will rightly point out that resources don’t really run out; as prices rise, substitutes are found. But, an energy system that looks a lot like our current one is almost guaranteed to become impractical within a time frame that is short compared to the written history of humanity.

Many other human activities are unsustainable as well. We rely heavily on phosphorus for fertilizer (as well as nitrate; see below). The Earth has huge amounts of phosphorus, but almost all of it is very widely scattered and not even vaguely commercial at modern prices. We are using the concentrated deposits very rapidly. With enough energy, we could re-concentrate phosphorus we have scattered, or that nature has scattered, but that takes us back to the unsustainable energy system.

Many scholars have attempted to calculate the “ecological footprint” of our lifestyle—how much land and ocean is required to grow the food we use or the fish we catch, process our wastes and provide the other things we rely on. Typically, these estimates find that with our current practices and technologies, the Earth cannot support the population already here with the lifestyle we are living. And, with expectations of improved lifestyle, and the population growing, many people expect this imbalance to increase.

Video: Rabbits - Exponential Growth (2:50)

Rabbits can reproduce rapidly, and under certain circumstances, their population may rise exponentially. But, exponential growth continues to infinity, and we can’t have infinitely many rabbits, so the exponential behavior must end. The economy has been growing more-or-less exponentially recently, and integrated assessment models often assume that exponential growth continues well into the future. But, thinking about the rabbits raises questions. Click on the picture for more discussion.

DR. RICHARD ALLEY: This is one cute Eastern Cottontail rabbit. Young ones often have a little white mark on their forehead. If you have one cute rabbit, you have one cute rabbit.

But if you have two rabbits, before you know it, you may have four rabbits. And then you may have eight rabbits. And then you may have 16 rabbits. And then 32 rabbits. And then 64 rabbits, and more rabbits.

This is an example of what is often called exponential growth. The more you have, the faster the growth, and it clearly can't go on forever or the whole world would be rabbits. Now, this is a picture of something that looks like exponential growth, but this happens to be the growth of the size of the world economy per person over time from the year 1500, on your left, up to the year 2000, on your right.

So this is something like dollars per person per year or euros per person per year. And you can see it cranking up very rapidly. The economy has grown, and that's what economists normally assume is going to happen. But exponential growth is exponential growth, and it can't go on to infinity. You can't actually just keep running up forever and ever and ever. No, because ultimately, there are limits. You run out of things. Infinity can't be reached.

The very interesting question then is what does the future hold. Will the growth roll over to some sort of stable economy? Will growth spike up and then crash down before stabilizing or before crashing completely? And those are very interesting questions that drive a lot of people to ask very big things.

But the sort of will grow forever is built into some models, or at least that we aren't close enough to rolling over that we have to worry about it. If we are close to rolling over, and that starts to show up, then our future generations won't be as wealthy as we think they are. And they won't have as easy a time dealing with climate change as we think it is, and it would be wiser for us now to do more to head off climate change.

Activate Your Learning

Technology is surely improving, as it always has, helping us deal with such challenges. But, as we bumped up against limits in the past, we used improved technologies, but we also used unoccupied space. Thus, when a shortage of natural sodium nitrate made fertilizing crops difficult, Fritz Haber figured out a new technology, using energy to convert the nitrogen from the air into nitrogen fertilizer. But, when the Yankee whalers could no longer find right whales in the Atlantic, the fleet moved to the Pacific and then into the Arctic. And for whales, when the whole ocean was utilized, that option was no longer available. True, we might have some huge breakthrough and start mining asteroids, or we might get nuclear fusion working to provide power. But without major jumps in technology, we are increasingly finding that wherever we go, someone is already there and using the resources.

Suppose we ask the question “Are there practical limits to growth, that will cause economic expansion to slow down, soon enough to affect the present value of events considered in the integrated assessment models?” You could probably find well-respected scholars making convincing but conflicting arguments that would give different answers to this question. The correct answer might be “No, there aren’t”, or “Yes, there are very strong limits that cannot be breached and that will be reached soon.” Or, the correct answer may be somewhere in-between, with the limits making growth more difficult in some areas.

Economists are well aware of these issues, and many informative discussions are available. You may be interested in the essay by R.M. Solow, 1991, Sustainability: An Economist’s Perspective, presented as the Eighteenth J. Seward Johnson Lecture to the Marine Policy Center, Woods Hole Oceanographic Institution, and available at many libraries and at sites on the web when we checked. Also see Nordhaus, W.D., 1994, Reflections on the Concept of Sustainable Economic Growth, in Economic Growth and the Structure of Long-Term Development, L.L. Pasinetti and R.M. Solow, eds., Oxford University Press, p. 309-325.

Some integrated assessment models, such as the DICE Model mentioned earlier (which you will work with in the summative assessment for this module), do consider the influence of limits to growth on economic expansion.  Indeed, the version of the DICE model we will use has the global GDP growing at increasingly slower rates as we move through the next century. Uncertainty about how GDP will grow means that such models may overestimate or underestimate the present value of future damages from emitting CO2. However, other models have worked with the assumption that there are no practical limits to growth that will affect us soon enough to be included, using a constant discount rate over a century, for example. If we do hit limits to growth before then, such studies are underestimating the optimal effort to reduce warming now.

An extreme application of discounting can lead to absurd results. For example, with a constant discount rate, you could show that investing a penny now to stop the destruction of civilization 10,000 years from now would not be economically efficient. Such apparent silliness again is recognized in the research community, and motivates interesting scholarship, including the work by R.G. Newell and W.A. Pizer, 2003, discounting the distant future: how much do uncertain rates increase valuations, Journal of Environmental Economics and Management 46, 52-71. They found that uncertainty about future discount rates translates into a lower discount rate over longer times. Importantly, this in turn almost doubles the estimated value of taking actions now to reduce global warming from fossil-fuel CO2. See the Enrichment linked below.

Enrichment

Want to learn more?

Read the Enrichment titled Uncertainty Lowers the Discount Rate.

Getting What You Measure

Getting What You Measure azs2

As discussed earlier, the economic studies in this field often seek to identify the optimum path to maximize the utility of consumption. Consumption is often estimated by subtracting investment (in the economy or in avoiding climate change) from the Gross Domestic Product (GDP), the sum of the goods and services in the economy.

But, total consumption as estimated through GDP is a very imperfect measure of the good, or enjoyment, we get from the economy. Consider an odd example. If family A has children and raises them, and family B has children and raises them, then no economic activity has occurred. But if family A pays family B to raise the A kids, and family B pays family A to raise the B kids, then raising kids is part of the GDP. Many economic studies would find that people are better off in the second case because GDP has risen, but few people would agree, especially if taxes were extracted from the payments in the second case.

Perhaps more relevant, after a hurricane destroys a city, economic activity is lost because people are not working their usual jobs for a while, but economic activity is gained because people must clean up and rebuild. Very few people would agree that money spent fixing hurricane damage is good, but such money appears in the GDP. On the other side, if technological progress means you get a better computer for the same cost, GDP misses the improvement.

Video: Hurricane GDP (1:38)

Here are before-and-after pictures of destruction by Hurricane Katrina, from 2005, near Biloxi, Mississippi, USA. The original caption from the United States Geological Survey is: “In the top image, taken in 1998, notice the pier, pier house, and the antebellum house. The bottom image shows the same location on August 31, 2005, two days after Hurricane Katrina made landfall. This photo shows the complete destruction of these landmarks.” Note that repairing such damage is generally counted in the Gross Domestic Product, and a larger Gross Domestic Product is often taken to be a good thing. The owners of the buildings indicated by the red arrows might disagree.

DR. RICHARD ALLEY: Many economic analyses say that sort of the gross domestic product-- the GDP-- is good. And a bigger GDP, spending more money in the economy is a good thing. Well, there's a lot of useful information to this, but it's not completely accurate.

These pictures from the United States Geological Survey are showing the effect of Hurricane Katrina on the coast of Mississippi near Biloxi in the USA. What you see here is a picture on top from September 19, 1998, which is well before the hurricane-- and one on the bottom from August 31, 2005 after the hurricane.

You will notice things such as there was a pier house, and then it was gone. And there was a pier, and then it was gone. And there was this beautiful pre-civil war mansion, and well, try to find it down below and you know it's not there anymore. Now, if they spend money to fix these things that money spent fixing these will show up in the GDP. And people will say, oh, look the economy grew, but that might not be a good thing.

If we see more disasters in the future, those disasters break things that we have to fix. Those will show up as a growing economy, but that doesn't mean that people are better off. And in that case, we probably need better measures of what we're seeing.

Credit: Dutton Institute. EARTH 104 Module 10 Hurricane GDP. YouTube. January 13, 2015.
Source: Coastal Change Hazards: Hurricanes and Extreme Storms, St. Petersburg Coastal and Marine Science Center, Coastal Change Hazards: Hurricanes and Extreme Storms, Hurricane Katrina, United States Geological Survey.

Various alternatives to the GDP have been developed by economists, such as the Measure of Economic Welfare (MEW; Nordhaus, W. and J. Tobin, 1972, Is growth obsolete? Columbia University Press, New York), or the Genuine Progress Indicator (e.g., Lawn, P. and M. Clarke, 2010, The end of economic growth? A contracting threshold hypothesis, Ecological Economics 69, 2213-2223). These alternatives seek to more accurately characterize real growth, or sustainable growth, in some fashion. There is much interesting and important scholarship, and much more than we can cover here.

But, if a general conclusion can be drawn from this work, it is that the recent growth of well-being probably has been slower than indicated by the recent growth of GDP. And, if this general summary is correct, then economically optimal behavior now involves greater actions to reduce climate change than indicated because our descendants will not gain wealth and thus the ability to solve the problems from global warming as rapidly as indicated above.

One also might ask whether it is really accurate that wealth allows the solution of all problems. What if global warming generates crises that wealthy future generations cannot solve? The optimizations now generally assume that this will not happen, but if problems that resist money can arise, more action now to head off climate change may be economically justified.

Even bigger questions of whether economic growth is even desirable, or whether our future goals should be very different from our past, are beyond the scope of the instructional materials of this class. However, such questions are not beyond the scope of interest of the class participants—you might wish to think about it.

Summative Assessment

Summative Assessment jls164

Reminder!

After completing your Summative Assessment, don't forget to take the Module 10 Quiz. If you didn't answer the Learning Checkpoint questions, take a few minutes to complete them now. They will help you study for the quiz, and you may even see a few of those questions on the quiz!

Modeling the Economics of Climate Change Activity

The global climate system and the global economic system are intertwined — warming will entail costs that will burden the economy, there are costs associated with reducing carbon emissions, and policy decisions about regulating emissions will affect the climate. In the language of systems thinking, this means that there are important feedback mechanisms in this system — a change in the economics realm will affect the climate realm, which will then influence the economics realm. These interconnections make for a complicated system — one that is difficult to predict and understand — thus the need for a model to help us make sense of how these interconnections might work out. In this activity, we’ll do some experiments with a model (a modified version of Nordhaus' DICE model mentioned earlier in this module) that will help us do a kind of informal cost-benefit analysis of emissions reductions and climate change. As with the other STELLA-based exercises you've done, this one will help you develop your abilities as a systems thinker.

Instructions

Read the following pages for an introduction to this model (this introductory material& is also on the worksheet you download below) and then run the experiment using the directions given on the worksheet. As before, there is a practice version, with answers on the worksheet, and a graded version. Once you have completed the graded version and entered your answers on the worksheet, go to Module 10 Summative Assessment: Graded to enter your answers.

Files to Download

Download worksheet to use when working on your assignment

Submitting Your Assessment

Once you have answered all of the questions on the worksheet, go to Module 10 Summative Assessment: Graded. The questions listed in the worksheet will be repeated in this Canvas Assessment quiz. So all you will have to do is read the question and select the answer that you have on your worksheet. 

Grading and Rubric

Scoring Information
ItemPossible Points
Questions 1-81 point
Questions 9-102 points

Activity: Modeling the Economics of Climate Change

Activity: Modeling the Economics of Climate Change azs2

Video: Model Introduction (2:24)

Model Introduction

PRESENTER: For the module ten summative assessment, we're going to be working with this very large and complicated model, that consists of a number of different parts. You can see down in here this is the global carbon cycle and then that includes the percent or the concentration of CO2 in the atmosphere. That concentration of CO2 in the atmosphere then feeds into a climate model that tells us the temperature. And that temperature then goes into determining the sort of climate damages caused by a global temperature, global warming. Those climate damage costs then affect the amount of money that we have leftover to invest in the economy. So here's global capital - this is the whole kind of the heart of the economic model up in here. So climate damages come into play here. Another important cost that comes into play are the abatement costs. These are the costs related to reducing carbon emissions. And so there's something down here called the emissions control rate that we'll fiddle around with. It represents, essentially, different choices we make about how much we're going to try to limit carbon emissions. That limits how much goes in the atmosphere, it limits the temperature, and so on. But it costs money, so there's a certain abatement cost per gigaton of carbon that you are not emitting into the atmosphere. There are a whole bunch of other parts of this global climate and climate and economic model, including something that keeps track of what Nordhaus calls social utility. The global population here is sort of fixed and these are a bunch of things that just sort of sum up some of these economic components of the model. So this is the big model that's behind the scenes. When you look at the actual model, you'll be seeing something like this - an interface where you're just going to change a few basic things. And for this summative assessment, we're really just going to change the emissions control rate here, which is a graphical function of time.

Credit: Dutton InstituteMod 10 SA Model Intro, YouTube. March 16, 2020.

The global climate system and the global economic system are intertwined — warming will entail costs that will burden the economy, there are costs associated with reducing carbon emissions, and policy decisions about regulating emissions will affect the climate. These interconnections make for a complicated system — one that is difficult to predict and understand — thus the need for a model to help us make sense of how these interconnections might work out. In this activity, we’ll do some experiments with a model that will help us do a kind of informal cost-benefit analysis of emissions reductions and climate change.

The economic part of the model we will explore here is based on work by William Nordhaus of Yale University, who is considered by many to be the leading authority on the economics of climate change. His model is called DICE, for Dynamic, Integrated Climate, and Economics model. It consists of many different parts and to fully understand the model and all of the logic within it is well beyond the scope of this class, but with a bit of background we can carry out some experiments with this model to explore the consequences of different policy options regarding the reduction of carbon emissions.

Nordhaus’ economic model has been connected to the global carbon cycle model we used in Module 8, connected to a simple climate model like the one we used in Module 4.

The economic components are shown in a highly simplified version of a STELLA model below:

STELLA model, see text below for image description.

Schematic of the DICE model as applied in STELLA

The image is a complex flowchart diagram representing a model with various interconnected components. The background is black, and the diagram uses different shapes and colors to denote different elements and flows:

Components:

  • Rectangles (Yellow): Represent key factors or inputs in the model:
    • ECON UTILITY: Located at the top left.
    • POPULATION: Positioned to the right of ECON UTILITY.
    • PRODUCTIVITY FACTOR: Located further to the right.
    • GLOBAL CAPITAL: Positioned below PRODUCTIVITY FACTOR.
  • Rectangles (Gray): Represent various environmental or physical components:
    • ATMOSPHERE: Positioned below ECON UTILITY.
    • LAND BIOTA: Located at the bottom left.
    • SOIL: Positioned to the right of LAND BIOTA.
    • SURFACE OCEAN: Positioned to the right of SOIL.
    • DEEP OCEAN: Located below SURFACE OCEAN.
  • Circles (Purple): Represent intermediate variables or processes within the model:

    • Several purple circles are interconnected with red arrows, indicating complex interactions. Labels include:
      • Per-Capita Consumption
      • Atmospheric Change
      • Other various processes
    • Circles (Green): Likely represent points of interaction or transition between components.

    Connections:

    • Arrows (Red): Indicate the flow of influence or interaction between components. These arrows are numerous and create a web of connections, particularly dense around the purple circles, suggesting many interactions among these processes.
      • For example, there are connections from ECON UTILITY to various purple circles, from POPULATION to GLOBAL CAPITAL, and from PRODUCTIVITY FACTOR to various parts of the model
    • Arrows (Black): Indicate simpler or perhaps less dynamic connections between components:

      • These arrows connect the gray rectangles (environmental components) in a more straightforward manner, with fewer interconnections compared to the red arrows

      Specific Flows:

      • ECON UTILITY has arrows leading to several purple circles and then to POPULATION.
      • POPULATION is connected to GLOBAL CAPITAL via a red arrow labeled "degradation."
      • PRODUCTIVITY FACTOR has connections to various parts of the model, including purple circles and GLOBAL CAPITAL.
      • GLOBAL CAPITAL has an arrow labeled "degradation" leading out of it.
      • ATMOSPHERE, LAND BIOTA, SOIL, SURFACE OCEAN, and DEEP OCEAN are connected in a chain with black arrows, suggesting a flow or cycle among these environmental components.

      Observations:

      • The diagram is highly schematic, indicating a simplified representation of a complex model, likely related to economic, environmental, and possibly climatic interactions.
      • The red arrows suggest dynamic and possibly feedback-driven relationships, particularly around economic and human-related factors.
      • The black arrows suggest more straightforward environmental processes or cycles.

      This diagram visually represents the interconnections and flows between economic utility, population, productivity, global capital, and various environmental components, illustrating a model where human activities and natural systems interact in a complex manner.

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

In this diagram, the gray boxes are reservoirs of carbon that represent in a very simple fashion the global carbon cycle model from Module 8; the black arrows with green circles in the middle are the flows between the reservoirs. The brown boxes are the reservoir components of the economic model, which include Global Capital, Productivity, Population, and something called Social Utility. The economic sector and the carbon sector are intertwined — the emission of fossil fuel carbon into the atmosphere is governed by the Emissions Control part of the economics model, and the global temperature change part of the carbon cycle model affects the economic sector via the Climate Damage costs. Let’s now have a look at the economic portions of the model. You should view this video about the DICE Economic Model first, and then study the text that follows.

The Global Capital Reservoir

The Global Capital Reservoir azs2

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

Consumption

Consumption azs2

Also related to the Global Capital reservoir is a converter called Consumption. A central premise of most economic models is that consumption is good and more consumption is great. This sounds shallow, but it makes more sense if you realize that consumption can mean more than just using things it up; in this context, it can mean spending money on goods and services, and since services include things like education, health care, infrastructure development, and basic research, you can see how more consumption of this kind can be equated with a better quality of life. So, perhaps it helps to think of consumption, or better, consumption per capita, as being one way to measure quality of life in the economic model, which provides a measure for the total value of consumed goods and services (in trillions of dollars), which is defined as follows:

Consumption = Gross Output – Climate Damages – Abatement Costs – Investment

This is essentially what remains of the GDP after accounting for the damages related to climate change, abatement costs, and investment.

The model also calculates the per capita consumption by just dividing the Consumption by the Population, and it also includes a converter called relative per capita consumption, which is just the per capita consumption divided by the GDP. In the model, this is in thousands of dollars per person.

Population & Productivity Factor

Population & Productivity Factor azs2

Population

The population in this model is highly constrained — it is not free to vary according to other parameters in the model. Instead, it starts at 6.5 billion people in the year 2000 and grows according to a net growth rate that steadily declines until it reaches 12 billion, at which point the population stabilizes. The declining rate of growth means that as time goes on, the rate of growth decreases, so we approach 12 billion very gradually.

Productivity Factor

The model assumes that our economic productivity will increase due to technological improvements, but the rate of increase will decrease (but will not go negative), just like the rate of population growth.  So the productivity keeps increasing, but it does not accelerate, which would lead to exponential growth in productivity. This decline in the rate of technological advances is once again something that is based on observations from the past.

Emissions

Emissions azs2

The model calculates the carbon emissions as a function of the GDP of the global economy and two adjustable parameters, one of which (carbon intensity) sets the emissions per dollar value of the GDP (units are in gigatons of carbon per trillion dollars of GDP) and something called the Emissions Control Rate (ECR). The equation is simply:

Emissions = carbon intensity*(1 -ECR)*GDP ;

Currently, carbon intensity has a value of about 0.118, and the model assumes that this will decrease as time goes on due to improvements in the efficiency of our economy — we will use less carbon to generate a dollar’s worth of goods and services in the future, reflecting what has happened in the recent past. The ECR can vary from 0 to 1, with 0 reflecting a policy of doing nothing with respect to reducing emissions, and 1 reflecting a policy where we do the maximum possible. Note that when ECR = 1, then the whole Emissions equation above gives a result of 0 — that is, no human emissions of carbon to the atmosphere from the burning of fossil fuels.  In our model, the ECR is initially set to 0.005, but it can be altered as a graphical function of time to represent different policy scenarios. In other words, by changing this graph, we are effectively making a policy — and everyone follows this policy in our model world!

Making Comparisons — the Discount Rate

Making Comparisons — the Discount Rate azs2

We would like to be able to see whether one policy for reducing emissions of carbon is economically better than another. Different policies will call for different histories of reductions, and to compare them, we need to find a way to compare the expected future damages associated with each policy. A problem comes when we try to compare 200 million in damages at some time in the future vs. 20 million in damages today. Economists use something called a discount rate to do this. Here is an example to help you see how this idea works: imagine you have a pig farm with 100 pigs, and the pigs increase at 5% per year by natural means. If you do nothing but sit back and watch the pigs do their thing, you’d have 105 pigs next year. So 105 pigs next year can be equated to 100 pigs in the present, with a 5% discount rate.  Thus, the discount rate is kind of like the return on investment. Now think about climate damages. If we assume that there is a 4% discount rate, then \$1092 million in damages 100 years from now is \$20 million in present-day terms. Here is how this works in an equation:

FutureCost = PresentCost × e (rt) 

$1092E6 = $20E6 × e (0.04 × 100 yrs) 

This is a standard exponential growth equation is called Euler’s number and has a value of about 2.7. Now, let’s say we calculate some cost in the future — 8 million dollars 200 years from now — we can apply a discount rate to this future cost in order to put it into today’s context. Here is how that would look:

PresentCost = $8E6 × e (-0.04×200 yrs) = $2684 

It is important to remember that this assumes our global economy will grow at a 4% annual rate for the next 200 years. The 4% figure is the estimated long-term market return on capital, but this may very well grow smaller in the future, as it does in our model. Although we’re not going to dwell on the discount rate any more in this exercise, it is good to understand the basic concept.

A simpler way of comparing future costs or benefits with respect to the present is to express these costs and benefits relative to the size of the economy at any one time — which our model will calculate. This gets around the kind of shaky assumption that the economy is going to grow at some fixed rate. These relative economic measures are easy to do — just divide some parameter from the model, like the per capita consumption, by the GDP. Below is a list of the model parameters that we will keep an eye on in the following experiments:

Below is a list of the model parameters that we will keep an eye on in the following experiments:

Global capital — the size of the global economy in trillions of dollars;

GDP — the yearly global economic production in trillions of dollars

Per capita consumption — consumption/population; this is a good indicator of the quality of life — the higher it is, the better off we all are; units are in thousands of dollars per person

Relative per capita consumption — annual per capita consumption x (GDP/initial GDP); again, a good indicator of the quality of life, in a form that enables comparison across different times; units are in thousands of starting time dollars per person

Sum of relative pc consumption — the sum of the above— kind of like the final grade on quality of life. If you take the ending sum and divide by 200 yrs, it gives the average per capita consumption for the whole period of the model run.

Relative climate costs — an annual measure of (abatement costs + climate damages) x (GDP/initial GDP); this combines the costs of reducing emissions with the climate damages, in a form that can be compared across different times; the units are trillions of dollars.

Sum of relative climate costs — sum of the relative climate costs — the final grade on costs related to dealing with emissions reductions (abatement) and climate; this is the sum of a bunch of fractions, so it is still dimensionless.

Global temp change — in °C, from the climate model

Experiment 1

Experiment 1 azs2

Experiment 1 - Changing the Emissions Control Rate (ECR)

In the model, the ECR can vary from 0 to 1, and it expresses the degree to which we take steps to curb emissions; a value of 0 means we do nothing, while a value of 1 means that we essentially bring carbon emissions to a halt. According to Nordhaus, the most efficient way of implementing this control is through some kind of carbon tax, in which case a value close to 1 represents a very hefty carbon tax that would provide strong incentives to develop other forms of energy. In this experiment, we’ll explore 3 scenarios — in A, we’ll keep ECR at a very low level — this is the “do nothing” policy scenario, in B we'll ramp it up steadily through time — this is the “slow and steady” policy scenario, and in C, we’ll ramp it much more quickly, eventually reaching a value of 1.0 — this is the “get serious” policy scenario. You can make these changes in the ECR by altering the graphical converter.

The three different scenarios consist of 5 numbers that are the ECR values for 5 points in time (corresponding to the five vertical lines in the graph); these times are the years 2000, 2050, 2100, 2150, and 2200. There are 2 videos to watch in Module 10 Summative Assessment— the Model Introduction, which gives you an overview of the model and ECR Scenarios, which explains how to modify the model to do these problems.

Data for 3 Emissions Scenarios
Data1. Do nothing2. Slow and Steady3. Get Serious
PracticeUse defaults values (no need to change anything)0.005; 0.15; 0.3; 0.45; 0.6

(see video about adjusting these)
0.005; 0.33; .66; 1.0; 1.0
GradedUse defaults values (no need to change anything)0.005; 0.2; 0.4; 0.6; 0.80.005; 0.5; 1.0; 1.0;1.0

For each scenario, run the model, study the model results, and record the results indicated in the table below and then refer to your results in answering the questions below.

SRC Scenarios

Scenario

Practice

Graded

ECR scenarioA. Do nothingB. Slow & steadyC. Get seriousA. Do nothingB. Slow & steadyC. Get serious
  1. Global temp change @2200 Graph #2
6.8°C5.4°C2.8°Cempty cellempty cellempty cell
  1. Global capital @2200 ($trillion) Graph #15
7699041103   
  1. Per capita consumption @2200 Graph #17 (k$/person)
293442   
  1. Per capita consump. rel. to GDP @2200 Graph #18 (k$/person)
3.23.64.2   
  1. Total Abartement Costs @2200 Graph #7 ($trillion)
9055104   
  1. Total Climate Damages @2200 Graph #9 ($trillion)
14101112166908   
  1. Total Climate and Abatement Costs @2200 (just add rows 5 and 6 above)
14191112717012   

This short video below explains how to make changes to the model. Please take a few minutes to watch the ECR Scenarios video. You will be happy you did later!

Video: ECR Scenarios (5:45)

ECR Scenarios

PRESENTER: For this summative assessment, we're basically going to do three different runs with this model. Each one will have a different history of the emissions control rate. So when you open the model up, just reset everything first. The reset button clears everything. Then we're gonna run it with the default values. So for the practice version we use the default values, we're not gonna change anything, we're just gonna run it. We run it and see what happens. Here you can see in red the temperature rising, and it gets up to about six point eight degrees Celsius warming. In blue is the carbon emissions that rises and it reaches a peak of about thirty-one gigatonnes of carbon. And then it starts to decrease and then it just sort of ;falls off a cliff right here. It falls off a cliff right there because we actually would run out of fossil fuels at that point. And if you click ahead a few graphs, you can see...there's the emissions. Sorry, go back one. This graph shows the fossil fuels remaining. That drops to zero at this point, so we've totally run out of fossil fuels at that point. So that's a scenario number one. That's they do-nothing scenario.

The next scenario B is called the slow and steady one. And if you look over here in this table, there are some numbers that tell us the values of this emissions control rate at different points in time. So here's what you do. You click on the emissions control right here. You click on table and then these Y values here, ;the numbers that are reflected over here. So .005 point is already there. Now we're gonna put in 0.15, and then 0.3, and then 0.45, and then finally 0.60, and hit okay. And now we see we have a nice slow steady increase in the emissions control rate. That means as time goes on we're gonna kind of slowly do more and more in terms of reducing carbon emissions. That's all we have to change and then we run the model and you see that that results in a somewhat lower global temperature change. Still rises to 5.45 degrees C which is a pretty serious warming by the year 2200.

Now, will it will do one more scenario. This is the get-serious scenario and the values here according to the table are .33, .66, and then 1.0. Now when this has a value one, that effectively means we're going all out, we're going to do whatever it takes to eliminate all carbon emissions. And so we set that up and you can see here it tops out and stays at one there. We run that scenario and sure enough the temperature changes quite a bit less. We have 2.8 degrees of temperature change by the end of time. And you know if you look at the carbon emissions, let's see if you go to this one here, this is all three runs carbon emissions. So the third one would get serious. The carbon emissions they actually drop to zero by the time we get to the year 2152. And they stay at zero at that point.

So then, you've done these three runs. On a number of these graphs, the different curves are presented...run one, run two, run three. So run one would be the do-nothing scenario, run two would be the slow and steady scenario, and run three would be the get-serious scenario. And so there are a whole bunch of different graphs here. Everything is plotted. Here, by the way, these are the total abatement costs. And you can see in the first run the abatement costs are essentially zero all the way along. And then the abatement costs get very big once we've run out of fossil fuels. We have to make up for that with renewable energy and so that's going to be associated with some significant cost. The abatement costs rise up dramatically there and then level off as time goes on.

So then, in this worksheet, you see there are a whole bunch of questions to answer. What is the global temperature change at the year 2200 for a scenario A, ;B, and C? And these are the answers that you could get off of these graphs. Graph number 2, graph number 15, 17, 18, 7, 9, and so on. from doing these three scenarios and then toggling back and forth between these graphs, running your cursor along here until you get to the year 2200, and then recording the values, and filling them in in this table. So, if you fill in this part of the table with those values, then you can use these numbers to help you answer the various questions that go along with this experiment.

Credit: Dutton Institute. Mod 10 SA ECR scenarios. YouTube. March 16, 2020

If you haven't already run the model for this experiment: run the Model now!

For each scenario, study the model results, and record the results indicated in the table below and then refer to your results in answering the questions below.

Your Results
ItemsDo nothingSlow and SteadyGet Serious
1. Global temp change @ 2200   
2. Global capital @ 2200   
3. Per capita consumption @ 2200   
4. Relative per capita consumption @ 2200   
5. Sum of relative per capita consumption @ 2200   
6. Relative climate costs @ 2200   
7. Sum of relative climate costs @ 2200   

Questions

1. Which of these 3 scenarios leads to the lowest global temperature change?

  1. Do nothing
  2. Slow and steady
  3. Get serious

2. For answer to #1, global temp change @2200 = ____________ (±0.5°C)

3. Which of these 3 scenarios leads to the highest global capital?

  1. Do nothing
  2. Slow and steady
  3. Get serious

4. For answer to #2, global capital @2200 = ____________ (trillion$ ±50)

5. Which of these 3 scenarios leads to the lowest relative climate costs?

  1. Do nothing
  2. Slow and steady
  3. Get serious

6. For answer to #5, relative climate costs @2200 = _______________ (±0.5)

7. Which of these 3 scenarios leads to the greatest relative per capita consumption?

  1. Do nothing
  2. Slow and steady
  3. Get serious

8. In terms of both economic costs (lowest relative climate costs) and benefits (highest relative per capita consumption), which scenario is the best?

  1. Do nothing — best in both costs and benefits
  2. Slow and steady — best in both costs and benefits
  3. Get serious — best in both costs and benefits
  4. Do nothing — best in benefits; Get serious — best in costs
  5. Slow and steady — best in benefits; Do nothing — best in costs

Now we step back and consider what we’ve done and learned by responding to the following questions.

9. You have probably heard people (mainly from the realms of business and politics) say that we should not do anything about global climate change because it is too expensive and will hurt our economy. After experimenting with this model, do you agree with them, or do you think they are missing something (and if so, what is it they are missing)?

10. Remember that each ECR history reflects a different economic/political policy. Briefly explain how you came to figure out which policy was the best. In answering this, you have to think about what “best” means — the least environmental damage; the greatest economic gain per person; the easiest policy to implement; or some combination of these?

Summary and Final Tasks

Summary and Final Tasks jls164

The part of economics dealing with climate change goes much deeper than we have covered here. If you are interested, check out some of the references in this module. But, you should now have a working sketch of many of the main results.

Because the climate changes driven by the CO2 from our fossil fuels will make life harder for people in the future, as well as for at least some people now, there is a social cost of emitting carbon dioxide to the atmosphere. This cost can be understood by first discounting the future damages to their present value. But, if we spend money to reduce CO2 emissions and thus lower the damages from climate change, we are not spending money on consumption today, or on other investments for the future.

By using integrated assessment models, economists can compare the economic costs and benefits of different possible divisions of money among consumption, investment in the broad economy, and investment in reducing climate change. The optimal path is almost always found to involve doing some of all of those. Thus, rather surprisingly to some people, hard-nosed economics motivates serious responses to climate change, beginning as soon as possible. Typically, this response involves small actions now, increasing over the next decades, and relying on consistency in policies.

Because some of the damages of climate change are not yet accounted for quantitatively in these studies, they probably underestimate the size and speed of the optimal response. Similarly, if future economic growth is going to be more limited by the finite nature of the planet than assumed in the models, or by other issues, or if current calculations are overestimating the good that comes from increasing economic activity, then it is likely that more action to limit climate change would be recommended now. On the other hand, if future economic growth is faster than expected, or if we are underestimating the good from increasing economic activity, less action would be recommended now to reduce climate change. However, the balance of the literature seems to suggest overall that following the optimal path from the models or doing a little more now to reduce climate change is the economically best path.

Reminder - Complete all of the Module 10 tasks!

You have reached the end of Module 10! Double-check the to-do list in the Module Roadmap to make sure you have completed all of the activities listed there before you begin Module 11.

Enrichments

Enrichments azs2

Discount Rate

Discount Rate azs2

The discount rate is often approximated as the real rate of return on capital, R, along an optimal path. This is given by the Ramsey equation, which in turn is made up of three parts.

The first is the growth rate of consumption per person in the economy, Ġ.

The second is the elasticity of the marginal utility of consumption, S. The marginal utility of consumption is how much good you get from consuming something, and its elasticity here is taken as how this good changes as you consume more. Wealthy people get less good from the next dollar than poor people do, but how much less? If we think that the good decreases rapidly as people get richer, and we don't want to help rich people in the future who won't appreciate the help, then we have a large discount rate and tend to help ourselves rather than them by spending on us rather than investing for them.

The third part of the discount rate is the pure rate of time preference, E. This is related to our observed tendency to choose to have something, such as an apple, or an Apple, now rather than in the future.

The Ramsey equation puts these together to give the real rate of return on capital as R=E+ĠS. And, economists often set this as being equal to the discount rate.

Interesting Discounts

Interesting Discounts azs2

In the example in the text, 1000 dollars this year becomes 1040 dollars next year after the bank adds the interest. You can say that the present value is P, the future value F, the interest i=F-P, and the interest rate r=i/P=(F-P)/P. The discount rate is d=(F-P)/F. A little algebra will show you that d=r/(1+r) and r=d/(1-d). Here r and d are in the decimal forms (0.04, not 4%). In the main text, we will use D=100d for the discount rate in percent. The economic models eventually assume a discount rate, such as 4%, but often you will see calculations made with 3% and 5%, and sometimes 1% and 7% because the discount rate is quite uncertain. This uncertainty in the discount rate is much larger than the difference between the interest and discount rates, so using either one will get you close.

The example in the text used an interest rate of 0.04, which gives d = 0.04 / ( 1 + 0.04 ) = 0.03846 . . . , which looks messy. But, we could have taken d=0.04, which would have given r = 0.04 / ( 1  0.04 ) = 0.041666 . . ., which makes the interest rate look messy. Your bank may indeed advertise interest rates such as '4.17%!!!'

Inflation is the tendency for all prices and wages to rise in an economy. Measuring inflation is not a trivial task, but useful estimates are available for the inflation rate at different times in different places. Mathematically, it is not difficult to remove the effects of inflation - if everything goes up together, we can correct everything together, reducing the values back to what they would have been at some chosen time (or inflating them to what they will be at some other chosen time). When the effects of inflation have been removed from a calculation, you may see costs and benefits referred to in 'constant dollars' or '2005 dollars' or '(some other specific year) dollars' in a government report on decision-making about energy.

Uncertainty Lowers the Discount Rate

Uncertainty Lowers the Discount Rate azs2

This module has covered the techniques for calculating the present value of future events. But, how uncertainty shows up in this is possibly surprising.

Suppose you estimate that damages of $1000 will occur in 100 years, and you want to estimate their present value as properly as possible. But, you aren’t sure whether the discount rate is D=1% or D=7%—you think that 1% and 7% are equally likely to be correct. You decide to split the difference, by assuming that the average of the present values of these cases is your best estimate of the present value.

You recall that earlier in this module we found that P = F / ( 1 + d ) t , allowing you to calculate the present value P from the future value F=1000 for time t=100 using the discount rate d=D/100.

You might be tempted to assume that the answer can be obtained by averaging 1% and 7% to get 4% and then calculating P for this discount rate of 4%. You would be wrong.

If you got out your calculator, you would find
For D=7%, P=1.15
For D=4%, P=19.80
For D=1%, P=369.71

You want the average of the present values for the 1% and 7% cases, which is (369.71+1.15)/2=185.43. That is almost 10 times larger than the value P=19.80 you get for a 4% discount rate.

What happened? For sufficiently high discount rate and sufficiently long time, the present value of any future event is very small, and you can’t lower a small value very much more by using a higher discount rate or longer time. Under those conditions, the average of the present values with an uncertain discount rate is not too far from being half of the present value, with the lower discount rate.

You could put the average present value, 185.43, into the equation above and solve for the discount rate that would give it. The result is D=1.7%, far below the 4% you would get by averaging 1% and 7%.

If you then decided to look at the present value of damages of 1000 occurring 200 years in the future rather than 100 years, you would find
D=7%, P=0.001 (that’s one-tenth of a cent)
D=4%, P=0.39 (that’s 39 cents)
D=1%, P=137.69

The average of 137.69 and 0.001 is 68.85, almost exactly half of the low-discount case. And if you calculate the one discount rate that would give this, it is 1.3%, even lower than the 1.7% for 100 years.

So, if you want to use a single number for the discount rate, but you know that there really is uncertainty about what that number should be, the single number is lower than the average of the possible discount rates, and the single number gets smaller as you look further into the future. In turn, our lack of knowledge about the future means that an economically efficient response involves more actions now to prevent global warming than you would calculate by simply taking a discount rate in the middle of the possible values.

For additional insights on why the discount rate should be made smaller when looking further into the future, motivating more action now to reduce global warming, see K. Arrow et al., 2013, Determining benefits and costs for future generations, Science 341, 349-350. (Note that in the Newell and Pizer paper referenced in the main text, and in this Arrow paper, time is made continuous and discounting is exponential; their equation looks different from ours, but the numerical difference from what we did here with annual values is very small—for example, Newell and Pizer get 34 cents rather than 39 cents for the present value of 4% discounting of 1000 in damages 200 years in the future.)