Efficiency & Fairness

Where I want to talk about the concepts of negotiation. We’re entering a negotiation among the parties to the U.N. Framework Convention on Climate Change, the 193 parties. A few are very decisive parties to the convention, the largest economies, the largest emitting countries. They’re going to be bargaining with each other. And the question is what is the nature of that bargaining? What are the problems, the challenges, the obstacles? What’s the right way to reach a cooperative agreement? What are the barriers to reach cooperation? That’s the subject of this lecture.

I’m going to ask you to bear with me as we introduce some economics style diagrams. You’ll have a chance to practice those in some assignments and some special problems to hone your skills on these kinds of diagrams that are standard for economic analysis.

The lecture is about the, two crucial concepts of negotiation, efficiency and fairness. And it’s important to keep these concepts distinct. And I’m going to use a lot of examples to highlight the differences of efficiency and fairness.

We’ll start with a, an economist’s diagram that links the amount of mitigation that’s undertaken, that is the reduction of CO2 emissions shown on the horizontal axis and measures for any given level of emissions, the cost of an incremental increase of mitigation or an incremental reduction of a ton of CO2.

What you see here is a rising curve, essentially drawn as a line. The more mitigation that’s undertaken, that is the more reduction of CO2 emissions compared to business-as-usual, the higher is the cost of each incremental tone of carbon dioxide that is pulled out of the emissions or sometimes it’s called the marginal cost of the emissions. And when you see a rising curve or a line such as this, it means that the marginal cost of mitigation is increasing.

The first few billion tons of CO2 that are reduced compared to baseline don’t cost very much, maybe it’s a bit of insulation in, in the homes, a bit of energy efficiency, turning off the lights when they should have been turned off in the first place. Improving some of the efficiency of industrial operations.

But if you want to get deeper reduction of CO2, you have to introduce new technologies, maybe not just efficiency but substituting coal fired power plants by wind or solar plants. Now those can be cleaner, they can be environmentally safer of course, but maybe they’re more expensive to implement than a standard baseline traditional coal fired power plant. And so to implement that next stage of emissions reduction or that incremental mitigation of emissions, it’s going to cost more to reduce that extra ton of CO2.

If you continue and we want to drive carbon emissions way, way down, perhaps using really very fancy technologies, the direct air capture of carbon dioxide in the air and then sequestering it geologically, at least with the technologies we have right now, each ton of carbon dioxide that is removed from emissions using that technology would be very expensive, perhaps hundreds of dollars per ton of carbon dioxide reduced.

The result is this upward sloping schedule or curve as we would say in economics, linking the extent of mitigation on the horizontal axis with the cost of each incremental ton of carbon dioxide removed from emissions compared to the baseline. Those are the costs. What about the benefits of doing this?

Well that’s a different kind of curve. Again, we put on the horizontal axis, the extent of mitigation compared to a business-as-usual trajectory and on the vertical axis we measure in dollars per ton of carbon dioxide reduced emission, now much benefit there is.

Now why is there a benefit of lower emissions of CO2? Well that’s what we’ve been talking about for many lectures now. The climate will be safer. And the idea is that at a low level of mitigation compared to baseline, we would have a huge increase of temperature. The baseline, the business-as-usual remember is an increase of temperatures of maybe four or even six degrees Celsius. So at that point, incremental warming is disastrous. We’re already suffering massively and any further warming adds to the disaster. That means that the benefits of mitigating carbon dioxide, of reducing emissions are very, very high. That’s why the curve is at a high vertical point at low levels of mitigation.

But suppose we’re successful, we have deep Decarbonization and a lot of carbon dioxide is reduced from the emissions flow because of a successful change of the energy system? Suppose that we reduce carbon dioxide enough so that the temperature increase is held even to one degree Celsius or one and a half degree Celsius, a very deep decarbonization of the energy system? What would the gains be of a further reduction of carbon dioxide at that point? Well maybe because the climate is already stable, if there has been a lot of mitigation, an incremental reduction of yet another ton of CO2 wouldn’t really get too much benefit for world society. And so the amount of benefit shown on the curve for a high level of mitigation, that is the marginal benefit of an extra ton of carbon dioxide removed through further mitigation would be a quite low level.

That’s why a marginal benefit curve or schedule as is sometimes said in economics would be downward sloping. At low levels of mitigation, in other words, being close to business-as-usual, every ton of CO2 is really a burden for society.

But for very high levels of mitigation, so that the climate is already in the safety zone, further extent of mitigation would not add so much benefit. Now the trick of economics always is to put a cost and a benefit schedule on the same graph as is done here.

And the miracle of economics is where the two curves cross. Why is that? Again, on the horizontal axis we have the extent of mitigation, on the vertical axis, the costs and benefits of an incremental ton of carbon dioxide removed.

Whenever the benefit curve is above the cost curve, which is towards the left-hand side, it means that the cost of removing one more ton of carbon dioxide is less than the benefit that society enjoys by that carbon dioxide being pulled out of emissions.

In other words, the climate safety that is the result is worth more than the direct extra costs of undertaking that mitigation through some kind of deep decarbonization program. On the right-hand side, where the cost curve is above the benefit curve, it means that further units of carbon dioxide reduction are more costly per ton than the benefits that society enjoys by having that extra ton of CO2 pulled out of the emissions stream.

Everything measured compared to the business-as-usual. Well  What is the social optimum? What is the optimal extent of mitigation? It is where the marginal benefit of removing an extra ton of carbon dioxide equals the marginal cost of removing the extra ton. And that’s shown in this case at a level of mitigation of 20 billion tons of CO2.

Think of that as the reduction in the flow of carbon emissions, say in the year 2050 and on the vertical axis, that cross occurs at a level of $50 per ton of CO2. What does that $50 signify?

It signifies that in terms of the cost of mitigation that is the cost incurred for that last bit of mitigation undertaken at a level of 20 billion tons CO2 removed and it signifies that the benefit of removing that CO2 is the same, also $50 per ton when you factor in how much climate damage is avoided by having that extra ton of CO2 removed.

Now we give a name for that equilibrium point. That is called the social cost of carbon dioxide. It is the measure both of the benefit of removing that ton of CO2 and in a social optimum policy, it is also the cost, because you want to go just to the point where the extra benefit and the extra cost or I should say, the benefit of the extra ton removed and the, and the cost of the extra ton removed are just equal.

Now does society benefit from undertaking that level of mitigation? It sure does, because for that level of mitigation effort, removing 20 billion tons of CO2 per year, the costs of removing that CO2 is less than the benefit, unit by unit, just up to the last ton of CO2 that’s removed.

And you can compare the benefit level for an incremental unit of mitigation on the upper curve with the cost of reducing that level of CO2 on the lower curve and that vertical distance is the net social benefit, the benefit minus the cost of undertaking that level of mitigation.

Well if you add up all of those units of mitigation effort up to the 20 billion tons removed, each one of them has a benefit level higher than the cost level. Add up all of those and you get the area between these two lines.

When you take the total area, as we would in basic geometry, you can say, that’s the sum of society’s gains from this mitigation effort. And in the particular diagram that I have here, that would add up to one trillion tons, that’s the area of the triangle shown as the difference between the marginal benefit line and the marginal cost line. So far so good.

This is the basic economics of why we want to undertake deep decarbonization in the first place, because the benefits of the safer climate, unit for unit of emission reduction or emission mitigation are higher than the costs, unit by unit of CO2 emission reduction.

Now comes the big issue for negotiations. If we were just one person or one country, we’d probably work out more easily, okay, let’s have a 20 billion tons reduction, our society is going to benefit and we’ll undertake these costs, the benefits will be bigger than the costs and we’ll figure out how to do that.

But now suppose we have two countries, or two regions or the developed world and the developing world. Of course it’s even more complicated. We have a 193 countries that are party to this negotiation, it’s a little hard to draw with 193 countries, so I’ll stick with just two negotiating countries. Think of them as the developed countries and the developing countries. And think of these on the horizontal axis for the moment as country one or region one.

And on the vertical axis is country two or region two. And for simplicity, think about this as the income or the well-being of these two groups. Now before we undertake the optimum deep decarbonization, there’s a certain level of income of country one and country two on the baseline or the business-as-usual trajectory. Of course that’s a path of incomes over many years but I’m compressing this to just one point of time, just to give us clarity of the discussion.

And if we graph the level of income of the first country and the level of income of the second country, just on a, a normal plane, we’d have a point which is shown as the business-as-usual point. Now we can do better than the business-as-usual.

That’s the beauty of the fact that at low cost we can reduce carbon emissions and enjoy benefits, for instance, more productivity of agriculture, better human health, more safety as a result of that reduction.

So we can actually have both country one and country two enjoy higher income than in the business-as-usual point. And indeed we can draw all of the potential levels of income of country one and country two on a downward sloping line that says if the world income is allocated all to country two, the point would be on the vertical axis, country two would have all the income, country one would have no income.

That would be pretty miserable for country one. On the other hand, if all the income is allocated to country one, we’d be on the horizontal axis down in the bottom right of that curve. And more normally, both country one and country two would have some level of gross domestic product. And the beauty of climate mitigation is that both of these countries can be better off than they were at the business-as-usual level.

So start at the business-as-usual income point for these two countries and there is a range from point A to point B of what’s possible for how to share the improvement from climate control. And point A, country one is made a lot richer through climate control and country B is left off just as it was in the business-as-usual baseline. At point B, country two reaps all the benefits from climate control and country one is left just as it was in the baseline, the business-as-usual path. Country C is the sweet spot.

It is the cooperative agreement of both country one and country two to say, let’s share the increased well-being that will come from undertaking an optimum global mitigation effort.

We’ll share the burden, we’ll both benefit from a safer climate and we’ll both be left better off than we were in a business-as-usual trajectory. That is what’s called in negotiations, a Pareto improvement. Pareto is the name of a great Italian economist and sociologist at the beginning of the 20th Century, Vilfredo Pareto. And Pareto said, an improvement in a bargaining situation is when all parties of that bargain are better off than they were in the baseline or in the business-as-usual situation. So shifting from BAU to point C is a Pareto improvement.

Now let’s try to understand how this will work at the country level. And we’re going to see a problem now.

I’ll start with a simple case and then we’re going to go to a more complicated problem. Let’s start with a symmetrical situation where these two groups of countries have the same technologies, basically the same income levels, the same potential for mitigation, the same gains from successful climate control.

So the first country, we’ll call it the developed country group, has a mitigation, marginal cost curve, like the one we saw that’s shown here. And this is a schedule of mitigation costs up to ten billion tons per year, reduced by the developed countries compared to the baseline. And I’m going to draw this curve backwards for the developing countries.

Now you go from no mitigation in the bottom right-hand origin of this curve. It’s now reversed in direction. And as you move to the left of that diagram, there’s more mitigation being undertaken by this second group of countries, country two,which I’m calling for our purposes, the developing countries.

If I superimpose these two figures and say that the world as a whole is going to undertake the optimum level of CO2 reduction of 20 billion tons, the one we found in the earlier diagram and we superimpose these two symmetric cost curves they meet right in the middle, where the developed country group reduces by 10 billion tons, the developing country group reduces by ten billion tons and the marginal cost of mitigation for each of these countries is the same, $50 per ton of CO2 reduced.

That’s also the social cost of capital in equilibrium for the whole world. So we have a situation where there is one social cost of capital that applies to both negotiating parties.

They each mitigate in this case, half of the total world need. They share the costs. They have equal benefits. And if the world were so balanced, we probably wouldn’t have any difficulty in reaching such a symmetric, balanced, obviously fair equilibrium.

Now here’s a problem. What if the cost curves are very, very different? And different in a way which is, I’m going to put it in a way which some people will object to, but actually could be realistic.

Suppose that mitigation is actually more expensive in the high-income countries and less expensive in the low-income countries? Why would that be? Well the high income countries like the city of New York where I’m sitting right now has an infrastructure that was built 50 years ago or a 100 years ago. To retrofit that is incredibly expensive. We spend billions of dollars to add a kilometer of subway miles in this city, whereas if you’re building a system from the beginning, it’s much less expensive.

For a developing country that is fast-growing, but is building its infrastructure for the first time, it may be much less expensive to build a green field plant that is clean and low emitting than to retrofit an old plant.

The result is peculiar because now we have a steep marginal cost curve of the high income, or the developed countries, that’s shown starting from the left-hand side of the graph and the upward sloping line that is quite steep. And we have a relatively flat marginal cost curve of the developing countries signifying that the cost per ton of carbon dioxide reduced just doesn’t increase all that much for the developing countries.

Now here is the paradox or the problem in terms of fairness and efficiency. What would be for this kind of world, these two blocks of countries with these distinct cost curves the least cost way of reducing total emissions by 20 billion tons?

It would be where the marginal costs for the two groups of countries of mitigation are equal. That’s where these two lines cross. And interestingly, because it’s cheaper and the marginal costs of mitigation are lower in the developing countries, the least cost worldwide formula for reducing 20 billion tons of CO2 emissions is no longer  symmetrical, it’s that the developing countries should do the hard lift.

They should do 15 billion of the 20 billion tons of emission and the developed countries, only 5 billion of the 20 billion tons. That way the total cost that the world would bear in reducing the emissions, which comes out to a total cost of $600 billion dollars in this example would be minimized.

But the developing countries would say, are you crazy? That is so unfair. Yes, of course we could do it more cheaply, but take a look Professor Sachs, you’re asking us to bear $450 billion dollars of the $600 billion cost, whereas the rich countries who are richer to begin with would only be bearing a $150 billion. Why should we be the ones to undertake all that mitigation? That’s not fair.

So perhaps developing countries would suggest, even given the asymmetry of costs, a solution like this. Some negotiators might say, look, fair is fair, we’ll each do ten. We’ll do half each. The rich countries mitigate by ten billion tons, we’ll mitigate by ten billion tons and that will be it.

Now if you look closely at this graph, the problem is that this is a very expensive solution for the world as a whole, though it is cheaper for the developing countries. In this case, the rich countries are spending a tremendous amount for those incremental units of mitigation, the amount of mitigation between five and ten billion tons that they are bearing compared to the previous diagram.

In fact, if this equal division is taken then in this case the developed countries would have $600 billion dollars of mitigation costs, the developing countries, $225 billion, the world total cost of undertaking climate change mitigation would therefore be $825 billion dollars compared to what was $600 billion dollars before.

Fairer? Absolutely fairer in some sense, but more expensive? For sure. So not very efficient but perhaps more equitable.

Now the rich countries would say, okay, that’s not equitable, you’re making us pay a tremendous amount for this. Yes, it’s divided 10 and 10, but you understand, we have to retrofit. You have green field, how about if we each bear an equal share of the costs? Well if you get out a pencil and paper and take the specific assumptions and solve a little quadratic equation, it turns out in the example of this diagram that the equal cost sharing would have the developing countries mitigate 13.2 billion tons and the high income countries reduce 6.8 billion tons for that total worldwide reduction of 20 billion tons.

Each of the two groups would be spending about $347 billion dollars or about $695 billion dollars for this total effort, $95 billion more than in the first example where the developing countries do more. So you might say, well that’s fairer. It’s a little bit less imbalanced. I suppose you can see where I’m about to go and that is that in some circumstances it’s possible to eat your cake and have it too. And that is, it’s possible to combine both efficiency and fairness in the negotiations. How can that be done? It can be done through side transfers.

The idea is that countries agree on a deep decarbonization pathway that minimizes the global costs of mitigation, but then countries make side financial payments to share the burden in a fair manner. So if we go back to the low cost solution where the developing countries put in 15 billion tons of mitigation, the developed countries only 5 billion tons, remember that that is the minimum cost solution for the world, 600 billion in total, the least cost all the examples. But since the rich countries bear only a cost in that case of $150 billion and the developing countries, $450 billion, one way to equalize the burden,

I’m not saying it’s the only to judge fairness, but one way to equalize the burden would be for the developed countries to say, let’s do it the least cost way and we will transfer a  $150 billion dollars per year to you, the low cost countries to compensate you for having undertaken the extra heavy lift. And in that case, each country ends up bearing a $300 billion dollar cost. The total costs are equally divided. And the total cost that is shared equally among the two sides is thereby minimized. Here is the bottom line. The bottom line is that because climate change is a disaster for the world, there are benefits, net benefits, economic gains to mitigation.

That’s the whole point of this course and it’s the whole point of the framework convention on climate change. Those benefits should be shared among countries. The idea of Pareto, that these can be benefits in which all countries gain is an important idea. So that every country sees the benefit of moving from the baseline. How do share? Well one can separate two concepts. The efficient mitigation is the way of reducing emissions at least cost for the world as a whole. The fair way is to share the costs appropriately.

We can do both if we’re smart, by having a least cost mitigation strategy worldwide and then having side transfers from rich to poor countries, if the poor countries are bearing an unfair burden in the least cost construction.

This I think I, and I hope gives some sense of the complexity of the challenge but also of the nature of the negotiations.

Countries need to formulate pathways so that we satisfy the 2-degree limit and then they need to formulate financial transfer programs so that the cost of achieving those pathways is fair.

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