Hi. This is part two of my Science-Based Targets lecture. It looks at the simplest and the first attempt at Science-Based Target setting, Absolute Contraction or an Annual Fixed Rate of Emission Reductions. The absolute contraction method has all emitters reduce by a rate that will reach the desired 2 ℃ or 1.5 ℃ target. In this case, the compound annual growth rate, that's the CAGR, has to be -3.1% per year. This is exponential decline or exponential decay and it produces a slightly curved path. To find this year's emissions target, multiply last year's emissions by 1 - 3.1%, 1 - 0.031 or you multiply by 0.969 or 96.9%. Every year, emissions declined by 3.1%. The absolute reduction is greater at the beginning and it gets smaller over time because you're multiplying the 0.969 by a smaller level of emissions from the previous year. Absolute contraction avoids the problem of allocation because it treats every company the same. There is no differential allocation based on the capacity to reduce emissions or importance to society or growth or really anything else. It's a method that completely avoids the allocation problem of context-based sustainability. Now you could devise a linear version instead of the exponential or the compound growth model that we just looked at. In a linear model, you reduce the same amount of emissions each year, so you're going to reduce by this many kilograms, or this many tons, each year and that reduction will be safe. For example, if you needed to reduce annual emissions by 500 tons over 10 years, you'd reduce 50 tons per year. If the starting point was 800, emissions would have to be 750 in year two, 700 year three, 650 in year four and so on. The exponential decay model is probably better because, initially, reduction should be easier to find. Later on, after all the low-hanging fruit has been picked, things are going to get harder and more expensive and so with the exponential decay, the smaller absolute reductions, later in the test period, are probably helpful for the companies. We can also have peak-and-decline pathways. These have been suggested to give companies time to reduce emissions. We introduced this idea in the first video. Initially, companies increase their emissions but at a slower and slower rate until there's no growth. That's when the peak is reached and then they go into a period of annual reductions. We've got linear exponential decay and peak-and-decline pathways that we can use. I want to talk about the pros and cons of absolute contraction or exponential decay. The method is very simple to explain and implement, but it's not very efficient or fair. All companies and industries are treated the same and that takes care of the allocation problem, right? But we know that some sectors and some companies can reduce their emissions much more easily than others. Applying a universal reduction mandate or rate means that some companies will have some very expensive reduction bills or they simply won't be able to meet the targets. If the reduction rate is set to just to meet the target, then there's no room for growth or for new entrants so this could stifle innovation. Absolute contraction is environmentally very effective, but it's not very fair or very cost effective. Let me talk about the idea of cost efficiency. This notion is that low cost reductions are identified and implemented before the next most expensive reductions are implemented. That makes sure that all participants are burdened with about the same costs. In this picture, the high emitter always emits more than the low emitter. If the cost of reducing emissions increases, as a company cleans up, that is, reductions get harder to find and implement or more expensive to find and implement, then, the low-emitting company has to make much more costly reductions than the high emitter. Look at the paths below 200 tons of emissions that's on the vertical axis. Now those can be very expensive for the low-emitting, the blue line, company to find and implement, but the higher emitter avoids all these costs because it never gets to that level of emissions. This method is called a compression method because companies see emissions paths get closer together over time but never quite converge. Almost always, when we have compression instead of convergence, we're going to have some sort of cost inefficiencies and those companies that are making the most effort to clean up can have the most expensive emissions reductions. I've created a spreadsheet titled Absolute Contraction Worksheet. It helps you determine the compound annual reduction rate to reach a designated target given a baseline emissions amount and the start and end years. You enter data in the yellow, the green, the orange, and the blue cells. Then the results should display in the tan cells. Part of the spreadsheet bordered in dark blue is for immediate decline so emissions reductions begin at once. The worksheet also has an option for having the company follow peak-and-decline pathway and this is bordered in light green. In peak-and-decline, the company slows its emission growth over three years. That was my choice and it's fixed in the spreadsheet. The first year emissions growth 2%, 1% year two, and a 0.50% year three, and that reaches the peak, then the decline phase begins. The compound annual rate of reduction to reach a designated target is going to be higher than in the immediate decline model because the extra emissions in years one, two, and three and a shorter time to reach that target means that with peak-and-decline, companies have to reduce a little faster. If the peak-and-decline pathway meets the same endpoint, target emissions level as the immediate decline path, the peak-and-decline pathway will produce more emissions than the immediate decline path. These extra emissions are shown in gold. The gold area of extra emissions could be high enough so accumulated emissions, remember that's what matters, exceed the 2℃ carbon budget for this particular company. So, when using peak-and-decline, we need to try and adjust for this problem. I've posted a second spreadsheet that will help you do that. It's titled Equalizing Absolute Emissions and it works for a real limited set of scenarios. It has to be 35 years, the peak is defined in a certain way, but it'll give you an idea of what needs to be done. In this equalizing accumulated emissions, what you have to do is enter slightly different reduction rates until two numbers are equal. We know what the accumulated emissions for the immediate decline pathway are. You keep increasing or decreasing the reduction rate for the peak-and-decline until you get zero difference between the two pathways. Now, there's a search tool in Excel, but I didn't have time to figure out how to apply it to the situation, so maybe somebody can help me with that. Absolute contraction or exponential decay is the simplest of the various science-based approaches. It's easy to explain and implement and can be designed to satisfy any pathway or any endpoint. However, it doesn't recognize important differences between sectors in terms of growth and the capacity or capability to reduce emissions. It's also a compression approach so it's not very cost-efficient. Those are problems with it and we'll go on to the next lecture, part three, Value-Added Approaches, which try to address some of the problems in the exponential decay absolute contraction method. Thanks a lot and I'll be with you in the next video.